單指標條件分配模型之擬最小平方估計法相關推論

Pseudo Least Integrated Squares Estimation For Single-Index Conditional Distribution Models

黃名鉞(Ming-Yueh Huang)

指導教授 ： 江金倉

國立臺灣大學/理學院/數學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02925

摘要

在單指標條件分配模型之下，我們提出擬最小平方估計法來估計模型中的單指標係數。數值實驗顯示此估計式的表現比傳統的擬最大概似估計式以及半參數化最小平方估計式要好。此外，根據所考量之資料結構，提出交互驗證法作為帶寬選取標準，同時借助自助重取法提供估計式的變異估計及信賴區間之建立。利用定義的殘差統計量，我們進一步建立模型適當性之檢定方法。當模型中之單指標有零係數發生狀況，多階段的Adaptive LASSO 演算法有效偵測出此類群變數。在數值方面，廣泛的模擬與實際資料之驗證呈現所提出方法之可行性。

關鍵字

交互驗證法 ； 自助重取法 ； 單指標模型 ； 擬最小平方法 ； 擬最大概似估計

並列摘要

A more flexible single-index regression model is employed to characterize the conditional distribution. For this emiparametric model, a pseudo least integrated squares pproach is developed for the estimation of index oefficients. It is shown in the numerical studies that our estimator outperforms both the pseudo maximum likelihood and semiparametric least squares ones. In addition, we propose the generalized cross-validation criteria for bandwidth selection and the bootstrap implementation for the estimation of asymptotic variance and the construction of confidence intervals. With our defined residual process, a test rule is established to check the adequacy of the considered single-index conditional distribution model. To tackle with the problem of sparse variables, a multiple-stage adaptive Lasso algorithm is developed to identify significant variables and achieve the semiparametric efficiency bound. In this study, a class of simulation scenarios was conducted to assess the finite sample properties of the proposed estimators and inference procedures. Two empirical examples from the house-price study in Boston and the environmental study in New York are further used to illustrate the usefulness of our approaches.

並列關鍵字

adaptive Lasso ； cross-validation ； naive bootstrap ； oracle properties ； single-index model ； pseudo least squares estimator ； pseudo least integrated squares estimator ； pseudo maximum likelihood estimator ； random weighted bootstrap

參考文獻

Cheng, B. and Tong, H. (1993). On residual sums of squares in nonparametric autoregression. Stochastic Processes and their Applications. 48, 157-174.

Delecroix, M., H‥ardle, W., and Hristache, M. (2003). Efficient estimation in conditional single-index regression. Journal of Multivariate Analysis. 86, 213-226.

Efron, B. (1979). Bootstrap methods: another look at the Jackknife. Annals of Statistics. 7, 1-26.

Fan, J. and Li, R. (2001). Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties. Journal of the American Statistical Association. 96, 1348-1360.

Geyer, C. J. (1994). On the asymptotics of constrained M-estimation. Annals of Statistics. 22, 1993-2010.