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) |
|---|---|
| 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 |
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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 journal › Article
}
TY - JOUR
T1 - A partially linear model with its applications
AU - Li, Chin-Shang
PY - 2013/8/1
Y1 - 2013/8/1
N2 - 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.
AB - 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.
KW - B-splines
KW - Method of Lagrange multipliers
KW - P-splines
KW - Penalized least-squares
KW - Wald-type spline-based test
UR - http://www.scopus.com/inward/record.url?scp=84873408880&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84873408880&partnerID=8YFLogxK
U2 - 10.1080/03610918.2012.674597
DO - 10.1080/03610918.2012.674597
M3 - Article
VL - 42
SP - 1673
EP - 1680
JO - Communications in Statistics Part B: Simulation and Computation
JF - Communications in Statistics Part B: Simulation and Computation
SN - 0361-0918
IS - 7
ER -