Lack-of-fit tests for generalized linear models via splines

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Cubic B-splines are used to estimate the nonparametric component of a semiparametric generalized linear model. A penalized log-likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the nonparametric function. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one df. The smoothing parameter is determined by giving a specified value for its asymptotically expected value under the null hypothesis. A simulation study is conducted to evaluate its power performance; a real-life dataset is used to illustrate its practical use.

Original languageEnglish (US)
Pages (from-to)4240-4250
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Volume41
Issue number23
DOIs
StatePublished - Dec 1 2012

Fingerprint

Lack-of-fit Test
Generalized Linear Model
Null hypothesis
Spline
Cubic B-spline
Likelihood Ratio Test Statistic
Chi-squared
Log-likelihood Ratio
Smoothing Parameter
Null Distribution
Limiting Distribution
Expected Value
Linearity
Knot
Linear Combination
Random variable
Simulation Study
Evaluate
Estimate

Keywords

  • B-spline
  • Generalized linear model
  • Generalized partially linear model
  • Penalized log-likelihood ratio test
  • Semiparametric generalized linear model

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Lack-of-fit tests for generalized linear models via splines. / Li, Chin-Shang.

In: Communications in Statistics - Theory and Methods, Vol. 41, No. 23, 01.12.2012, p. 4240-4250.

Research output: Contribution to journalArticle

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