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Measure of the error of an estimator
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures
Mean_squared_error
Statistical error measure
to the mean squared error, the equivalent for mean absolute error is least absolute deviations. MAE is not identical to root-mean square error (RMSE)
Mean_absolute_error
Statistical measure
processes. Root mean square Mean absolute error Average absolute deviation Mean signed deviation Mean squared deviation Squared deviations Errors and residuals
Root_mean_square_deviation
Estimation method that minimizes the mean square error
and Stirling. Johnson, D. "Minimum Mean Squared Error Estimators". Connexions. Archived from Minimum Mean Squared Error Estimators the original on 25 July
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Statistics concept
In statistics the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression
Mean_squared_prediction_error
Statistics concept
arises in the expression mean squared error (MSE). The mean squared error of a regression is a number computed from the sum of squares of the computed residuals
Errors_and_residuals
Average of squared values of a sample
may be known as mean square deviation. When the reference value is the assumed true value, the result is known as mean squared error. A typical estimate
Mean_square
Rule for calculating an estimate of a given quantity based on observed data
may have a lower mean squared error than any unbiased estimator (see estimator bias). This equation relates the mean squared error with the estimator
Estimator
Statistical model validation technique
continuously distributed, the mean squared error, root mean squared error or median absolute deviation could be used to summarize the errors. When users apply cross-validation
Cross-validation_(statistics)
Statistical property
estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased estimators (notably in shrinkage estimators);
Bias_of_an_estimator
Method for estimating the unknown parameters in a linear regression model
least squares, not biased) parameter estimates and biased standard errors, resulting in misleading tests and interval estimates. The mean squared error for
Ordinary_least_squares
Measure of statistical error
zero. Percentage error Mean absolute percentage error Mean squared error Mean squared prediction error Minimum mean-square error Squared deviations Peak
Mean_percentage_error
Test statistic
statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD)
Reduced_chi-squared_statistic
Property of a model
y_{n})\}} . We make "as well as possible" precise by measuring the mean squared error between y {\displaystyle y} and f ^ ( x ; D ) {\displaystyle {\hat
Bias–variance_tradeoff
Statistical theorem
arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. The Rao–Blackwell
Rao–Blackwell_theorem
Concept in signal processing
average squared difference between two signals. Unlike the maximum error, mean squared error takes into account the overall magnitude and spread of errors, offering
Similarity (signal processing)
Similarity_(signal_processing)
Theory about lossy data compression
defined as the expected value of the square of the difference between input and output signal (i.e., the mean squared error). However, since we know that most
Rate–distortion_theory
Process of mapping a continuous set to a countable set
the mean squared error produced by such a rounding operation will be approximately Δ 2 / 12 {\displaystyle \Delta ^{2}/12} . Mean squared error is also
Quantization (signal processing)
Quantization_(signal_processing)
Statistical property
population mean. In regression analysis, the term "standard error" can also be used to refer to the square root of the reduced chi-squared statistic in
Standard_error
Probability distribution
distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two
Gamma_distribution
Measure of the accuracy of probabilistic predictions
For unidimensional predictions, it is strictly equivalent to the mean squared error as applied to predicted probabilities. The Brier score is applicable
Brier_score
In statistics, the mean integrated squared error (MISE) is used in density estimation. The MISE of an estimate of an unknown probability density is given
Mean_integrated_squared_error
Correction for sample variance bias
population standard deviation. However, the correction often increases the mean squared error in these estimations. This technique is named after Friedrich Bessel
Bessel's_correction
Stein's unbiased risk estimate (SURE) is an unbiased estimator of the mean-squared error of "a nearly arbitrary, nonlinear biased estimator." In other words
Stein's unbiased risk estimate
Stein's_unbiased_risk_estimate
Statistical measure of the discrepancy between data and an estimation model
sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals
Residual_sum_of_squares
Use of multiple antennas in radio
minimum mean squared error (MMSE) algorithm detects the transmitted signals, x ~ {\displaystyle {\tilde {\mathbf {x} }}} , through minimizing the mean squared
MIMO
Rule for estimating the mean of a dataset
"ordinary" least squares approach in the sense that the James–Stein estimator has a lower mean squared error than the "ordinary" least squares estimator for
