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Ignoring measurement errors in conventional regression analyses can lead to biased estimation and inference results. Reducing such bias is challenging when the error-prone covariate is a functional curve. In this paper, we propose a new corrected loss function for a partially functional linear quantile model with functionvalued measurement errors. We establish the asymptotic properties of both the functional coefficient and the parametric coefficient estimators. We also demonstrate the finite-sample performance of the proposed method using simulation studies, and illustrate its advantages by applying it to data from a children obesity study [ABSTRACT FROM AUTHOR]

Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid inference. Thus, identifying weak signals accurately and making valid inferences are crucial in penalized likelihood models. We develop a unified approach to identify weak signals and make inferences in penalized likelihood models, including the special case when the responses are categorical. To identify weak signals, we use the estimated selection probability of each covariate as a measure of the signal strength and formulate a signal identification criterion. To construct confidence intervals, we propose a two-step inference procedure. Extensive simulation studies show that the proposed procedure outperforms several existing methods. We illustrate the proposed method by applying it to the Practice Fusion diabetes data set. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new clustering approach for multivariate responses in a longitudinal analysis. Clustering analyses for multiple outcomes can be challenging, owing to multiple sources of correlation from multiple outcomes of the same subject and longitudinal measurements. The proposed method enhances clustering analyses by integrating multiple sources of correlations. Specifically, we incorporate random effects to capture correlations from multivariate responses, and group individuals by penalizing the pairwise distances between the B-spline coefficient vectors. We implement an alternating directions and method of multipliers (ADMM) algorithm for optimization in clustering. Furthermore, we study the asymptotic convergence rate of the proposed nonparametric estimator in the presence of longitudinal correlations for the random-effects model. The results of simulations and a real-data analysis show that the proposed method outperforms existing clustering methods. [ABSTRACT FROM AUTHOR]