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Efficient Inference for Parameters and Error Distribution of Unobservable Time Series

Mei, Jingning
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1461084750

Abstract Details

2016, Doctor of Philosophy, University of Toledo, Mathematics.
First, a smooth kernel estimator is proposed for a multivariate cumulative distribution function, extending the work on Yamato (1973) on univariate distribution function estimation. Under assumptions of strict stationarity and geometrically strong mixing, we establish that the proposed estimator follows the same pointwise asymptotically normal distribution of the empirical cdf, while the new estimator is smooth instead of a step function as is the empirical cdf. We also show that under stronger assumptions the smooth kernel estimator has asymptotically smaller mean integrated squared error than the empirical cdf, and converges to the true cdf uniformly almost surely. Second, we propose a kernel estimator for the distribution function of unobserved errors in autoregressive time series with an unknown trend function, based on residuals computed by estimating the autoregressive coefficients with the Yule-Walker method. Under mild assumptions, we establish oracle efficiency of the proposed estimator, i.e., it is asymptotically as efficient as the kernel estimator of the distribution function based on the unobserved error sequence itself. The proposed estimator is also asymptotically indistinguishable from the empirical distribution function based on the unobserved errors. Simulation examples support the asymptotic theory.
Qin Shao, Dr. (Advisor)
Rong Liu, Dr. (Advisor)
Donald White, Dr. (Committee Member)
Tian Chen, Dr. (Committee Member)
126 p.
Statistics

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Citations

  • Mei, J. (2016). Efficient Inference for Parameters and Error Distribution of Unobservable Time Series [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1461084750

    APA Style (7th edition)

  • Mei, Jingning. Efficient Inference for Parameters and Error Distribution of Unobservable Time Series. 2016. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1461084750.

    MLA Style (8th edition)

  • Mei, Jingning. "Efficient Inference for Parameters and Error Distribution of Unobservable Time Series." Doctoral dissertation, University of Toledo, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1461084750

    Chicago Manual of Style (17th edition)

toledo1461084750
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© 2016, all rights reserved.
This open access ETD is published by University of Toledo and OhioLINK.