Abstract
A semiparametric logistic regression model is proposed in which its nonparametric component is approximated with fixed-knot cubic B-splines. To assess the linearity of the nonparametric component, we construct a penalized likelihood ratio test statistic. When the number of knots is fixed, the null distribution of the test statistic is shown to be asymptotically the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. We set the asymptotic null expectation of this test statistic equal to a value to determine the smoothing parameter value. Monte Carlo experiments are conducted to investigate the performance of the proposed test. Its practical use is illustrated with a real-life example.
Original language | English (US) |
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Pages (from-to) | 461-475 |
Number of pages | 15 |
Journal | Journal of Applied Statistics |
Volume | 43 |
Issue number | 3 |
DOIs | |
State | Published - Feb 17 2016 |
Keywords
- B-spline
- generalized linear model
- generalized partially linear model
- penalized likelihood ratio test
- semiparametric logistic regression
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty