Random Sieve Likelihood and General Regression Models

Xiaotong Shen, Jian Shi, Wing Hung Wong

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Consider a semiparametric regression model Y = f(θ, X, ϵ), where f is a known function, θ is an unknown vector, ϵ consists of a random error and possibly of some unobserved variables, and the distribution F(·) of (ϵ, X) is unspecified. This article introduces, in a general setting, new methodology for estimating θ and F(·). The proposed method constructs a profile likelihood defined on random-level sets (a random sieve). The proposed method is related to empirical likelihood but is more generally applicable. Four examples are discussed, including a quadratic model, high-dimensional semiparametric regression, a nonparametric random-effects model, and linear regression with right-censored data. Simulation results and asymptotic analysis support the utility and effectiveness of the proposed method.

Original languageEnglish (US)
Pages (from-to)835-846
Number of pages12
JournalJournal of the American Statistical Association
Volume94
Issue number447
DOIs
StatePublished - Sep 1999

Keywords

  • Empirical likelihood
  • General regression model
  • Profile likelihood
  • Random sieve likelihood

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