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Covariance and correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This
Cross-correlation
Concept in digital signal processing
The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors
Cross-correlation_matrix
Statistical relationship
In statistics, correlation is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which
Correlation
Function in discrete mathematics
DTFT of a finite length sequence. (§ Sampling the DTFT) It is the cross correlation of the input sequence, x n {\displaystyle x_{n}} , and a complex sinusoid
Discrete_Fourier_transform
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself.
Autocorrelation
Correlation as a function of distance
made up of autocorrelations. Correlation functions of different random variables are sometimes called cross-correlation functions to emphasize that different
Correlation_function
Technique to find image offset
particularly to a subset of cross-correlation techniques that isolate the phase information from the Fourier-space representation of the cross-correlogram. The following
Phase_correlation
Concepts in probability and statistics
the variable Y). In this case the cross-covariance and cross-correlation are functions of the time difference: cross-covariance σ X Y ( m ) = E [ ( X n
Covariance_and_correlation
Measure of linear correlation
In statistics, the Pearson correlation coefficient (PCC), also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), or simply
Pearson correlation coefficient
Pearson_correlation_coefficient
Nonparametric measure of rank correlation
In statistics, Spearman's rank correlation coefficient or Spearman's ρ is a number ranging from −1 to 1 that indicates how strongly two sets of ranks
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Table that displays the frequency of variables
Interactive cross tabulation, chi-squared independent test, and tutorial Fisher and chi-squared calculator of 2 × 2 contingency table More Correlation Coefficients
Contingency_table
Numerical measure of a statistical relationship between variables
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a linear function between two variables. The variables may
Correlation_coefficient
Type of statistical analysis
Fluorescence correlation spectroscopy (FCS) is a statistical analysis, via time correlation, of stationary fluctuations of the fluorescence intensity.
Fluorescence correlation spectroscopy
Fluorescence_correlation_spectroscopy
Coherence (signal processing) Convolution Correlation Cross-correlation Phase correlation Spectral density Cross-spectrum Wiener–Khinchin theorem Nikolić
Scaled_correlation
Statistical model validation technique
specification like swap sampling and prospective studies. Due to correlations, cross-validation with random splits might be problematic for time-series
Cross-validation_(statistics)
Technique in digital image processing
additional variable of color is either not present or not relevant. Cross correlation techniques compare the similarities of the search and template images
Template_matching
Integral expressing the amount of overlap of one function as it is shifted over another
similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f ∗ g {\displaystyle f*g} differs from cross-correlation
Convolution
Fluorescence cross-correlation spectroscopy (FCCS) is a spectroscopic technique that examines the interactions of fluorescent particles of different colours
Fluorescence cross-correlation spectroscopy
Fluorescence_cross-correlation_spectroscopy
Statistical measure of association for two binary variables
known as the mean square contingency coefficient or Yule coefficient of correlation and commonly denoted by φ or rφ, is a measure of association between
Phi_coefficient
When a radio signal reaches a remote receiver
Figure 4a (third plot) is the cross-correlation function ( P 1 ⋆ P 0 ) {\displaystyle (P_{1}\star P_{0})} . The cross-correlation function slides one curve
Time_of_arrival
Radar system that does not transmit
processing techniques to exploit a variety of broadcast signals and to use cross-correlation techniques to achieve sufficient signal processing gain to detect
Passive_radar
Way of inferring information from cross-covariance matrices
statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices
Canonical_correlation
Concept in probability and statistics
by these two fixed locations. Autoregressive process Correlation Cross-covariance Cross-correlation Noise covariance estimation (as an application example)
Autocovariance
Signal processing technique
additive noise having a normal distribution. In other words, the cross-correlation of the received signal with the transmitted signal is computed. This
Pulse_compression
Technique for determining size distribution of particles
the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic light scattering – QELS). In the
Dynamic_light_scattering
Type of study based on universal sampling
research, epidemiology, social science, and biology, a cross-sectional study (also known as a cross-sectional analysis, transverse study, prevalence study)
Cross-sectional_study
Measure of a system's order
mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Sequence of data points over time
auto-correlation and cross-correlation analysis. In the time domain, correlation and analysis can be made in a filter-like manner using scaled correlation
Time_series
Random variable with multiple component dimensions
]\operatorname {E} [\mathbf {X} ]^{T}} . Similarly for the cross-correlation matrix and the cross-covariance matrix: R X Y = K X Y + E [ X ] E [ Y ] T
Multivariate_random_variable
produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes
Fourier_shell_correlation
Plot using the dispersal of scattered dots to show the relationship between variables
positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it indicates a negative correlation. A
Scatter_plot
Experiment methodology
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
A/B_testing
Statistical property
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Standard_error
Middle quantile of a data set or probability distribution
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Median
Measure of variation in statistics
parameters Coefficient of variation Cumulant Deviation (statistics) Distance correlation Distance standard deviation Error bar Geometric standard deviation Mahalanobis
