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Abstract: In this paper, we develop a new variable selection procedure for quantile varying coefficient models with longitudinal data. The proposed method is based on basis function approximation and a class of group versions of the adaptive LASSO penalty, which penalizes the norm of the within-group coefficients with . We show that with properly chosen adaptive group weights in the penalization, the resulting penalized estimators are consistent in variable selection, and the estimated functional coefficients retain the optimal convergence rate of nonparametric estimators under the true model. We assess the finite sample performance of the proposed procedure by an extensive simulation study, and the analysis of an AIDS data set and a yeast cell-cycle gene expression data set. [Copyright &y& Elsevier]

Like human beings, many animals produce sounds for communication and social interactions. The vocalizations of mice have the characteristics of songs, consisting of syllables of different types determined by the frequency modulations and structure variations. To characterize the impact of social environments and genotypes on vocalizations, it is important to identify the patterns of syllables based on the shapes of frequency contours. Using existing hypothesis testing methods to determine the shape classes would require testing various null and alternative hypotheses for each curve, and is impractical for vocalization studies where the interest is on a large number of frequency contours. A new penalization-based method is proposed, which provides function estimation and automatic shape identification simultaneously. The method estimates the functional curve through quadratic B-spline approximation, and captures the shape feature by penalizing the positive and negative parts of the first two derivatives of the spline function in a group manner. It is shown that under some regularity conditions, the proposed method can identify the correct shape with probability approaching one, and the resulting nonparametric estimator can achieve the optimal convergence rate. Simulation shows that the proposed method gives more stable curve estimation and more accurate curve classification than the unconstrained B-spline estimator, and it is competitive to the shape-constrained estimator assuming prior knowledge of the curve shape. The proposed method is applied to the motivating vocalization study to examine the effect of Methyl-CpG binding protein 2 gene on the vocalizations of mice during courtship. [ABSTRACT FROM AUTHOR]

A weighted approach is developed to improve estimation efficiency in varying-coefficient quantile regression model, with longitudinal data. The weights are obtained from empirical likelihood of varying-coefficient mean model, where the nonparametric functions are approximated by basis splines, and the matrix expansion idea in quadratic inference function method is used, to model the inverse of conditional correlation matrix within subject. Theoretical results show that, the weighted estimators of the varying coefficients in quantile regression, can achieve higher efficiency than conventional estimators without weighting scheme. Simulation studies are used to assess the finite sample performance and a real data analysis is also conducted. [ABSTRACT FROM AUTHOR]