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972期 12月28日 :Identification and Estimation of a Semiparametric Single Index Transformation Model(涂云东, 北京大学光华管理学院和北京大学统计科学中心联席副教授,研究员)

【主讲】涂云东 (北京大学光华管理学院和北京大学统计科学中心联席副教授,研究员)

【主题】Identification and Estimation of a Semiparametric Single Index Transformation Model

【时间】2018年12月28日 (周五) 15:30-17:00

【地点】上海财经大学经济学院楼401室

【语言】英文

【摘要】In this paper, we consider a semiparametric single index model in which the dependent variable is subject to a nonparametric transformation. The model has the form $G(Y)=g(X' heta)+e$, where $X$ is a random vector of regressors,$Y$ is the dependent variable and $e$ is the random noise, the monotonic function $G$, the smooth function $g$ and the index vector $ heta$ are all unknown. This model is quite general in the sense that it nests many popular regression models as special cases.We first propose identification strategies for the three unknown quantities, based on which estimators are then constructed. The density weighted average derivative estimator of $delta$ (proportional to $ heta$) is shown to be a $V$-statistic, which converges at the standard $sqrt{n}$-rate and is asymptotically normal. The estimator of the transformation function $G$ is a functional of the conditional distribution estimator of $Y$ given $X$ and is shown to be $sqrt{n}$-consistent and asymptotically normal. The estimator of $g$ is shown to enjoy the standard nonparametric asymptotic properties. Numerical studies illustrate the nice finite sample performance of the proposed estimators.

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