Standard_deviation
Model of differential privacy
protection, a personalized differential privacy protection method based on cross-correlation constraints is proposed by researcher Hu. By protecting sensitive
Local_differential_privacy
Measure of joint variability in statistics
[X_{t_{1}}Y_{t_{2}}]-\mu _{X}(t_{1})\mu _{Y}(t_{2}).\,} Cross-covariance is related to the more commonly used cross-correlation of the processes in question. In the case
Cross-covariance
Mathematical image techniques
been extended to almost any imaging technology. The concept of using cross-correlation to measure shifts in datasets has been known for a long time, and
Digital image correlation and tracking
Digital_image_correlation_and_tracking
Relative importance of certain frequencies in a composite signal
the cross-correlation of x ( t ) {\displaystyle x(t)} with y ( t ) {\displaystyle y(t)} and R y x ( τ ) {\displaystyle R_{yx}(\tau )} is the cross-correlation
Spectral_density
Measure of statistical dispersion
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Interquartile_range
above SRP objective function can be expressed as a sum of generalized cross-correlations (GCCs) for the different microphone pairs at the time-lag corresponding
Steered-response_power
Chart of correlation statistics
h\,} (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram. The correlogram is a commonly used
Correlogram
Type of statistics
two different variables. Quantitative measures of dependence include correlation (such as Pearson's r when both variables are continuous, or Spearman's
Descriptive_statistics
Statistical measure of variability
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Median_absolute_deviation
Processes that maintain quality at a constant level
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Quality_control
Function describing the distribution of galaxies in the universe
astronomy, a correlation function describes the distribution of objects (often stars or galaxies) in the universe. By default, "correlation function" refers
Correlation function (astronomy)
Correlation_function_(astronomy)
Test of normality in frequentist statistics
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Shapiro–Wilk_test
Diagnostic plot of binary classifier ability
prediction from the real class) and their geometric mean is the Matthews correlation coefficient.[citation needed] Whereas ROC AUC varies between 0 and 1
Receiver operating characteristic
Receiver_operating_characteristic
Unit of information
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Data
Probabilistic problem-solving algorithm
method for modified geometry of Macpherson suspension based on Pearson Correlation Coefficient". Vehicle System Dynamics. 55 (6): 827–852. Bibcode:2017VSD
Monte_Carlo_method
Statistical measure of association
of their maximum possible variation. φc2 is the mean square canonical correlation between the variables.[citation needed] In the case of a 2 × 2 contingency
Cramér's_V
Statistical hypothesis test
t_{\text{score}}={\frac {r{\sqrt {n-2}}}{\sqrt {1-r^{2}}}},} where r is the Pearson correlation coefficient. The tscore, intercept can be determined from the tscore
Student's_t-test
Statistical hypothesis test
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
F-test
Concept in machine learning
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Double_descent
Comparison of two distributions
"probability plot correlation coefficient" (PPCC plot) is the correlation coefficient between the paired sample quantiles. The closer the correlation coefficient
Q–Q_plot
Sampling from a population which can be partitioned into subpopulations
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Stratified_sampling
Statistical modeling method
In contrast, the marginal effect of xj on y can be assessed using a correlation coefficient or simple linear regression model relating only xj to y;
Linear_regression
Type of chart
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Bar_chart
Conditional probability used in Bayesian statistics
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Posterior_probability
Simultaneous observation and analysis of more than one outcome variable
over time. Iconography of correlations consists in replacing a correlation matrix by a diagram where the "remarkable" correlations are represented by a solid
Multivariate_statistics
Study of health and disease within a population
understanding of this science is that of discovering causal relationships. "Correlation does not imply causation" is a common theme for much of the epidemiological
Epidemiology
Method of data analysis
is also related to canonical correlation analysis (CCA). CCA defines coordinate systems that optimally describe the cross-covariance between two datasets
Principal_component_analysis
Topics referred to by the same term
chronological equivalence between geological phenomena in different regions. Cross-correlation, a measure of similarity between two signals, used e.g. in seismology
Correlation_(disambiguation)
Concept in probability theory and statistics
In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of
Partial_correlation
Statistical measure of how far values spread from their average
the average correlation remains constant or converges too. So for the variance of the mean of standardized variables with equal correlations or converging
Variance
Signal processing algorithm
with known spectral characteristics or known autocorrelation and cross-correlation Requirement: the filter must be physically realizable/causal (this
Wiener_filter
Statistic measuring inter-rater agreement for categorical items
unweighted kappa calculation given above. Bangdiwala's B Intraclass correlation Krippendorff's alpha Statistical classification Banerjee, M.; Capozzoli
Cohen's_kappa
Data transformation of statistics into rank
include: Friedman test Kruskal–Wallis test Rank products Spearman's rank correlation coefficient Mann–Whitney U test Wilcoxon signed-rank test Van der Waerden
Ranking_(statistics)
Statistic comparing ordinal rankings
In statistics, a rank correlation is any of several statistics that measure an ordinal association — the relationship between rankings of different ordinal
Rank_correlation
Unbiased statistical estimator minimizing variance
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Mathematical sequences