James–Stein_estimator
Statistical modeling method
of the least squares cost function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Use of the Mean Squared Error (MSE) as the cost
Linear_regression
Statistical algorithm
mean squared error, ∑ e 2 / n {\displaystyle \sum e^{2}/n} . The realization of the causal Wiener filter resembles the solution to the least squares estimate
Least_mean_squares_filter
Phenomenon in decision theory and estimation theory
estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately. It is named
Stein's_example
Lower bound on variance of an estimator
be (fully) efficient. Such a solution achieves the lowest possible mean squared error among all unbiased methods, and is, therefore, the minimum variance
Cramér–Rao_bound
Measure of accuracy of predictions
terms of metrics such as correlation, root mean squared error, mean absolute error, relative mean absolute error, bias, and the Brier score, among others
Forecast_skill
Statistical accuracy measure
arithmetic mean. Relative change and difference Mean absolute error Mean absolute percentage error Mean squared error Root mean squared error Armstrong
Symmetric mean absolute percentage error
Symmetric_mean_absolute_percentage_error
Theorem related to ordinary least squares
_{j}\beta _{j}} be some linear combination of the coefficients. Then the mean squared error of the corresponding estimation is E [ ( ∑ j = 1 K λ j ( β ^ j −
Gauss–Markov_theorem
Type of filter in signal processing
common: Window design method Frequency sampling method Least MSE (mean square error) method Parks–McClellan method (also known as the equiripple, optimal
Finite_impulse_response
Ballistics measure of a weapon system's precision
associated concept, the DRMS (distance root mean square), calculates the square root of the average squared distance error, a form of the standard deviation. Another
Circular_error_probable
Statistical measure of how far values spread from their average
as the expected value of the squared deviation from the mean of a random variable. The standard deviation is the square root of the variance. Technically
Variance
Machine learning technique
form y ^ = F ( x ) {\displaystyle {\hat {y}}=F(x)} by minimizing the mean squared error 1 n ∑ i ( y ^ i − y i ) 2 {\displaystyle {\tfrac {1}{n}}\sum _{i}({\hat
Gradient_boosting
Measure of prediction accuracy of a forecast
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting
Mean absolute percentage error
Mean_absolute_percentage_error
Graphical representation of the distribution of numerical data
normally distributed data, in the sense that it minimizes the integrated mean squared error of the density estimate. This is the default rule used in Microsoft
Histogram
Prediction of digital video quality
other techniques such as mean squared error (MSE) or peak signal-to-noise ratio (PSNR) that instead estimate absolute errors. Structural information is
Structural similarity index measure
Structural_similarity_index_measure
Australian statistician (born 1967)
error, such as mean absolute error, geometric mean absolute error, and mean squared error, have shortcomings related to dependence on scale of data and/or
Rob_J._Hyndman
Class of artificial neural network
presented to the network which propagates the input signals forward. The mean-squared error is returned to the fitness function. This function drives the genetic
Recurrent_neural_network
Square root of the mean square
in that the RMS includes the squared deviation (error) as well. Physical scientists often use the term root mean square as a synonym for standard deviation
Root_mean_square
Summary statistic of variability
accuracy is very closely related to the mean squared error (MSE) method which is just the average squared error of the forecasts. Although these methods
Average_absolute_deviation
Model-free reinforcement learning algorithm
sample KL-divergence constraint. Fit value function by regression on mean-squared error: ϕ k + 1 = arg min ϕ 1 | D k | T ∑ τ ∈ D k ∑ t = 0 T ( V ϕ ( s t
Proximal_policy_optimization
Mathematical decision rule
risk function used for Bayesian estimation is the mean square error (MSE), also called squared error risk. The MSE is defined by M S E = E [ ( θ ^ ( x
Bayes_estimator
Quality measure of a statistical method
calculated by finding the mean squared error. More formally, let T be an estimator for the parameter θ. The mean squared error of T is the value MSE (
Efficiency_(statistics)
Type of average of a collection of numbers
{x}})^{2}} . The sample mean is also the best single predictor because it has the lowest root mean squared error. If the arithmetic mean of a population of
Arithmetic_mean
Index of articles associated with the same name
see Least squares For the "sum of squared differences", see Mean squared error For the "sum of squared error", see Residual sum of squares For the "sum
Sum_of_squares
Online vector quantization algorithm
of two related algorithms: TurboQuantmse, which is optimized for mean squared error (MSE), and TurboQuantprod, which is optimized for unbiased inner product
TurboQuant
In statistics, the mean signed difference (MSD), also known as mean signed deviation, mean signed error, or mean bias error is a sample statistic that
