Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Dissertation.pdf (622.33 KB)

ETD Abstract Container

Abstract Header

Efficient Inference for Periodic Autoregressive Coefficients with Polynomial Spline Smoothing Approach

Tang, Lin
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1449770216

Abstract Details

2015, Doctor of Philosophy, University of Toledo, Mathematics (statistics).
First, we propose a two-step estimation method for periodic autoregressive parameters via residuals when the observations contain trend and periodic autoregressive time series. In the first step, the trend is estimated and the residuals are calculated; in the second step, the autoregressive coefficients are estimated from the residuals. To overcome the drawback of a parametric trend estimation, we estimate the trend nonparametrically by polynomial spline smoothing. Polynomial spline smoothing is one of the nonparametric methods commonly used in practice for function estimation. It does not require any assumption about the shape of the unknown function. In addition, it has advantages of computational expediency and mathematical simplicity. The oracle efficiency of the proposed Yule-Walker type estimator is established. The performance is illustrated by simulation studies and real data analysis. Second, we consider time series that contain a trend, a seasonal component and periodically correlated time series. A semiparametric three-step method is proposed to analyze such time series. The seasonal component and trend are estimated by means of B-splines, and the Yule-Walker estimates of the time series model coefficients are calculated via the residuals after removing the estimated seasonality and trend. The oracle efficiency of the proposed Yule-Walker type estimators is established. Simulation studies suggest that the performance of the estimators coincides with the theoretical results. The proposed method is applied to three data sets. Third, we will make the inference for the logistic regression models using the nonparametric estimation method. The primary interest of this topic is the estimation of the conditional mean for the logistic regression models. We propose the local likelihood logit method with linear B-spline to estimate the conditional mean. Simulation studies shows that our method works well.
Qin Shao (Committee Chair)
Donald White (Committee Member)
Rong Liu (Committee Member)
Jing Wang (Committee Member)
127 p.
Statistics
periodic autoregressive time series; partially linear models; Yule-Walker estimator; B-splines; oracle efficiency; University of Toledo Department of Mathematics and Statistics

Recommended Citations

Citations

  • Tang, L. (2015). Efficient Inference for Periodic Autoregressive Coefficients with Polynomial Spline Smoothing Approach [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1449770216

    APA Style (7th edition)

  • Tang, Lin. Efficient Inference for Periodic Autoregressive Coefficients with Polynomial Spline Smoothing Approach. 2015. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1449770216.

    MLA Style (8th edition)

  • Tang, Lin. "Efficient Inference for Periodic Autoregressive Coefficients with Polynomial Spline Smoothing Approach." Doctoral dissertation, University of Toledo, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1449770216

    Chicago Manual of Style (17th edition)

toledo1449770216
367
© 2015, all rights reserved.
This open access ETD is published by University of Toledo and OhioLINK.