The Experts below are selected from a list of 471 Experts worldwide ranked by ideXlab platform
Tenko Raykov - One of the best experts on this subject based on the ideXlab platform.
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a wiener germ approximation of the noncentral chi square distribution and of its quantiles
Computational Statistics, 2000Co-Authors: Spiridon Penev, Tenko RaykovAbstract:The cumulative distribution function (cdf) of the noncentral χ2 distribution with positive degrees of freedom ν > 0 and a Noncentrality Parameter δ2 ≥ 0 is usually expressed as an infinite weighted sum of central χ2 cdf’s. For the purpose of numerical evaluation this infinite sum is being approximated by a finite sum. For large values of the Noncentrality Parameter, the sum converges slowly. Alternative approximation algorithms have been proposed instead in the literature. A comparison of these is given in Johnson & Kotz (1970). Most of the approximation algorithms have advantages for certain values of the arguments/Parameters and perform poorly for other values. We are proposing an approximation algorithm that has a very solid theoretical background and is surprisingly accurate for extremely large set of arguments/Parameter values. It is also applied for a reliable approximation of the quantiles of the distribution for large values of Noncentrality and degrees of freedom. Although being asymptotic in spirit (with respect to degrees of freedom ν), the algorithm gives quite accurate approximation even down to ν = 1.
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on the large sample bias variance and mean squared error of the conventional Noncentrality Parameter estimator of covariance structure models
Structural Equation Modeling, 2000Co-Authors: Tenko RaykovAbstract:The conventional Noncentrality Parameter estimator of covariance structure models, which is currently implemented in widely circulated structural modeling programs (e.g., LISREL, EQS, AMOS, RAMONA), is shown to possess asymptotically potentially large bias, variance, and mean squared error (MSE). A formal expression for its large-sample bias is presented, and its large-sample variance and MSE are quantified. Based on these results, it is suggested that future research needs to develop means of possibly unbiased estimation of the Noncentrality Parameter, with smaller variance and MSE.
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On the Relationship Between Validity and Power
2024Co-Authors: Tenko RaykovAbstract:effect-size, F-distribution, validity, Noncentrality Parameter, power, prediction,
Suhasini Subba Rao - One of the best experts on this subject based on the ideXlab platform.
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a test for second order stationarity of a time series based on the discrete fourier transform
Journal of Time Series Analysis, 2011Co-Authors: Yogesh Dwivedi, Suhasini Subba RaoAbstract:We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It can be shown that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a generalised noncentral chi-square, where the Noncentrality Parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power.
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A test for second order stationarity of a time series based on the Discrete Fourier Transform,” arXiv:0911.4744
2009Co-Authors: Yogesh Dwivedi, Suhasini Subba RaoAbstract:We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It can be shown that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a generalised noncentral chi-square, where the Noncentrality Parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power
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A test for second order stationarity of a time series based on the Discrete Fourier Transform,” arXiv:0911.4744
2009Co-Authors: Yogesh Dwivedi, Suhasini Subba RaoAbstract:We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical Fourier frequencies. It is well known that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a type of noncentral chi-square, where the Noncentrality Parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power. Some real examples are also included to illustrate the test. Kew words and phrases Discrete Fourier Transform, local stationarity, Portmanteau test, test for second order stationarity.
Yogesh Dwivedi - One of the best experts on this subject based on the ideXlab platform.
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a test for second order stationarity of a time series based on the discrete fourier transform
Journal of Time Series Analysis, 2011Co-Authors: Yogesh Dwivedi, Suhasini Subba RaoAbstract:We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It can be shown that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a generalised noncentral chi-square, where the Noncentrality Parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power.
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a test for second order stationarity of a time series based on the discrete fourier transform technical report
arXiv: Methodology, 2009Co-Authors: Yogesh DwivediAbstract:We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It is well known that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a type of noncentral chi-square, where the Noncentrality Parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power. Some real examples are also included to illustrate the test.
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A test for second order stationarity of a time series based on the Discrete Fourier Transform,” arXiv:0911.4744
2009Co-Authors: Yogesh Dwivedi, Suhasini Subba RaoAbstract:We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It can be shown that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a generalised noncentral chi-square, where the Noncentrality Parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power
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A test for second order stationarity of a time series based on the Discrete Fourier Transform,” arXiv:0911.4744
2009Co-Authors: Yogesh Dwivedi, Suhasini Subba RaoAbstract:We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical Fourier frequencies. It is well known that the discrete Fourier transform is asymptotically uncorrelated at the canonical frequencies if and if only the time series is second order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a type of noncentral chi-square, where the Noncentrality Parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power. Some real examples are also included to illustrate the test. Kew words and phrases Discrete Fourier Transform, local stationarity, Portmanteau test, test for second order stationarity.
Sándor Kemény - One of the best experts on this subject based on the ideXlab platform.
