Two-stage efficient estimation of longitudinal nonparametric additive models

• Published in: Statistics & probability letters Vol. 77; no. 17; pp. 1666 - 1675
• Main Authors: You, Jinhong, Zhou, Haibo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2007; Elsevier
• Series: Statistics & Probability Letters
• Subjects: Additive model; Distribution theory; Efficiency; Exact sciences and technology; General topics; Longitudinal data; Longitudinal data Additive model Two-stage estimation Efficiency Oracle property; Mathematics; Nonparametric inference; Oracle property; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Two-stage estimation; secondary 62A10; Efficiency; Oracle property; Two-stage estimation; Longitudinal data; primary 62H12; Additive model; Smoothing methods; Probability theory; Asymptotic behavior; Finite sample; Nonparametric regression; Non parametric estimation; Statistical estimation; Statistical simulation; primary 62H12; secondary 62A10; Statistical method; Estimator efficiency; Smoothing; Regression model; Asymptotic normality; Longitudinal data; Additive model; Two-stage estimation; Efficiency; Oracle property
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2007.04.006

Nonparametric smoothings are useful tool to model longitudinal data. In this paper we study the estimating problem of longitudinal nonparametric additive regression models. A two-stage efficient approach is developed to estimate the unknown additive components. We show the resulted estimators have some advantages over the existed ones. For example, they are asymptotically more efficient than those neglecting the dependence of repeated observations over time within the same subject, have an oracle property, that is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty, and can be naturally extended to deal with generalized longitudinal nonparametric additive regression model. The asymptotic normality is established for the underlying additive components. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. Applying the proposed procedure to a real data set is also made.