A Test for Normality Based on Kullback—Leibler Information

Arizono, Ikuo; Ohta, Hiroshi

doi:10.1080/00031305.1989.10475600

Cited by 44 publications

(32 citation statements)

References 4 publications

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“…We apply the proposed approach to construct a powerful two-sample nonparametric likelihood ratio test based on samples entropy. Despite the fact that many statistical inference procedures have been developed to construct very efficient entropy-based tests for goodness-of-fit (e.g., Arizono and Ohta 1989;Dudewicz and Van Der Meulen 1981;Tian 2002, 2004;Tusnady 1977;Vasicek 1976;Vexler and Gurevich 2010;Zhang 2002), to our knowledge, there does not exist an inference procedure for two-sample empirical likelihood ratio comparisons based on samples entropy.…”

Section: Introductionmentioning

confidence: 92%

A two-sample empirical likelihood ratio test based on samples entropy

Gurevich

Vexler

2010

Stat Comput

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Powerful entropy-based tests for normality, uniformity and exponentiality have been well addressed in the statistical literature. The density-based empirical likelihood approach improves the performance of these tests for goodness-of-fit, forming them into approximate likelihood ratios. This method is extended to develop two-sample empirical likelihood approximations to optimal parametric likelihood ratios, resulting in an efficient test based on samples entropy. The proposed and examined distribution-free twosample test is shown to be very competitive with well-known nonparametric tests. For example, the new test has high and stable power detecting a nonconstant shift in the two-sample problem, when Wilcoxon's test may break down completely. This is partly due to the inherent structure developed within Neyman-Pearson type lemmas. The outputs of an extensive Monte Carlo analysis and real data example support our theoretical results. The Monte Carlo simulation study indicates that the proposed test compares favorably with the standard procedures, for a wide range of null and alternative distributions.

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Section: Introductionmentioning

confidence: 92%

A two-sample empirical likelihood ratio test based on samples entropy

Gurevich

Vexler

2010

Stat Comput

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“…There is no standard procedure for testing uniformity on a group, but there are many competing tests for the Gaussian distribution. In [9], [10] and [11] it has been shown by simulations that tests based on estimation entropy are more powerful than many other test for normality that one can find in the literature. The author has done some simulation to compare these tests with the test proposed here.…”

Section: Discussionmentioning

confidence: 99%

Testing goodness-of-fit via rate distortion

Harremoës

2009

2009 IEEE Information Theory Workshop on Networking and Information Theory

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Abstract-A framework is developed using techniques from rate distortion theory in statistical testing. The idea is first to do optimal compression according to a certain distortion function and then use information divergence from the compressed empirical distribution to the compressed null hypothesis as statistic. Only very special cases have been studied in more detail, but they indicate that the approach can be used under very general conditions.

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“…In [36] Monte-Carlo simulations are presented to demonstrate the superiority of the KL compared to other statistical methods to test gaussianity. The KL divergence formula is…”

Section: Test Of Gaussianitymentioning

confidence: 99%

On discrete-time modeling of the filtered and symbol-rate sampled continuous-time signal affected by Wiener phase noise

Mandelli

Magarini

Spalvieri

et al. 2015

Optical Switching and Networking

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This paper investigates the differences between the symbol-spaced discrete-time Wiener phase noise channel model, commonly assumed in the literature to represent the effect of phase noise, and that obtained by symbol-rate sampling the filtered continuous-time received signal affected by continuous-time Wiener phase-noise. In particular, for comparison, we consider some statistical tests to check temporal and distributional properties of the two models. We show that the fit between the two models is very good even for quite strong values of phase noise. The main result is that when the standard deviation of the discrete-time Wiener phase noise increment σ P N is below a threshold of approximatelyσ P N ≃ 0.1 rad, the discrete-time Wiener model provides a good approximation to the actual symbol-spaced sampled filtered signal affected by continuous-time Wiener phase noise. We show that when σ P N is below σ P N the ratio between the power of the signal and the power of the model mismatch is greater than 20 dB. Simulation results are also presented to compare bit error rates of the two models in case of QPSK and 16-QAM transmission and to compare the power spectral densities of their associated complex exponential phase noises. Our results suggest that the discrete-time Wiener phase noise model can be adopted for many real-world systems, where, according to experimental results available in the literature, σ P N in the order of 0.1 rad is rarely found even when the nonlinearity of the optical channel is deeply stressed.

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A Test for Normality Based on Kullback—Leibler Information

Cited by 44 publications

References 4 publications

A two-sample empirical likelihood ratio test based on samples entropy

A two-sample empirical likelihood ratio test based on samples entropy

Testing goodness-of-fit via rate distortion

On discrete-time modeling of the filtered and symbol-rate sampled continuous-time signal affected by Wiener phase noise

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