Kasami sequences have good cross-correlation values approaching the Welch lower bound. They are used as low-correlation spreading sequences in spread-spectrum
Kasami_code
Potential for two waves to interfere
well correlated the waves are as quantified by the cross-correlation function. Cross-correlation quantifies the ability to predict the phase of the second
Coherence_(physics)
Model for generating observable data in probability and statistics
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Generative_model
Statistic which divides a data set into 100 parts and analyzes it as a percentage
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Percentile
Type of average of a collection of numbers
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Arithmetic_mean
Statistics concept
example, x and x2 have correlation around 0.97 when x is uniformly distributed on the interval (0, 1). Although the correlation can be reduced by using
Polynomial_regression
Measure of covariance of components of a random vector
related to the covariance matrix is the matrix of Pearson product-moment correlation coefficients between each of the random variables in the random vector
Covariance_matrix
Statistical test
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Z-test
Medical imaging technique of the heart
(Sum of absolute difference), SSD (Sum of squared difference) and Cross correlation. Assume X 0 ( i , j ) {\displaystyle X_{0}(i,j)} is a pixel in the
Doppler_echocardiography
Statistical measure to determine how suited data is for factor analysis
there are large partial correlations compared to the sum of correlations. In other words, there are widespread correlations which would be a large problem
Kaiser–Meyer–Olkin_test
Fundamental theorem in probability theory and statistics
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Central_limit_theorem
Study of collection and analysis of data
Chi-squared test Correlation Factor analysis Mann–Whitney U Mean square weighted deviation (MSWD) Pearson product-moment correlation coefficient Regression
Statistics
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
Square Deviation (RMSD). While many natural processes indeed show a correlation between the average value and the amount of variation around it, accurate
Coefficient_of_variation
Graphical representation of the distribution of numerical data
can be generalized beyond normal distributions, by using leave-one out cross validation: a r g m i n h J ^ ( h ) = a r g m i n h ( 2 ( n − 1 ) h − n
Histogram
Criterion for model selection
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Bayesian information criterion
Bayesian_information_criterion
Method of statistical inference
testing are discussed by statisticians in other contexts, particularly correlation does not imply causation and the design of experiments. Hypothesis testing
Statistical_hypothesis_test
Nonparametric test of the null hypothesis
measure of rank correlation known as the rank-biserial correlation. Edward Cureton introduced and named the measure. Like other correlational measures, the
Mann–Whitney_U_test
Refutation of a logical fallacy
proposed that use correlation as the basis for hypothesis tests for causality, including the Granger causality test and convergent cross mapping. The Bradford
Correlation does not imply causation
Correlation_does_not_imply_causation
Algorithmically generated data that have a similar distribution as sampled data
help construct datasets exhibiting specific properties, such as auto-correlation or degree disparity, proximity can generate synthetic data having one
Synthetic_data
Range to estimate an unknown parameter
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Confidence_interval
Data visualization
The unusual percentiles 2%, 9%, 91%, 98% are sometimes used for whisker cross-hatches and whisker ends to depict the seven-number summary. If the data
Box_plot
Type of numerical analysis
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Isotonic_regression
Class of statistical tests
standardized data against the standard normal distribution. Here the correlation between the sample data and normal quantiles (a measure of the goodness
Normality_test
Statistic for rank correlation
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
Statistical test that compares goodness of fit
distribution Grouped data Dependence Partial correlation Pearson product-moment correlation Rank correlation Kendall's τ Spearman's ρ Scatter plot Graphics
Likelihood-ratio_test
How many standard deviations apart from the mean an observed datum is
standardized regression coefficients are affected not only by the presence of correlations among the predictor variables but also by the spacings of the observations
Standard_score
Class of statistical models
(GEEs) allow for the correlation between observations without the use of an explicit probability model for the origin of the correlations, so there is no explicit
Generalized_linear_model
Collection of statistical models
formal analysis in a 1918 article on theoretical population genetics, The Correlation Between Relatives on the Supposition of Mendelian Inheritance. His first
Analysis_of_variance
Condition in which the value of a measurement or observation is only partially known
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Censoring_(statistics)
Type of statistical measure over subsets of a dataset
Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional
Moving_average
travel, tourism, insurance
CROSS CORRELATION
CROSS CORRELATION
Surname or Lastname
English
English : topographic name for someone who lived near a stone cross set up by the roadside or in a marketplace, from Old Norse kross (via Gaelic from Latin crux, genitive crucis), which in Middle English quickly and comprehensively displaced the Old English form crūc (see Crouch). In a few cases the surname may have been given originally to someone who lived by a crossroads, but this sense of the word seems to have been a comparatively late development. In other cases, the surname (and its European cognates) may have denoted someone who carried the cross in processions of the Christian Church, but in English at least the usual word for this sense was Crozier.Irish : reduced form of McCrossen.In North America this name has absorbed examples of cognate names from other languages, such as French Lacroix.
