A partially linear model with its applications

Chin-Shang Li

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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
Issue number7
StatePublished - Aug 1 2013


  • 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


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