Mean_signed_deviation
Measure of the deviation of position over time
statistical mechanics, the mean squared displacement (MSD), also called mean square displacement, average squared displacement, or mean square fluctuation, is a
Mean_squared_displacement
Algorithm that estimates unknowns from a series of measurements over time
the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided
Kalman_filter
Mathematical relation assigning a probability event to a cost
}})^{2}\right].} An estimator found by minimizing the mean squared error estimates the posterior distribution's mean. In density estimation, the unknown parameter
Loss_function
Concept in statistics
parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle
Kernel_density_estimation
Study of collection and analysis of data
prediction). Mean squared error is used for obtaining efficient estimators, a widely used class of estimators. Root mean square error is simply the square root
Statistics
Form of statistical factor analysis
the chi-squared test, the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardised root mean square residual
Confirmatory_factor_analysis
Branch of statistics to estimate models based on measured data
estimators Cramér–Rao bound Least squares Minimum mean squared error (MMSE), also known as Bayes least squared error (BLSE) Maximum a posteriori (MAP)
Estimation_theory
Method of estimating the parameters of a statistical model, given observations
infinity. This means that no consistent estimator has lower asymptotic mean squared error than the MLE (or other estimators attaining this bound), which also
Maximum_likelihood_estimation
Theory of stochastic processes
yields the best such basis in the sense that it minimizes the total mean squared error. In contrast to a Fourier series where the coefficients are fixed
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Measure of variation in statistics
probability distribution is the square root of its variance (the variance being the average of the squared deviations from the mean). A useful property of the
Standard_deviation
Phenomenon in statistics
estimation schemes. Many standard estimators can be improved, in terms of mean squared error (MSE), by shrinking them towards zero (or any other finite constant
Shrinkage_(statistics)
Topics referred to by the same term
common error metrics are: Mean Squared Error (MSE) Root Mean Square Error (RMSE) Mean absolute error (MAE) Mean Absolute Scaled Error (MASE) Mean Absolute
Error_metric
Least squares approximation of linear functions to data
}}}} is known, then a Bayes estimator can be used to minimize the mean squared error, E { ‖ β − β ^ ‖ 2 } {\displaystyle E\left\{\|{\boldsymbol {\beta
Linear_least_squares
Approximation method in statistics
In regression analysis, least squares is a method to determine the best-fit model by minimizing the sum of the squared residuals—the differences between
Least_squares
Calculations in probability theory
Squared deviations from the mean (SDM) result from squaring deviations. In probability theory and statistics, the definition of variance is either the
Squared deviations from the mean
Squared_deviations_from_the_mean
Matrix of second derivatives of the log-likelihood function
information matrix gives the minimum mean squared error as an approximation of the true information if an error term of O ( n − 3 / 2 ) {\displaystyle
Observed_information
Probability distribution
}}^{2}} is better than the s 2 {\textstyle s^{2}} in terms of the mean squared error (MSE) criterion. In finite samples both s 2 {\textstyle s^{2}} and
Normal_distribution
Condition for optimality of Bayesian estimator
the orthogonality principle says that the error vector of the optimal estimator (in a mean square error sense) is orthogonal to any possible estimator
Orthogonality_principle
Statistical technique
{\boldsymbol {\beta }}}_{\mathrm {ols} }),} where, MSE denotes the mean squared error. Now, if for some k ∈ { 1 , … , p } {\displaystyle k\in \{1,\ldots
Principal component regression
Principal_component_regression
Statistical hypothesis test
statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used
Chi-squared_test
Performance indicator for hydrologic models
Harald (2011). "On typical range, sensitivity, and normalization of Mean Squared Error and Nash–Sutcliffe Efficiency type metrics". Water Resources Research
Kling–Gupta_efficiency
Stochastic process generalizing Brownian motion
than T R ( D ) {\textstyle TR(D)} bits and recover it with expected mean squared error less than D. On the other hand, for any ε > 0 {\textstyle \varepsilon
Wiener_process
Deep learning software
train neural network on classical tasks. Common criteria are the mean squared error criterion implemented in MSECriterion and the cross-entropy criterion
Torch_(machine_learning)
Empirical law on the variance of species in a habitat
the overall mean of the population. Values of D > 1 are considered to suggest aggregation. D( n − 1 ) is distributed as the chi squared variable with
Taylor's_law
Forecast errors can be evaluated using a variety of methods namely mean percentage error, root mean squared error, mean absolute percentage error, mean squared
Forecast_error
