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On power chi expansions of f-divergences [article]

Frank Nielsen, Gaëtan Hadjeres
2019 arXiv   pre-print
We consider both finite and infinite power chi expansions of f-divergences derived from Taylor's expansions of smooth generators, and elaborate on cases where these expansions yield closed-form formula  ...  , bounded approximations, or analytic divergence series expressions of f-divergences.  ...  On the other hand, we can express the f -divergences using power chi expansions [20] yielding to power chi series when these expansions converge.  ... 
arXiv:1903.05818v1 fatcat:skkriahcmjdkvov4prur3heugi

On the chi square and higher-order chi distances for approximating f-divergences

Frank Nielsen, Richard Nock
2014 IEEE Signal Processing Letters  
We then describe an analytic formula for the f-divergences based on Taylor expansions and relying on an extended class of Chi-type distances.  ...  We report closed-form formula for calculating the Chi square and higher-order Chi distances between statistical distributions belonging to the same exponential family with affine natural space, and instantiate  ...  When bounded, the f -divergence I f can be expressed as the power series of higher order Chi-type distances: I f (X 1 : X 2 ) = x 1 (x) ∞ i =0 1 i !  ... 
doi:10.1109/lsp.2013.2288355 fatcat:mu7upctpqzhfpnqxywr2s57dhu

Effective Truncation of a Student's t-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture

Daniel T. Cassidy
2012 Open Journal of Statistics  
of a left-truncated chi and a normal distribution are given for selected degrees of freedom .  ...  The effect of truncation of the chi distribution in a chi-normal mixture is investigated and expressions for the pdf, the variance, and the kurtosis of the t-like distribution that arises from the mixture  ...  The results show the origins of the slowly decaying power tails of Student's t-distributions and suggest an approach to deal with the divergence of moments and integrals based on the t-distribution.  ... 
doi:10.4236/ojs.2012.25067 fatcat:rmht3m33o5h5xh5e6fmk64maye

Improved Lagrange multiplier tests in spatial autoregressions

Peter M. Robinson, Francesca Rossi
2014 Econometrics Journal  
We develop refined tests for lack of spatial error correlation in regressions, based on Edgeworth expansion.  ...  In Monte Carlo simulations, these tests, and bootstrap tests, generally significantly outperform χ 2 -based tests. where y = (y i ) is an n × 1 vector of observations, X = (x ij ) is an n × k matrix of  ...  The research of P. M. Robinson was supported by ESRC Grant ES/J007242/1.  ... 
doi:10.1111/ectj.12025 fatcat:c7gxuq2snnbz3ls4q7gpafzln4

Page 484 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
The results obtained are applied to the asymptotic expansion of f- and F-distributions. The results provide refinements of previous work on uniform error bounds. Adnan M.  ...  Chapter 4 deals with testing the models using the power-divergence statistic.  ... 

On the robustness of a divergence based test of simple statistical hypotheses

Abhik Ghosh, Ayanendranath Basu, Leandro Pardo
2015 Journal of Statistical Planning and Inference  
Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density power divergence; however, although the robustness properties of the latter test were intuitively  ...  This superfamily derives from the class of S-divergences recently proposed by Basu et al. (2013a).  ...  The authors also gratefully acknowledge the comments of a referee which led to an improved version of the manuscript.  ... 
doi:10.1016/j.jspi.2015.01.003 fatcat:l5biuszqf5e7nfwgpkakzrq3j4

Improved transformation of ϕ-divergence goodness-of-fit test statistics based on minimum ϕ*-divergence estimator for GLIM of binary data

Nobuhiro Taneichi, Yuri Sekiya, Jun Toyama
2016 SLUT journal of mathematics  
The family of statistics C ϕϕ * includes a power divergence family of statistics R a,b that is based on a minimum power divergence estimator.  ...  For testing the null hypothesis that the considered model is correct, the ϕ-divergence family of goodness-offit test statistics C ϕϕ * that is based on a minimum ϕ * -divergence estimator is considered  ...  Acknowledgments This research is partially supported by the Grants-in-aid for Scientific Research of Japan Society for the Promotion of Science (C) 24540133.  ... 
doi:10.55937/sut/1483720971 fatcat:ows65ri6xzdvtleyl3hydrf4fe

Improved Approximations for the Distributions of Multinomial Goodness-of-fit Statistics Based on ^|^phi;-divergence under Nonlocal Alternatives

