Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data

Pardo, J. A.; Pardo, M. C.

doi:10.1007/s11009-007-9054-2

Cited by 14 publications

(13 citation statements)

References 19 publications

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“…This is not a surprise as this choice of λ is supported by simulation studies in [6,20,21,25]. Downloaded by [Selcuk Universitesi] at 00:57 03 February 2015 Table 3 gives frequency of zero estimates of zero coefficients in the above example based on 500 repetitions.…”

Section: Selection Of λmentioning

confidence: 77%

“…Minimum φ-divergence estimator [20] in logistic regression emerged as an attractive alternative to maximum likelihood estimator (MLE) when sample size is small. Based on this fact, Pardo and Pardo [21] introduced a method for variable selection using φ-divergence statistic. This method is a two-stage method which requires fitting and testing of several models to arrive at the best sub model.…”

Section: Introductionmentioning

confidence: 99%

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Variable selection via penalized minimum φ-divergence estimation in logistic regression

Sakate

Kashid

2013

Journal of Applied Statistics

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We propose penalized minimum φ-divergence estimator for parameter estimation and variable selection in logistic regression. Using an appropriate penalty function, we show that penalized φ-divergence estimator has oracle property. With probability tending to 1, penalized φ-divergence estimator identifies the true model and estimates nonzero coefficients as efficiently as if the sparsity of the true model was known in advance. The advantage of penalized φ-divergence estimator is that it produces estimates of nonzero parameters efficiently than penalized maximum likelihood estimator when sample size is small and is equivalent to it for large one. Numerical simulations confirm our findings.

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Section: Selection Of λmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Variable selection via penalized minimum φ-divergence estimation in logistic regression

Sakate

Kashid

2013

Journal of Applied Statistics

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“…171) used by Pardo and Pardo (2008) to illustrate the variable selection method based on minimum ϕ-divergence estimator. The data consists of observations on 6 objective indicators (X 1 , …, X 6 ) of the actual indoor climate in 10 classrooms of a Danish Institute, the number of students in the class and the number of yes-answers to the question whether they felt that the indoor climate at the moment was pleasant or not so pleasant.…”

Section: Example 3: Multiple Predictors Casementioning

confidence: 99%

“…Other distance estimators like minimum chi-square estimator (λ = 1) and minimum Hellinger distance estimator (λ = −1/2) are particular cases as well. An extensive simulation study in Pardo et al (2005) and Pardo and Pardo (2008) to choose among the estimators in logistic regression concluded that 2/3 is a good choice for λ. Hence, minimum ϕ-divergence estimator with λ = 2/3 emerged as an alternative to MLE in the sense of MSE for small size.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Estimators in GLM with Binary Data

Sakate

Kashid

2014

J. Mod. App. Stat. Meth.

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Maximum likelihood estimates (MLE) of regression parameters in the generalized linear models (GLM) are biased and their bias is non negligible when sample size is small. This study focuses on the GLM with binary data with multiple observations on response for each predictor value when sample size is small. The performance of the estimation methods in Cordeiro and McCullagh (1991), Firth (1993) and Pardo et al. (2005) are compared for GLM with binary data using an extensive Monte Carlo simulation study. Performance of these methods for three real data sets is also compared.

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“…where λ was defined in (12). From (13), the asymptotic quadratic bias for the different estimators considered in this paper is given by…”

Section: Proof a Second Taylor Expansion Givesmentioning

confidence: 99%

Preliminary test estimators and phi-divergence measures in generalized linear models with binary data

Menéndez¹,

Pardo²,

Pardo³

2008

Journal of Multivariate Analysis

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We consider the problem of estimation of the parameters in Generalized Linear Models (GLM) with binary data when it is suspected that the parameter vector obeys some exact linear restrictions which are linearly independent with some degree of uncertainty. Based on minimum φ-divergence estimation (Mφ E), we consider some estimators for the parameters of the GLM: Unrestricted Mφ E, restricted Mφ E, Preliminary Mφ E, Shrinkage Mφ E, Shrinkage preliminary Mφ E, James-Stein Mφ E, Positive-part of Stein-Rule Mφ E and Modified preliminary Mφ E. Asymptotic bias as well as risk with a quadratic loss function are studied under contiguous alternative hypotheses. Some discussion about dominance among the estimators studied is presented. Finally, a simulation study is carried out.

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Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data

Cited by 14 publications

References 19 publications

Variable selection via penalized minimum φ-divergence estimation in logistic regression

Variable selection via penalized minimum φ-divergence estimation in logistic regression

Comparison of Estimators in GLM with Binary Data

Preliminary test estimators and phi-divergence measures in generalized linear models with binary data

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