Boy/Male
English
By the cross.
Boy/Male
Christian & English(British/American/Australian)
Wood
Girl/Female
Spanish
Holy cross.
Surname or Lastname
English
English : variant of Close 1.German : variant of Kloss.
Boy/Male
English Norse Teutonic
By the cross.
Surname or Lastname
English and Irish
English and Irish : variant spelling of Cross.
Boy/Male
American, Australian, Chinese, Latin, Spanish
Cross
Boy/Male
American, Australian, British, Chinese, Christian, English, French, Gaelic, German, Irish, Latin, Scandinavian, Scottish, Teutonic
Red Haired; Headland; Red; Surname; Wood; Rose; Having a Big Heart
Surname or Lastname
German and Jewish (Ashkenazic)
German and Jewish (Ashkenazic) : nickname for a big man, from Middle High German grÅz ‘large’, ‘thick’, ‘corpulent’, German gross. The Jewish name has been Hebraicized as Gadol, from Hebrew gadol ‘large’.English : nickname for a big man, from Middle English, Old French gros (Late Latin grossus, of Germanic origin, thus etymologically the same word as in 1 above). The English vocabulary word did not develop the sense ‘excessively fat’ until the 16th century.
Boy/Male
English
Literally 'cross land'.
Boy/Male
English
Literally 'cross land'.
Boy/Male
African, Hindu, Indian
To Cross
Male
English
Scottish surname transferred to forename use, derived from the Gaelic word ros, ROSS means "headland, promontory."
Surname or Lastname
Scottish and English (of Norman origin)
Scottish and English (of Norman origin) : habitational name for someone from Rots near Caen in Normandy, probably named with the Germanic element rod ‘clearing’. Compare Rhodes. This was the original home of a family de Ros, who were established in Kent in 1130.Scottish and English : habitational name from any of various places called Ross or Roos(e), deriving the name from Welsh rhós ‘upland’ or moorland, or from a British ancestor of this word, which also had the sense ‘promontory’. This is the sense of the cognate Gaelic word ros. Known sources of the surname include Roos in Humberside (formerly in East Yorkshire) and the region of northern Scotland known as Ross. Other possible sources are Ross-on-Wye in Herefordshire, Ross in Northumbria (which is on a promontory), and Roose in LancashireEnglish and German : from the Germanic personal name Rozzo, a short form of the various compound names with the first element hrÅd ‘renown’, introduced into England by the Normans in the form Roce.German and Jewish (Ashkenazic) : metonymic occupational name for a breeder or keeper of horses, from Middle High German ros, German Ross ‘horse’; perhaps also a nickname for someone thought to resemble a horse or a habitational name for someone who lived at a house distinguished by the sign of a horse.Jewish : Americanized form of Rose 3.
Male
Italian
Short form of Italian Crocifisso, or Croccifixio, CROSS means "cross; crucifix" or "way of the cross."
Boy/Male
German American Scottish Shakespearean Teutonic
Red. Surname.
Boy/Male
Armenian
Small cross.
Boy/Male
Basque
Holy cross.
Surname or Lastname
English
English : nickname from Old French, Middle English cras ‘big’, ‘fat’ (Latin crassus).Possibly an altered spelling of German Krass.
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travel, tourism, insurance