A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator

Basu, Ayanendranath; Ghosh, Abhik; Mandal, Abhijit; Martín, Nirian; Pardo, Leandro

doi:10.1214/17-ejs1295

Cited by 49 publications

(38 citation statements)

References 34 publications

(47 reference statements)

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“…where β λ is the asymptotic mean of β λ and β * is the true target parameter value. As pointed out by Basu et. al (2017a), the estimation of the variance component should not assume the model to be true for a better robustness trade-off.…”

Section: On the Choice Of Tuning Parameter λmentioning

confidence: 72%

“…As noted in Section , the robustness of the Wald‐type test directly depends on that of the MDPDE used. A useful procedure of the data‐based selection of

λ

for the MDPDE was proposed by Warwick and Jones () under IID data, which is recently extended for the non‐homogeneous data by Ghosh and Basu (, , ) and Basu et al (). We can adopt a similar approach to obtain a suitable data‐driven

λ

in our PLRM.…”

Section: On the Choice Of Tuning Parameter λmentioning

confidence: 99%

“…As pointed out by Basu et. al (), the estimation of the variance component should not assume the model to be true for a better robustness trade‐off. So, following the general formulation of Ghosh and Basu (), model robust estimates of

{boldV}_{λ}

and

{boldJ}_{λ}

can be obtained as

{\overset{trueˆ}{V}}_{N, λ} = {boldΩ}_{N, λ} false({\overset{trueˆ}{β}}_{λ} false)

and

\begin{matrix} right {\overset{boldJ}{true}}_{N, λ} & center = & left (λ + 1) Ψ_{N, λ} ({\overset{boldβ}{true}}_{λ}) \\ right & center & left + \frac{1}{N} \sum_{i = 1}^{N} Δ ((), π_{i}^{*} false({\overset{trueˆ}{boldβ}}_{λ} false)) ({}, \sum_{j = 1}^{d + 1} π_{ij} false({\overset{trueˆ}{β}}_{λ} {false)}^{λ + 1}) \otimes x_{i} x_{i}^{T} \\ right & center & left - \frac{1}{N} \sum_{i = 1}^{N} ({, λ {boldu}_{i} false({boldy}_{i}^{*}, {\overset{trueˆ}{β}}_{λ} false) {boldu}_{i} {false({boldy}_{i}^{*}, {\overset{trueˆ}{β}}_{λ} false)}^{T}) \\ right & center & left (}, + Δ (π_{i}^{*} ({\overset{boldβ}{true}}_{λ})) \otimes {boldx}_{i} {boldx}_{i}^{T<...>}) \end{matrix}

…”

Section: On the Choice Of Tuning Parameter λmentioning

confidence: 99%

“…In this article, we present an alternative simple robust generalization of the MLE for the general PLRM by using the density power divergence (DPD) measure of Basu et al (1998). The DPD based inference has become very popular in recent time specially because of its strong robustness properties against outliers; see, for example, Basu et al (, , ), Ghosh et al (), among others. In this article, we first develop the estimator of

boldβ

in the PLRM by minimizing a suitably defined DPD measure and derive its asymptotic distribution in Section .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New Robust Statistical Procedures for the Polytomous Logistic Regression Models

et al. 2018

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This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data-driven selection of the robustness tuning parameter is proposed with empirical justifications.

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Section: On the Choice Of Tuning Parameter λmentioning

confidence: 72%

“…As noted in Section , the robustness of the Wald‐type test directly depends on that of the MDPDE used. A useful procedure of the data‐based selection of

λ

λ

in our PLRM.…”

Section: On the Choice Of Tuning Parameter λmentioning

confidence: 99%

{boldV}_{λ}

and

{boldJ}_{λ}

can be obtained as

{\overset{trueˆ}{V}}_{N, λ} = {boldΩ}_{N, λ} false({\overset{trueˆ}{β}}_{λ} false)

and

\begin{matrix} right {\overset{boldJ}{true}}_{N, λ} & center = & left (λ + 1) Ψ_{N, λ} ({\overset{boldβ}{true}}_{λ}) \\ right & center & left + \frac{1}{N} \sum_{i = 1}^{N} Δ ((), π_{i}^{*} false({\overset{trueˆ}{boldβ}}_{λ} false)) ({}, \sum_{j = 1}^{d + 1} π_{ij} false({\overset{trueˆ}{β}}_{λ} {false)}^{λ + 1}) \otimes x_{i} x_{i}^{T} \\ right & center & left - \frac{1}{N} \sum_{i = 1}^{N} ({, λ {boldu}_{i} false({boldy}_{i}^{*}, {\overset{trueˆ}{β}}_{λ} false) {boldu}_{i} {false({boldy}_{i}^{*}, {\overset{trueˆ}{β}}_{λ} false)}^{T}) \\ right & center & left (}, + Δ (π_{i}^{*} ({\overset{boldβ}{true}}_{λ})) \otimes {boldx}_{i} {boldx}_{i}^{T<...>}) \end{matrix}

…”

Section: On the Choice Of Tuning Parameter λmentioning

confidence: 99%

boldβ

in the PLRM by minimizing a suitably defined DPD measure and derive its asymptotic distribution in Section .…”

Section: Introductionmentioning

confidence: 99%

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New Robust Statistical Procedures for the Polytomous Logistic Regression Models

et al. 2018

Self Cite

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show abstract

“…In particular, density power divergence measures introduced in [ 1 ] have given good robust estimators: minimum density power divergences estimators (MDPDE) and, based on them, some robust test statistics have been considered for testing simple and composite null hypotheses. Some of these tests are based on divergence measures (see [ 2 , 3 ]), and some others are used to extend the classical Wald test; see [ 4 , 5 , 6 ] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Composite Likelihood Methods Based on Minimum Density Power Divergence Estimator

Castilla

Martín

Zografos

2017

Entropy

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Abstract:In this paper, a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered, and the robustness is studied on the basis of a simulation study. The composite minimum density power divergence estimator is also introduced, and its asymptotic properties are studied.

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Exact likelihood ratio and Wald tests for the balanced joint progressive censoring scheme

Mondal

Kundu

2022

Appl Stoch Models Bus & Ind

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Recently, the balanced joint progressive censoring (BJPC) for two samples has been introduced by the authors. This work comprises of developing testing of hypothesis for the BJPC scheme. An exact likelihood ratio test is developed to test the ratio of mean life times of two different products through joint life testing experiment. Along with this development, the Wald test has also been discussed, and an approximate power function has been used for power computation. Along with the study of testing of hypothesis, the optimal censoring scheme based on the power of the proposed tests has been determined. Meta heuristic variable neighborhood algorithm is exploited in this optimization task.

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A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator

Cited by 49 publications

References 34 publications

New Robust Statistical Procedures for the Polytomous Logistic Regression Models

New Robust Statistical Procedures for the Polytomous Logistic Regression Models

Composite Likelihood Methods Based on Minimum Density Power Divergence Estimator

Exact likelihood ratio and Wald tests for the balanced joint progressive censoring scheme

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