Shrinkage and Penalty Estimators of a Poisson Regression Model

Hossain, Shakhawat; Ahmed, Ejaz

doi:10.1111/j.1467-842x.2012.00679.x

Cited by 21 publications

(14 citation statements)

References 20 publications

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“…See, for example, Refs 3,4, and 6 for models with non‐normal and random coefficient autoregressive errors, respectively. Shrinkage and penalty estimation have been studied in a Poisson regression model, see Ref 7.…”

Section: Review Of Literaturementioning

confidence: 99%

Shrinkage and absolute penalty estimation in linear regression models

Ahmed

Raheem

2012

WIREs Computational Stats

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In predicting a response variable using multiple linear regression model, several candidate models may be available which are subsets of the full model. Shrinkage estimators borrow information from the full model and provides a hybrid estimate of the regression parameters by shrinking the full model estimates toward the candidate submodel. The process introduces bias in the estimation but reduces the overall prediction error that offsets the bias. In this article, we give an overview of shrinkage estimators and their asymptotic properties. A real data example is given and a Monte Carlo simulation study is carried out to evaluate the performance of shrinkage estimators compared to the absolute penalty estimators such as least absolute shrinkage and selection operator (LASSO), adaptive LASSO and smoothly clipped absolute deviation (SCAD) based on prediction errors criterion in a multiple linear regression setup.

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Section: Review Of Literaturementioning

confidence: 99%

Shrinkage and absolute penalty estimation in linear regression models

Ahmed

Raheem

2012

WIREs Computational Stats

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“…Interpretation of the model-scientists prefer a simpler model because it explains more light on the relationship between response and covariates. Parsimony is especially an important issue when the number of predictors is large [2].…”

Section: Introductionmentioning

confidence: 99%

Penalized Poisson Regression Model Using Elastic Net and Least Absolute Shrinkage and Selection Operator (Lasso) Penality

Mwikali¹,

Mwalili²,

Wanjoya³

2019

IJDSA

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Variable selection in count data using Penalized Poisson regression is one of the challenges in applying Poisson regression model when the explanatory variables are correlated. To tackle both estimate the coefficients and perform variable selection simultaneously, Lasso penalty was successfully applied in Poisson regression. However, Lasso has two major limitations. In the p > n case, the lasso selects at most n variables before it saturates, because of the nature of the convex optimization problem. This seems to be a limiting feature for a variable selection method. Moreover, the lasso is not welldefined unless the bound on the L1-norm of the coefficients is smaller than a certain value. If there were a group of variables among which the pairwise correlations are very high, then the lasso tends to select only one variable from the group and does not care which one is selected. To address these issues, we propose the elastic net method between explanatory variables and to provide the consistency of the variable selection simultaneously. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in the model together.

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“…homogeneity and independence) which are rarely satisfied by real data. For variable selection, Hossain and Ahmed [17] studied the performance of Lasso, adaptive Lasso and SCAD penalties in Poisson regression model for both low and high dimensional data. Since these are non-robust procedures, therefore, there is still the need of further studies on the implementation of penalized techniques for modeling count data.…”

Section: Introductionmentioning

confidence: 99%

Variable Selection via SCAD-Penalized Quantile Regression for High-Dimensional Count Data

et al. 2019

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This article introduces a quantile penalized regression technique for variable selection and estimation of conditional quantiles of counts in sparse high-dimensional models. The direct estimation and variable selection of the quantile regression is not feasible due to the discreteness of the count data and nondifferentiability of the objective function, therefore, some smoothness must be artificially imposed on the problem. To achieve the necessary smoothness, we use the Jittering process by adding a uniformly distributed noise to the response count variable. The proposed method is compared with the existing penalized regression methods in terms of prediction accuracy and variable selection. We compare the proposed approach in zeroinflated count data regression models and in the presence of outliers. The performance and implementation of the proposed method are illustrated by detailed simulation studies and real data applications. INDEX TERMS Count data, high dimensional, jittering, quantile regression, variable selection, zeroinflated.

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Shrinkage and Penalty Estimators of a Poisson Regression Model

Cited by 21 publications

References 20 publications

Shrinkage and absolute penalty estimation in linear regression models

Shrinkage and absolute penalty estimation in linear regression models

Penalized Poisson Regression Model Using Elastic Net and Least Absolute Shrinkage and Selection Operator (Lasso) Penality

Variable Selection via SCAD-Penalized Quantile Regression for High-Dimensional Count Data

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