A partially linear model with its applications

Research output: Contribution to journalArticle

Abstract

The nonparametric component in a partially linear model is approximated via cubic B-splines with a second-order difference penalty on the adjacent B-spline coefficients to avoid undersmoothing. A Wald-type spline-based test statistic is constructed for the null hypothesis of no effect of a continuous covariate. When the number of knots is fixed, the limiting null distribution of the test statistic is the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. A real-life dataset is provided to illustrate the practical use of the test statistic.

Original languageEnglish (US)
Pages (from-to)1673-1680
Number of pages8
JournalCommunications in Statistics: Simulation and Computation
Volume42
Issue number7
DOIs
StatePublished - Aug 1 2013

Fingerprint

Partially Linear Model
Splines
Test Statistic
Statistics
Cubic B-spline
Chi-squared
Null Distribution
B-spline
Limiting Distribution
Random variables
Null hypothesis
Knot
Spline
Penalty
Linear Combination
Covariates
Adjacent
Random variable
Degree of freedom
Coefficient

Keywords

  • B-splines
  • Method of Lagrange multipliers
  • P-splines
  • Penalized least-squares
  • Wald-type spline-based test

ASJC Scopus subject areas

  • Modeling and Simulation
  • Statistics and Probability

Cite this

A partially linear model with its applications. / Li, Chin-Shang.

In: Communications in Statistics: Simulation and Computation, Vol. 42, No. 7, 01.08.2013, p. 1673-1680.

Research output: Contribution to journalArticle

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