Testing statistical hypotheses based on the density power divergence

Basu, Ayanendranath; Mandal, Abhijit; Martín, Nirian; Pardo, Leonardo

doi:10.1007/s10463-012-0372-y

Cited by 43 publications

(49 citation statements)

References 17 publications

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“…Noting the similarity of the above asymptotic null distribution with the case of testing simple null hypothesis, we can find critical values of the proposed SDT following Remark 3 of Basu et al (2013a). We can also derive an asymptotic power approximation at any point θ * / ∈ Θ 0 ; if θ * / ∈ Θ 0 is the true parameter value then θ β…”

Section: S-divergence Based Test (Sdt) For Composite Hypothesismentioning

confidence: 85%

“…So, there have been many attempts for developing robust alternative to the likelihood ratio test (LRT) with good asymptotic and robustness properties. Ghosh et al (2015) proposed a general family of tests of hypothesis for the simple null problem; these tests are based on the family of S-divergences (Ghosh et al, 2013a), and extend the idea of Basu et al (2013a) who considered testing of hypothesis based on the density power divergence (Basu et al, 1998). In the present paper we provide a non-trivial generalization of the Ghosh et al (2015) paper, and the theoretical robustness properties described in this work also provide the theoretical underpinnings of the Basu et al (2013b) tests as a special case.…”

Section: Introductionmentioning

confidence: 99%

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Testing composite null hypotheses based onS-divergences

Ghosh

Basu

2016

Statistics & Probability Letters

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We present a robust test for composite null hypothesis based on the general Sdivergence family. This requires a non-trivial extension of the results of Ghosh et al. (2015). We derive the asymptotic and theoretical robustness properties of the resulting test along with the properties of the minimum S-divergence estimators under parameter restrictions imposed by the null hypothesis. An illustration in the context of the normal model is also presented.

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Section: S-divergence Based Test (Sdt) For Composite Hypothesismentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Testing composite null hypotheses based onS-divergences

Ghosh

Basu

2016

Statistics & Probability Letters

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“…That is, the bias-corrected Lq-likelihood function is to the density power divergence as the log-likelihood function is to the Kullback-Leibler distance. While we are revising our paper, we became aware of another test proposed by Basu et al (2013 3 Lq-LIKELIHOOD-RATIO-TYPE TEST…”

Section: Consistency and Bias Correctionmentioning

confidence: 99%

Robust Hypothesis Testing via Lq-Likelihood

Qin¹,

Priebe²

2018

STAT SINICA

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This article introduces a robust hypothesis testing procedure: the Lq-likelihoodratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and numerically, and they investigate the properties of both its influence function and its breakdown point. A proposed method to select the tuning parameter q offers a good efficiency/robustness trade-off, compared with the traditional likelihood ratio test (LRT) and other robust tests. A simulation and real data analysis provides further evidence of the advantages of the proposed LqRT method. In particular, for the special case of testing the location parameter in the presence of gross error contamination, the LqRT dominates the Wilcoxon-Mann-Whitney test and the sign test at various levels of contamination.

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“…samples. Many density-based minimum distance procedures have been observed to have strong properties in estimation and testing together with high efficiency, e.g., Basu et al (2011). The MDPDE has an advantage of not requiring smoothing methods and therefore one can avoid drawbacks and difficulties such as the selection of the bandwidth, that necessarily follows from the kernel smoothing method.…”

mentioning

confidence: 99%

“…This Wald-type statistic constructed through estimators based on MDPDE not only constitutes a robust test against outliers, but also keeps the same efficiency as the MLE-based CUSUM test when there are no outliers. Recently, in Basu et al (2013), new test statistics were proposed for some parametric hypothesis, based on density power divergences not only for estimation but also for constructing the test statistic. Since these test statistics exhibited strong robustness properties together with high efficiency, we think it might be interesting to explore them for change-point problems creating a link with the Wald-type test proposed by Lee and Na (2005).…”

mentioning

confidence: 99%

Comments on: Extensions of some classical methods in change point analysis

Martín

Pardo

2014

TEST

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Professor Horváth co-authored in 1997 the book entitled "Limit theorems in changepoint analysis". It can be seen as a milestone in the history of this topic that has a history of over 50 years. This review paper is very interesting, timely, highly informative and provides a comprehensive summary of the recent research on change-point analysis. This research has deserved considerable attention during the last years and is expected to develop new results in the near future. Professors Horváth and Rice are to be congratulated for this succinct and insightful presentation of the state-of-art of the change-point methodology. The review not only considers the most frequently used classical methods and ideas in change-point analysis but also some new methodology developed in the last years in relation to time series, multivariate, panel data and functional data. The applications of several classical results to real data sets permit us a better understanding as well as showing the importance and scope of this theory that was originated in the 1940s but is currently an active area of research. It is an almost an impossible task to review the very extensive literature on change-point analysis in a single paper. Nevertheless, the paper contains a very rich collection of the contributions not only from the classical results but also from the most recent papers in change-point analysis. We want to thank professors Horváth and Rice for their enormous effort in bringing us all this existing material on a topic of the highest relevance.This comment refers to the invited paper available at

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Testing statistical hypotheses based on the density power divergence

Cited by 43 publications

References 17 publications

Testing composite null hypotheses based onS-divergences

Testing composite null hypotheses based onS-divergences

Robust Hypothesis Testing via Lq-Likelihood

Comments on: Extensions of some classical methods in change point analysis

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