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Abstract:
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We focus on the problem of simultaneous variable selection and estimation in the heteroscedastic linear regression model. Doubly penalized likelihood methods which place penalties on both the mean and variance parameters have been proposed recently in the literature (Daye et al., 2012; Kolar and Sharpnack, 2012). We propose a new methodology, the adaptive penalized likelihood effects selection (APLES), which uses the adaptive LASSO penalty for both the mean and variance submodels. We utilize the cyclic coordinate descent algorithm for implementation of APLES. We prove oracle properties for the APLES estimator and demonstrate by simulation that it compares favorably with existing methods. Our procedure is applicable to data sets arising from many scientific disciplines such as biology, econometrics and industrial engineering which typically exhibit heteroscedasticity. Our method demonstrates the presence of heteroscedasticity in the diabetes data set from Efron et al. (2004).
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