Abstract
This paper considers partially linear additive models with the number of parameters diverging when some linear constraints on the parametric part are available. This paper proposes a constrained profile least-squares estimation for the parametric components with the nonparametric functions being estimated by basis function approximations. The consistency and asymptotic normality of the restricted estimator are given under some certain conditions. The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametric components, and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypotheses. The finite sample performance of the proposed method is illustrated by simulation studies and a data analysis.
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This research was supported by the National Natural Science Foundation of China under Grant No. 11771250, the Natural Science Foundation of Shandong Province under Grant No. ZR2019MA002, and the Program for Scientific Research Innovation of Graduate Dissertation under Grant No. LWCXB201803.
This paper was recommended for publication by Editor ZHU Lixing.
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Wang, X., Zhao, S. & Wang, M. Profile Statistical Inference for Partially Linear Additive Models with a Diverging Number of Parameters. J Syst Sci Complex 32, 1747–1766 (2019). https://doi.org/10.1007/s11424-019-7145-0
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DOI: https://doi.org/10.1007/s11424-019-7145-0