(3.231.166.56) 您好!臺灣時間:2021/03/08 12:10
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:黃名鉞
研究生(外文):Ming-Yueh Huang
論文名稱:單指標條件分配模型之擬最小平方估計法相關推論
論文名稱(外文):Pseudo Least Integrated Squares Estimation For Single-Index Conditional Distribution Models
指導教授:江金倉江金倉引用關係
指導教授(外文):Chin-Tsang Chiang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:35
中文關鍵詞: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
外文關鍵詞:adaptive Lassocross-validationnaive bootstraporacle propertiessingle-index modelpseudo least squares estimatorpseudo least integrated squares estimatorpseudo maximum likelihood estimatorrandom weighted bootstrap
相關次數:
  • 被引用被引用:0
  • 點閱點閱:241
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
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。

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.

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract (in Chinese) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract (in English) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
1 Introduction 1
2 Estimation and Inference Procedures 5
2.1 Estimation and Bandwidth Selection . . . . . . . . . . . . . . . . . . 5
2.2 Asymptotic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Bootstrap Inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Model Test and Sparse Models 14
3.1 Model Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Adaptive Lasso Estimation and Oracle Properties . . . . . . . . . . . 15
3.3 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Multiple-Stage Adaptive Lasso Procedure . . . . . . . . . . . . . . . 17
4 Simulation Experiments 19
4.1 Simulation I - Comparison of the Estimators . . . . . . . . . . . . . . 19
4.2 Simulation II - Assessment of Inference Procedures . . . . . . . . . . 20
4.3 Simulation III - Performance of Adaptive Lasso Estimation . . . . . . 22
5 Empirical Examples 28
5.1 Application to a Study of House Price . . . . . . . . . . . . . . . . . 28
5.2 Application to a Study of Air Quality . . . . . . . . . . . . . . . . . . 29
6 Concluding Remarks and Further Extensions 32
Reference 34

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.
Gorgens, T. (2004). Average derivatives for hazard functions. Econometric Theory. 20, 437-463.
H‥ardle, W., Hall, P., and Ichimura, H. (1993). Optimal smoothing in single-index models. Annals of Statistics. 21, 157-178.
Harrison, D. and Rubinfeld, D. L. (1978). Hedonic prices and the demand for clean air. Journal of Environmental and Economic Management. 31, 403-405.
Huang, J., Ma, S., and Zhang, C. H. (2008). Adaptive Lasso for sparse highdimensional regression models. Statistica Sinica. 18, 1603-1618.
Ichimura, H. (1993). Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. Journal of Econometrics. 58, 71-120.
Kong, E. and Xia, Y. (2007). Variable selection for the single-index model. Biometrika. 94, 217-229.
Nolan, D. and Pollard, D. (1987). U-processes: Rates of convergence. Annals of Statistics. 15, 780-799.
Pakes, A. and Pollard, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027-1057.
Pollard, D. (1984). Convergence of stochastic processes. Springer. New York.
Pollard, D. (1990). Empirical processes: Theory and applications. Hayward: Institute of Mathematical Statistics.
Powell, J. L., Stock, J. H., and Stoker, T. (1989). Semiparametric estimation of index coefficients. Econometrica. 57, 1403-1430.
Rice, J. A. and Silverman, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society. B53, 233-243.
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society. B58, 267-288.
Xia, Y. (2009). Model checking in regression via dimension reduction. Biometrika. 96, 133-148.
Zou, H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association. 101, 1418-1428.

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