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Square root of the mean square
In mathematics, the root mean square (abbrev. RMS, rms or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle
Root_mean_square
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
Average of squared values of a sample
In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable
Mean_square
Statistical measure
The root mean square deviation (RMSD) or root mean square error (RMSE) is a frequently used measure of the distances between actual observed values and
Root_mean_square_deviation
Measure of change in a periodic variable
mean square (RMS) amplitude is used especially in electrical engineering: the RMS is defined as the square root of the mean over time of the square of
Amplitude
Statistical error measure
related 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
Specific probability distribution function, important in physics
The mean square speed ⟨ v 2 ⟩ {\displaystyle \langle v^{2}\rangle } is the second-order raw moment of the speed distribution. The "root mean square speed"
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Statistics concept
with unknown mean and unknown variance. No correction is necessary if the population mean is known. It is remarkable that the sum of squares of the residuals
Errors_and_residuals
Notions of probabilistic convergence, applied to estimation and asymptotic analysis
{\displaystyle r} -th mean implies convergence in s {\displaystyle s} -th mean. Hence, convergence in mean square implies convergence in mean. Additionally,
Convergence of random variables
Convergence_of_random_variables
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
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
Concept in signal processing
n]-x[m,n]\right|)} Measuring the average squared difference between two signals. Unlike the maximum error, mean squared error takes into account the overall
Similarity (signal processing)
Similarity_(signal_processing)
Form of statistical factor analysis
acceptable model fit. The root mean square residual (RMR) and standardized root mean square residual (SRMR) are the square root of the discrepancy between
Confirmatory_factor_analysis
Statistical algorithm
Least mean squares (LMS) algorithms are a class of adaptive filter used to mimic a desired filter by finding the filter coefficients that relate to producing
Least_mean_squares_filter
Estimation method that minimizes the mean square error
signal processing, a minimum mean square error estimator (MMSE estimator) is an estimation method which minimizes the mean square error (MSE), which is a common
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Electric current that periodically reverses direction
DC component) is assumed. The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage. For an arbitrary periodic
Alternating_current
Type of algorithm
calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points. It is useful for point-set
Kabsch_algorithm
Measure of distance between atoms of superimposed proteins
In bioinformatics, the root mean square deviation of atomic positions, or simply root mean square deviation (RMSD), is the measure of the average distance
Root mean square deviation of atomic positions
Root_mean_square_deviation_of_atomic_positions
Type of filter in signal processing
are 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
Statistical measure of association for two binary variables
In statistics, the phi coefficient, also known as the mean square contingency coefficient or Yule coefficient of correlation and commonly denoted by φ
Phi_coefficient
Statistical model validation technique
squares is used to fit a function in the form of a hyperplane ŷ = a + βTx to the data (xi, yi) 1 ≤ i ≤ n, then the fit can be assessed using the mean
Cross-validation_(statistics)
Number taken as representative of a list of numbers
mean Logarithmic mean Moving average Neuman–Sándor mean Quasi-arithmetic mean Root mean square (quadratic mean) Rényi's entropy (a generalized f-mean)
Average
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
Rule for calculating an estimate of a given quantity based on observed data
can be judged by looking at their properties, such as unbiasedness, mean square error, consistency, asymptotic distribution, etc. The construction and
Estimator
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), and relative standard deviation (RSD), is a standardized
Coefficient_of_variation
Statistical measure of the magnitude of a phenomenon
size estimator for multiple comparisons (e.g., ANOVA) is the Ψ root-mean-square standardized effect: Ψ = 1 k − 1 ⋅ ∑ j = 1 k ( μ j − μ σ ) 2 {\displaystyle
Effect_size
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
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
Circular_error_probable
Machine learning technique
^{(t)})^{2}={\frac {1}{D}}\sum _{i=1}^{D}(x_{i}^{(t)}-\mu ^{(t)})^{2}} Root mean square layer normalization (RMSNorm): x i ^ = x i 1 D ∑ j = 1 D x j 2 , y i
Normalization (machine learning)
Normalization_(machine_learning)
Quantity derived from seismic data
computes the square root of the sum of squared amplitudes divided by the number of samples within the specified window used. With this root mean square amplitude
Seismic_attribute
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
statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance
Expected_mean_squares
Stochastic process that is a continuous function of time or index parameter
continuity in mean-square implies continuity in probability; continuity with probability one neither implies, nor is implied by, continuity in mean-square; continuity
Continuous_stochastic_process
Source of error in statistics
to the residual mean square rather than with respect to the among unit mean square. The F-ratio relative to the within unit mean square is vulnerable to
