國立虎尾科技大學 |

Statistical Inference for High-Dimensional Linear Models.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Statistical Inference for High-Dimensional Linear Models./
作者:	Guo, Zijian.
面頁冊數:	1 online resource (251 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
標題:	Statistics. -
電子資源:	click for full text (PQDT)
ISBN:	9780355095340

Statistical Inference for High-Dimensional Linear Models.
Guo, Zijian.

Statistical Inference for High-Dimensional Linear Models. - 1 online resource (251 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

High-dimensional linear models play an important role in the analysis of modern data sets. Although the estimation problem has been well understood, there is still a paucity of methods and theories on the inference problem for high-dimensional linear models. This thesis focuses on statistical inference for high-dimensional linear models and consists of the following three parts.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355095340Subjects--Topical Terms:

556824
Statistics.
Index Terms--Genre/Form:

554714
Electronic books.

Statistical Inference for High-Dimensional Linear Models.
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100 1 $a Guo, Zijian. $3 1182880
245 1 0 $a Statistical Inference for High-Dimensional Linear Models.
264 0 $c 2017
300 $a 1 online resource (251 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
500 $a Adviser: Tony Cai.
502 $a Thesis (Ph.D.) $c University of Pennsylvania $d 2017.
504 $a Includes bibliographical references
520 $a High-dimensional linear models play an important role in the analysis of modern data sets. Although the estimation problem has been well understood, there is still a paucity of methods and theories on the inference problem for high-dimensional linear models. This thesis focuses on statistical inference for high-dimensional linear models and consists of the following three parts.
520 $a 1. The first part of the thesis considers confidence intervals for linear functionals in high-dimensional linear regression. We first establish the convergence rates of the minimax expected length for confidence intervals. Furthermore, we investigate the problem of adaptation to sparsity for the construction of confidence intervals and identify the regimes in which it is possible to construct adaptive confidence intervals.
520 $a 2. In the second part of the thesis, we consider point and interval estimation of the lq loss of a given estimator in high-dimensional linear regression. For the class of rate-optimal estimators, we establish the minimax rates for estimating their lq losses, the minimax expected length of confidence intervals for their l q losses and the possibility of adaptivity of confidence intervals for their lq losses.
520 $a 3. In the third part of the thesis, we consider the problem in the framework of high-dimensional instrumental variable regression and construct confidence intervals for the treatment effect in the presence of possibly invalid instrumental variables. We develop a novel selection procedure, Two-Stage Hard Thresholding (TSHT) to select valid instrumental variables and construct honest confidence intervals for the treatment effect using the selected instrumental variables.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Statistics. $3 556824
655 7 $a Electronic books. $2 local $3 554714
690 $a 0463
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Pennsylvania. $b Statistics. $3 1182881
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10267773 $z click for full text (PQDT)