Statistical rule for bin-width in histograms
the theoretical probability distribution. In detail, the Integrated Mean Squared Error (IMSE) is IMSE = E [ ∫ I ( H ( x ) − f ( x ) ) 2 ] {\displaystyle
Freedman–Diaconis_rule
(GNN) estimate in place of the mean but compute the covariance matrix as in the normal JPDAF: as a mean-squared error matrix. MATLAB: The PDAF, JPDAF
Joint Probabilistic Data Association Filter
Joint_Probabilistic_Data_Association_Filter
Topics referred to by the same term
Canada–France–Hawaii Telescope Maximum spacing estimation, in statistics Mean squared error, in statistics Mechanically stabilized earth Mental status examination
MSE
Measure of forecasting quality
the Mean absolute error divided by the Mean Absolute Deviation. Mean squared error Mean absolute error Mean absolute percentage error Root-mean-square deviation
Mean_absolute_scaled_error
Expected value of a random variable given that certain conditions are known to occur
of the mean squared error. Example 1: Consider the case where Y is the constant random variable that is always 1. Then the mean squared error is minimized
Conditional_expectation
Probability distribution and special case of gamma distribution
variables which do not have mean zero yields a generalization of the chi-squared distribution called the noncentral chi-squared distribution. If Y {\displaystyle
Chi-squared_distribution
System to predict users' preferences
offline evaluations. The commonly used metrics are the mean squared error and root mean squared error, the latter having been used in the Netflix Prize. The
Recommender_system
Figure of merit for analog-to-digital conversion
Mean square quantization error (MSQE) is a figure of merit for the process of analog to digital conversion. In this conversion process, analog signals
Mean square quantization error
Mean_square_quantization_error
Statistical noise
{\operatorname {MSE} (f)}{\operatorname {var} [Y]}}} where MSE(f) is the mean squared error of the regression function ƒ. It is useful to consider the second
Fraction of variance unexplained
Fraction_of_variance_unexplained
residual errors as an input, the output must be re-associated with the data. Taking the average of all the squared errors (i.e., the mean-squared error) and
Peirce's_criterion
Systemic inaccuracy
hard to compute. Third, a biased estimator may have a lower value of mean squared error. A biased estimator is better than any unbiased estimator arising
Bias_(statistics)
Concept that permeates much of inferential statistics and descriptive statistics
the squared norms of orthogonal summands equals the squared norm of the sum. Least squares Mean squared error Squared deviations "Sum of Squares - Definition
Partition_of_sums_of_squares
Statistical measure in mathematical model
standard error of the estimate of βj is the square root of the j + 1 diagonal element of s2(X′X)−1, where s is the root mean squared error (RMSE) (note
Variance_inflation_factor
Tree-based ensemble machine learning methods
g. the following statistics can be used: Entropy Gini coefficient Mean squared error The normalized importance is then obtained by normalizing over all
Random_forest
Artificial neural network algorithm
the learning rule of the network can be as simple as an XOR gate or mean squared error, or as complex as the result of a system of differential equations
Learning_rule
{\lambda }{2}}\sum _{j=1}^{d}\theta _{j}^{2}} The first term is the mean squared error (MSE) term between the value of the learned model, h θ {\displaystyle
Structural_risk_minimization
Adaptive filter algorithm for digital signal processing
contrast to other algorithms such as the least mean squares (LMS) that aim to reduce the mean square error. In the derivation of the RLS, the input signals
Recursive least squares filter
Recursive_least_squares_filter
Computational model used in machine learning
products of the weights and the inputs is calculated at each node. The mean squared errors between these calculated outputs and the given target values are
Neural network (machine learning)
Neural_network_(machine_learning)
Type of artificial neural network
activation functions. It was trained by the least squares method for minimising mean squared error, also known as linear regression. Legendre and Gauss
Feedforward_neural_network
Overview of and topical guide to machine learning
regularization Matthews correlation coefficient Mean shift Mean squared error Mean squared prediction error Measurement invariance Medoid MeeMix Melomics
Outline_of_machine_learning
Rule for choosing histogram bins
approximation of some function f ( x ) {\displaystyle f(x)} . The integrated mean squared error (IMSE) is IMSE = E [ ∫ − ∞ ∞ d x ( f ^ ( x ) − f ( x ) ) 2 ] {\displaystyle
Scott's_rule
Type of kernel induced by artificial neural networks
function is mean-squared error, the final distribution over f ( x ; θ ) {\displaystyle f(x;\theta )} is still a Gaussian process, but with a new mean and covariance
Neural_tangent_kernel
Algorithm in numerical analysis
numbers in sequence has a worst-case error that grows proportional to n {\displaystyle n} , and a root mean square error that grows as n {\displaystyle {\sqrt
Kahan_summation_algorithm
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