Pseudoreplication
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
Statistical property
biased 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
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
Chain of inequalities of means of positive numbers
(GM), arithmetic mean (AM), and quadratic mean (QM; also known as root mean square). Suppose that x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots
QM–AM–GM–HM_inequalities
Mathematical decision rule
common 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 ^ (
Bayes_estimator
Measure of the accuracy of probabilistic predictions
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
SI unit of apparent power in an electrical circuit
electrical circuit. It is the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are usually
Volt-ampere
Dataflow programming language
sqroot(avg(square(a))) where square(x) = x*x; avg(y) = mean where n = 1 fby n+1; mean = first y fby mean + d; d = (next y - mean)/(n+1); end; sqroot(z)
Lucid_(programming_language)
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
Peak divided by the Root mean square (RMS) of the waveform
crest factor is the peak amplitude of the waveform divided by the root mean square (RMS) value of the waveform. The minimum possible crest factor is 1 or
Crest_factor
n_{2})+F[e(n_{1},n_{2})]} Least mean square (LMS) Adaptive Filters use the most common error measure method, the mean square error. The 2D LMS Adaptive filters
2D_adaptive_filters
Electrical noise due to thermal vibration within a conductor
approximately 13 nV/√Hz at room temperature. The square root of the mean square voltage yields the root mean square (RMS) voltage observed over the bandwidth
Johnson–Nyquist_noise
N-th root of the product of n numbers
numbers is the square root of their product, for example with numbers 2 {\displaystyle 2} and 8 {\displaystyle 8} the geometric mean is 2 ⋅ 8 = {\displaystyle
Geometric_mean
Algorithm in numerical analysis
worst-case error that grows proportional to n {\displaystyle n} , and a root mean square error that grows as n {\displaystyle {\sqrt {n}}} for random inputs (the
Kahan_summation_algorithm
Indicator for how well data points fit a line or curve
coefficient Proportional reduction in loss Regression model validation Root mean square deviation Stepwise regression Steel, R. G. D.; Torrie, J. H. (14 July
Coefficient_of_determination
Logarithmic unit expressing the ratio of physical quantities
{V_{\text{out}}}{V_{\text{in}}}}\right)\,{\text{dB}}} where Vout is the root-mean-square (rms) output voltage, Vin is the rms input voltage. A similar formula
Decibel
Process of mapping a continuous set to a countable set
that the mean squared error produced by such a rounding operation will be approximately Δ 2 / 12 {\displaystyle \Delta ^{2}/12} . Mean squared error is
Quantization (signal processing)
Quantization_(signal_processing)
N-th root of the arithmetic mean of the given numbers raised to the power n
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include
Generalized_mean
Distance from center of mass to axis of rotation
the SI unit metre. Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given
Radius_of_gyration
Regularization technique for ill-posed problems
variance and mean square estimator are often smaller than the least square estimators previously derived. In the ordinary least squares solution of Y
Ridge_regression
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
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
Algorithm that estimates unknowns from a series of measurements over time
over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but also relates to maximum likelihood statistics. The
Kalman_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
Stein's_example
Signal processing algorithm
and noise spectra, and additive noise. The Wiener filter minimizes the mean square error between the estimated random process and the desired process. The
Wiener_filter
Property of a model
(x_{n},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
Measurement of the harmonic distortion present in a signal
can be distinguished as THDF (for "fundamental"), and THDR (for "root mean square"). THDR cannot exceed 100%. At low distortion levels, the difference
Total_harmonic_distortion
contraharmonic mean of a set of positive real numbers is defined as the arithmetic mean of the squares of the numbers divided by the arithmetic mean of the numbers:
Contraharmonic_mean
difference Mean square quantization error Mean square weighted deviation Mean squared error Mean squared prediction error Mean time between failures Mean-reverting
List_of_statistics_articles
Unit of measurement for amplitude levels in digital systems
−6 dBFS, which is 6 dB below full scale. Conventions differ for root mean square (RMS) measurements, but all peak measurements smaller than the maximum
DBFS
Classical averages studied in ancient Greece
classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions
Pythagorean_means
Measure of the size of atomic nuclei
the scattering of electrons by the nucleus. Relative changes in the mean squared nuclear charge distribution can be precisely measured with atomic spectroscopy
Charge_radius
Arithmetic mean is greater than or equal to geometric mean
inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further
AM–GM_inequality
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 mean is unknown, the uncorrected sample variance is the mean of the squares of deviations of sample values from the sample mean (i.e., using
Bessel's_correction
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
Physical constant relating particle kinetic energy with temperature
the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. The root mean square speeds
Boltzmann_constant
Measure of statistical error