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on the computation of the noncentral f and noncentral beta distribution
Statistics and Computing, 2008Co-Authors: Ali Baharev, Sándor KeményAbstract:Unfortunately many of the numerous algorithms for computing the comulative distribution function (cdf) and Noncentrality Parameter of the noncentral F and beta distributions can produce completely incorrect results as demonstrated in the paper by examples. Existing algorithms are scrutinized and those parts that involve numerical difficulties are identified. As a result, a pseudo code is presented in which all the known numerical problems are resolved. This pseudo code can be easily implemented in programming language C or FORTRAN without understanding the complicated mathematical background. Symbolic evaluation of a finite and closed formula is proposed to compute exact cdf values. This approach makes it possible to check quickly and reliably the values returned by professional statistical packages over an extraordinarily wide Parameter range without any programming knowledge. This research was motivated by the fact that a very useful table for calculating the size of detectable effects for ANOVA tables contains suspect values in the region of large Noncentrality Parameter values compared to the values obtained by Patnaik's 2-moment central-F approximation. The cause is identified and the corrected form of the table for ANOVA purposes is given. The accuracy of the approximations to the noncentral-F distribution is also discussed.
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On the computation of the noncentral F and noncentral beta distribution
2008Co-Authors: Ali Baharev, Sándor KeményAbstract:Unfortunately many of the numerous algorithms for computing the comulative distribution function (cdf) and Noncentrality Parameter of the noncentral F and beta distributions can produce completely incorrect results as demonstrated in the paper by examples. Existing algorithms are scrutinized and those parts that involve numerical difficulties are identified. As a result, a pseudo code is presented in which all the known numerical problems are resolved. This pseudo code can be easily implemented in programming language C or FORTRAN without understanding the complicated mathematical background. \ud Symbolic evaluation of a finite and closed formula is proposed to compute exact cdf values. This approach makes it possible to check quickly and reliably the values returned by professional statistical packages over an extraordinarily wide Parameter range without any programming knowledge. \ud This research was motivated by the fact that a very useful table for calculating the size of detectable effects for ANOVA tables contains suspect values in the region of large Noncentrality Parameter values compared to the values obtained by Patnaik’s 2-moment central-F approximation. The cause is identified and the corrected form of the table for ANOVA purposes is given. The accuracy of the approximations to the noncentral-F distribution is also discussed. \ud \ud Keywords Minimal detectable differences - ANOVA - Noncentrality Parameter - Central-F approximations to noncentral F - Recursive algorithms - Symbolic computatio
Ali Baharev - One of the best experts on this subject based on the ideXlab platform.
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on the computation of the noncentral f and noncentral beta distribution
Statistics and Computing, 2008Co-Authors: Ali Baharev, Sándor KeményAbstract:Unfortunately many of the numerous algorithms for computing the comulative distribution function (cdf) and Noncentrality Parameter of the noncentral F and beta distributions can produce completely incorrect results as demonstrated in the paper by examples. Existing algorithms are scrutinized and those parts that involve numerical difficulties are identified. As a result, a pseudo code is presented in which all the known numerical problems are resolved. This pseudo code can be easily implemented in programming language C or FORTRAN without understanding the complicated mathematical background. Symbolic evaluation of a finite and closed formula is proposed to compute exact cdf values. This approach makes it possible to check quickly and reliably the values returned by professional statistical packages over an extraordinarily wide Parameter range without any programming knowledge. This research was motivated by the fact that a very useful table for calculating the size of detectable effects for ANOVA tables contains suspect values in the region of large Noncentrality Parameter values compared to the values obtained by Patnaik's 2-moment central-F approximation. The cause is identified and the corrected form of the table for ANOVA purposes is given. The accuracy of the approximations to the noncentral-F distribution is also discussed.
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On the computation of the noncentral F and noncentral beta distribution
2008Co-Authors: Ali Baharev, Sándor KeményAbstract:Unfortunately many of the numerous algorithms for computing the comulative distribution function (cdf) and Noncentrality Parameter of the noncentral F and beta distributions can produce completely incorrect results as demonstrated in the paper by examples. Existing algorithms are scrutinized and those parts that involve numerical difficulties are identified. As a result, a pseudo code is presented in which all the known numerical problems are resolved. This pseudo code can be easily implemented in programming language C or FORTRAN without understanding the complicated mathematical background. \ud Symbolic evaluation of a finite and closed formula is proposed to compute exact cdf values. This approach makes it possible to check quickly and reliably the values returned by professional statistical packages over an extraordinarily wide Parameter range without any programming knowledge. \ud This research was motivated by the fact that a very useful table for calculating the size of detectable effects for ANOVA tables contains suspect values in the region of large Noncentrality Parameter values compared to the values obtained by Patnaik’s 2-moment central-F approximation. The cause is identified and the corrected form of the table for ANOVA purposes is given. The accuracy of the approximations to the noncentral-F distribution is also discussed. \ud \ud Keywords Minimal detectable differences - ANOVA - Noncentrality Parameter - Central-F approximations to noncentral F - Recursive algorithms - Symbolic computatio
