Semiparametric Estimation of a Binary Response Model with a Change-Point Due to a Covariate Threshold
Semiparametric Estimation of a Binary Response Model with a Change-Point Due to a Covariate Threshold
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DOI：
10.1016/j.jeconom.2008.02.003
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
S. Lee;M. Seo
中科院分区：
文献类型：
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作者：
S. Lee;M. Seo
本文研究了一类门限二元反应模型的半参数估计。本文考虑的估计方法是半参数的，因为回归函数的参数是有限维的，同时允许未知形式的异方差。特别是，该文件认为曼斯基的[曼斯基，查尔斯F，1975.随机效用选择模型的最大得分估计。Journal of Econometrics 3（3），205-228; Manski，Charles F.，1985.离散响应的半参数分析。最大得分估计量的渐近性质。Journal of Econometrics 27（3），313-333]最大得分估计。本文中的模型是不规则的，因为变点是由于一个未知的阈值在协变量。这种不规则性加上最大得分估计的目标函数的不连续性使得估计的渐近行为的分析变得复杂。给出了参数辨识的充分条件，并得到了估计量的相合性。证明了阈值参数γ0的估计是n−1-相容的，其余回归参数θ0的估计是n−1/3-相容的。此外，我们还得到了估计量的渐近分布。事实证明，估计量γ和θ都是预言有效的，因为n（γ <$n−γ0）和n1/3（θ <$n−θ0）弱收敛到分布，如果其他参数已知，它们将弱收敛到该分布。
This paper is concerned with semiparametric estimation of a threshold binary response model. The estimation method considered in the paper is semiparametric since the parameters for a regression function are finite-dimensional, while allowing for heteroskedasticity of unknown form. In particular, the paper considers Manski’s [Manski, Charles F., 1975. Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3 (3), 205–228; Manski, Charles F., 1985. Semiparametric analysis of discrete response. Asymptotic properties of the maximum score estimator. Journal of Econometrics 27 (3), 313–333] maximum score estimator. The model in this paper is irregular because of a change-point due to an unknown threshold in a covariate. This irregularity coupled with the discontinuity of the objective function of the maximum score estimator complicates the analysis of the asymptotic behavior of the estimator. Sufficient conditions for the identification of parameters are given and the consistency of the estimator is obtained. It is shown that the estimator of the threshold parameter, γ0, is n−1-consistent and the estimator of the remaining regression parameters, θ0, is n−1/3-consistent. Furthermore, we obtain the asymptotic distribution of the estimator. It turns out that both estimators γˆ and θˆ are oracle-efficient in that n(γˆn−γ0) and n1/3(θˆn−θ0) converge weakly to the distributions to which they would converge weakly if the other parameter(s) were known.