Semiparametric regression models are very useful for longitudinal data analysis. The complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis. In this article, two new approaches are proposed for estimating the regression coefficients in a semiparametric model. The asymptotic normality of the resulting estimators is established. An innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models. The proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters. Rates of convergence of the resulting estimators are established. With a proper choice of regularization parameters and penalty functions, the proposed variable selection procedures

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I would like to congratulate Professor Antoniadis for successfully outlining the current state-of-art of wavelet applications in statistics. Since wavelet techniques were introduced to statistics in the early 90s, the applications of wavelet techniques have mushroomed. There is a vast forest of wavelet theory and techniques in statistics and one can find himself easily lost in the jungle. The review by Antoniadis, ranging from linear wavelets to nonlinear wavelets, addressing both theoretical issues and practical relevance, gives in-depth coverage of the wavelet applications in statistics and guides one entering easily into the realm of wavelets.

In this paper, we propose a penalised pseudo-partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients. Under certain regularity conditions, we show the consistency and asymptotic normality of the penalised likelihood estimators. We further demonstrate that, for certain penalty functions with proper choices of regularisation parameters, the resulting estimator can correctly identify the true model, as if it were known in advance. Based on a simple approximation of the penalty function, the proposed method can be easily carried out with the NewtonRaphson algorithm. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed procedures. We illustrate the proposed method by analysing a dataset from the Framingham Heart Study.

Consider a linear model Y= X + z, where X= X n, p and z~ N (0, I n). The vector is unknown and it is of interest to separate its nonzero coordinates from the zero ones (ie, variable selection). Motivated by examples in long-memory time series (Fan and Yao, 2003) and the change-point problem (Bhattacharya, 1994), we are primarily interested in the case where the Gram matrix G= X X is non-sparse but sparsifiable by a finite order linear filter. We focus on the regime where signals are both rare and weak so that successful variable selection is very challenging but is still possible.