On semiparametric regression for count explanatory variables

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• 作者：Belkacem Abdous^a ; ^{belkacem.abdous@msp.ulaval.ca} ; Cé ; lestin C. Kokonendji^b ; ^{celestin.kokonendji@univ-fcomte.fr} ; Tristan Senga Kiessé ; ^c ; ^{tristan.senga-kiesse@onf.fr} ; ^{sengatristan@yahoo.fr}
• 关键词：Asymptotic bias and variance ; Discrete associated kernel ; Discrete finite difference ; Multiplicative correction factor ; Nonparametric regression ; Nadaraya&ndash ; Watson estimator ; Logistic regression
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：142
• 期：6
• 页码：1537-1548
• 全文大小：283 K

文摘

This work deals with a semiparametric estimation of a count regression function m that can be represented as a product of an unknown discrete parametric function r and an unknown discrete ¡°smooth?function . We propose an estimation procedure in two steps: first, we construct an approximation of r, then we use a discrete associated kernel method to estimate nonparametrically the multiplicative correction factor . The asymptotic and small-sample properties of the proposed estimator are investigated. Its comparison with the classical Nadaraya-Watson type count regression estimator shows that an improvement in terms of bias is achieved.