Percentage error Mean absolute percentage error Mean squared error Mean squared prediction error Minimum mean-square error Squared deviations Peak signal-to-noise
Mean_percentage_error
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
Hypotenuse of right triangle from its sides
quadrature. A scaled version of this operation gives the quadratic mean or root mean square. It is available in many programming libraries as the hypot function
Pythagorean_addition
Unit for the arithmetic difference of two percentages
related descriptive statistics, including the standard deviation and root-mean-square error, the result should be expressed in units of percentage points instead
Percentage_point
Power carried by sound waves
and microphone spacing and directly proportional to the ratio of the mean square sound pressure to the sound intensity. If the pressure-to-intensity ratio
Sound_intensity
Condition for optimality of Bayesian estimator
principle says that the error vector of the optimal estimator (in a mean square error sense) is orthogonal to any possible estimator. The orthogonality
Orthogonality_principle
Statistical property
sampling distribution. It is the square root of the variance of an estimator of a parameter, as in the standard error of the mean. The standard error is often
Standard_error
Audible vibration that travels via pressure waves in matter
time and/or space, and a square root of this average provides a root mean square (RMS) value. For example, 1 Pa RMS sound pressure (94 dBSPL) in atmospheric
Sound
and it would often be used in conjunction with a sample version of the mean square error. For example, suppose a linear regression model has been estimated
Mean_signed_deviation
Type of motion in mechanical engineering
the usual ways to specify random vibrations. The root mean square acceleration (Grms) is the square root of the area under the ASD curve in the frequency
Random_vibration
Device for acoustic measurements
distinguishable by the voltage value produced when a known, constant root mean square sound pressure is applied. This is known as microphone sensitivity. The
Sound_level_meter
Clock deviation from perfect periodicity
quantified in the same terms as all time-varying signals, e.g., root mean square (RMS), or peak-to-peak displacement. Also, like other time-varying signals
Jitter
System with self-optimizing transfer function
the cost on the next iteration. The most common cost function is the mean square of the error signal. As the power of digital signal processors has increased
Adaptive_filter
Smallest length scales in turbulent fluid flow
of the Kolmogorov time scale can be obtained from the inverse of the mean square strain rate tensor, τ η = 1 2 ⟨ E i j E i j ⟩ , {\displaystyle \tau _{\eta
Kolmogorov_microscales
Optimization algorithm
descent in the least squares problem is very similar to the comparison between least mean squares (LMS) and normalized least mean squares filter (NLMS). Even
Stochastic_gradient_descent
Typical velocity of the thermal motion of particles
velocities: If v th {\displaystyle v_{\text{th}}} is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then
Thermal_velocity
Ratio of the desired signal to the background noise
[N^{2}]}}\,,} where E refers to the expected value, which in this case is the mean square of N. If the signal is simply a constant value of s, this equation simplifies
Signal-to-noise_ratio
Mathematical operation that predicts future values of a discrete-time signal
the root mean square criterion which is also called the autocorrelation criterion. In this method we minimize the expected value of the squared error E
Linear_prediction
Approximation method in statistics
arithmetic mean as the best estimate. Instead, his estimator was the posterior median. The first clear and concise exposition of the method of least squares was
Least_squares
Sports formula
season, Davenport was able to report a 3.991 root-mean-square error as opposed to a 4.126 root-mean-square error for an exponent of 2. Less well known but
Pythagorean_expectation
Topics referred to by the same term
Learning management system, education software Least mean squares filter, producing least mean square error Leiomyosarcoma, a rare form of cancer Lenz microphthalmia
LMS
distance (LSD), also referred to as log-spectral distortion or root mean square log-spectral distance, is a distance measure between two spectra. The
Log-spectral_distance
Expected value of a random variable given that certain conditions are known to occur
minimizers 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
Mean amplitude of a waveform in the time domain
JPEG. Electronics portal Energy portal Phantom power Root-mean-square amplitude Root-mean-square voltage Kees Schouhamer Immink (March 1997). "Performance
DC_bias
Topics referred to by the same term
Remote Manipulator System, a robotic arm on the Space Shuttle Residual mean square, a measure of the difference between data and a model of that data Revenue
RMS
Process forming a path from many random steps
any distribution with zero mean and a finite variance (not necessarily just a normal distribution), the root mean square translation distance after n
Random_walk
minimum mean square error (MMSE) estimate for the state of each target. At each time, it maintains its estimate of the target state as the mean and covariance
Joint Probabilistic Data Association Filter
Joint_Probabilistic_Data_Association_Filter
Phenomenon in statistics
coefficients are shrunk towards zero with the effect of reducing the mean square error of predicted values from the model when applied to new data. A
Shrinkage_(statistics)
Measure of accuracy of predictions
represented in terms of metrics such as correlation, root mean squared error, mean absolute error, relative mean absolute error, bias, and the Brier score, among
Forecast_skill
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