Pan Ei Htwe, Nobuhiro Taneichi, Yuri Sekiya
2012 Journal of the Japan Statistical Society  
By using the expansion, we propose a new approximation for the power of the statistic C φ .  ...  Sekiya and Taneichi (2004) derived the multivariate Edgeworth expansion assuming a continuous distribution for the distributions of power divergence statistics under a nonlocal alternative hypothesis.  ...  on the normalizing transformation of a power divergence statistic.  ... 
doi:10.14490/jjss.41.121 fatcat:jjhrpplgsfhjroijke6ugfy5qu

Page 4047 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
the Kullback-Leibler divergence, the Csiszar f-divergence and the Jef- freys divergence (or J-divergence).  ...  Simulations are used to compare the power of this test with the power of the likelihood ratio test of stochastic ordering of two multinomial populations.” 949:62060 62F30 62F10 Vijayasree, G. (6-PUNJ-S  ... 

Page 4711 of Mathematical Reviews Vol. , Issue 90H [page]

1990 Mathematical Reviews  
The same expansion produces the traditional non- central chi-squared power approximation by considering sequences of alternative distributions for the X; that approach the hypothe- sis F at a suitable  ...  Our power approximations are obtained from a Taylor series expansion that is valid for arbitrary sequences of alternatives.  ... 

On Bartlett correctability of empirical likelihood in generalized power divergence family

Lorenzo Camponovo, Taisuke Otsu
2014 Statistics and Probability Letters  
This paper strengthens Baggerly's result by showing that in a generalized class of the power divergence family, which includes the Cressie-Read family and other nonparametric likelihood such as Schennach's  ...  Baggerly (1998) showed that empirical likelihood is the only member in the Cressie-Read power divergence family to be Bartlett correctable.  ...  We focus on characterizing the third and fourth order joint cumulants of the signed root of the test statistic based on the generalized power divergence family, and show that those cumulants vanish at  ... 
doi:10.1016/j.spl.2013.12.008 fatcat:hzugoecmtrhibc7efwgbo3chom

pcadapt: an R package to perform genome scans for selection based on principal component analysis [article]

Keurcien Luu, Eric Bazin, Michael G.B. Blum
2016 bioRxiv   pre-print
Last, we find that pcadapt and hapflk are the most powerful software in scenarios of population divergence and range expansion.  ...  We also find that the power of BayeScan is severely impacted by the presence of admixed individuals whereas pcadapt is not impacted.  ...  Including admixed indi-294 viduals hardly changes their statistical power (Figure SI3). 295 Then, we compare statistical power in a divergence model where adaptation took place 296 in one of the external  ... 
doi:10.1101/056135 fatcat:zejnwj4xgrhphkxy7isa5zcosi

Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives

Nobuhiro Taneichi, Yuri Sekiya, Akio Suzukawa
2002 Journal of Multivariate Analysis  
B 46, 440-464) introduced a class of multinomial goodness-of-fit statistics R a based on power divergence.  ...  By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation  ...  We consider the multinomial goodness-of-fit tests based on power divergences.  ... 
doi:10.1006/jmva.2001.2002 fatcat:jvk2tgphxjctjp6o2wpvrz7wkq

Page 1159 of Mathematical Reviews Vol. , Issue 89B [page]

1989 Mathematical Reviews  
The corrections are in the form of a double expansion in powers of the volume fraction y and, formally, in powers of the inverse lattice coordination number z~'.  ...  the form of an expansion in powers of the nearest-neighbor interaction en- ergies.” 89b:82077 82A51 Bawendi, M.  ... 

Higher-Order Terms in a Perturbation Expansion for the Impedance of a Corrugated Wave Guide

S. Krinsky, R. L. Gluckstern
1981 IEEE Transactions on Nuclear Science  
Chatard-Moulln and Fapiernllc have introduced a perturbation expansion in powers of c for the longitudinal impedance of such a waveguide* We have reformulated the derivation of this expansion in a manner  ...  For a square-wave (SU) wall distortion, there are divergent coefficients In the perturbation expansion.  ...  Expanding ^ (for n fixed) In powers of c, che coefficients of all Che higher-order terms are divergent.  ... 
doi:10.1109/tns.1981.4331777 fatcat:lxxtdys3dzdatfheogux2hz56u
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