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 language | English (US) |
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Pages (from-to) | 1673-1680 |
Number of pages | 8 |
Journal | Communications in Statistics: Simulation and Computation |
Volume | 42 |
Issue number | 7 |
DOIs | |
State | Published - Aug 1 2013 |
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