Local rank inference for varying coefficient models

Lan Wang, Bo Kai, Runze Li

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

By allowing the regression coefficients to change with certain covariates, the class of varying coefficient models offers a flexible approach to modeling nonlinearity and interactions between covariates. This article proposes a novel estimation procedure for the varying coefficient models based on local ranks. The new procedure provides a highly efficient and robust alternative to the local linear least squares method, and can be conveniently implemented using existing R software package. Theoretical analysis and numerical simulations both reveal that the gain of the local rank estimator over the local linear least squares estimator, measured by the asymptotic mean squared error or the asymptotic mean integrated squared error, can be substantial. In the normal error case, the asymptotic relative efficiency for estimating both the coefficient functions and the derivative of the coefficient functions is above 96%; even in the worst case scenarios, the asymptotic relative efficiency has a lower bound 88.96% for estimating the coefficient functions, and a lower bound 89.91% for estimating their derivatives. The new estimator may achieve the nonparametric convergence rate even when the local linear least squares method fails due to infinite random error variance. We establish the large sample theory of the proposed procedure by utilizing results from generalized U-statistics, whose kernel function may depend on the sample size. We also extend a resampling approach, which perturbs the objective function repeatedly, to the generalized U-statistics setting, and demonstrate that it can accurately estimate the asymptotic covariance matrix.

Original languageEnglish (US)
Pages (from-to)1631-1645
Number of pages15
JournalJournal of the American Statistical Association
Volume104
Issue number488
DOIs
StatePublished - Dec 1 2009

Fingerprint

Varying Coefficient Model
Linear Least Squares
Local Linear Method
Asymptotic Relative Efficiency
U-statistics
Least Square Method
Covariates
Coefficient
Lower bound
Large Sample Theory
Mean Integrated Squared Error
Asymptotic Covariance Matrix
Estimator
Derivative
Linear Estimator
Random Error
Least Squares Estimator
Resampling
Regression Coefficient
Kernel Function

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Local rank inference for varying coefficient models. / Wang, Lan; Kai, Bo; Li, Runze.

In: Journal of the American Statistical Association, Vol. 104, No. 488, 01.12.2009, p. 1631-1645.

Research output: Contribution to journalArticle

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