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Statistical inference for high dimen...

Xia, Yin.

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Statistical inference for high dimensional data.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Statistical inference for high dimensional data./
Author:	Xia, Yin.
Description:	198 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.
Contained By:	Dissertation Abstracts International74-10B(E).
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3566481
ISBN:	9781303176715

Statistical inference for high dimensional data.
Xia, Yin.

Statistical inference for high dimensional data. - 198 p.

Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.

Thesis (Ph.D.)--University of Pennsylvania, 2013.

This thesis considers in the high dimensional setting two canonical testing problems in multivariate analysis, namely testing the equality of two mean vectors and testing the equality of two covariance matrices. The construction of adaptive confidence intervals for regression functions under shape constraints of monotonicity and convexity is also studied.

ISBN: 9781303176715Subjects--Topical Terms:

517247
Statistics.

Statistical inference for high dimensional data.
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020 $a 9781303176715
035 $a (MiAaPQ)AAI3566481
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040 $a MiAaPQ $c MiAaPQ
100 1 $a Xia, Yin. $3 1949177
245 1 0 $a Statistical inference for high dimensional data.
300 $a 198 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-10(E), Section: B.
500 $a Adviser: Tony Cai.
502 $a Thesis (Ph.D.)--University of Pennsylvania, 2013.
520 $a This thesis considers in the high dimensional setting two canonical testing problems in multivariate analysis, namely testing the equality of two mean vectors and testing the equality of two covariance matrices. The construction of adaptive confidence intervals for regression functions under shape constraints of monotonicity and convexity is also studied.
520 $a For testing two mean vectors, we introduce a new test statistic based on a linear transformation of the data by the precision matrix which incorporates the correlations among the variables. Limiting null distribution of the test statistic and the power of the test, both for the case the precision matrix is known and the case it is unknown, are analyzed. The test is particularly powerful against sparse alternatives and enjoys certain optimality. Numerical results show that the proposed test significantly outperforms other tests against sparse alternatives.
520 $a For testing two covariance matrices, the limiting null distribution of a new test statistic is derived. The test enjoys certain optimality and is especially powerful against sparse alternatives. Simulation results show that the test significantly outperforms existing methods both in terms of size and power. Analysis of prostate cancer datasets is carried out to demonstrate the application of the testing procedures. Motivated by applications in genomics, we also consider two related problems, recovering the support of the difference of two covariance matrices and testing the equality of two covariance matrices row by row. New testing procedures are introduced and their properties are studied.
520 $a For construction of adaptive confidence intervals, a natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of an analytic quantity, the local modulus of continuity. This bound depends not only on the function but also the assumed function class. These benchmarks show that the constructed confidence intervals have near minimum expected length for each individual function, while maintaining a given coverage probability for functions within the class. Such adaptivity is much stronger than adaptive minimaxity over a collection of large parameter spaces.
590 $a School code: 0175.
650 4 $a Statistics. $3 517247
690 $a 0463
710 2 $a University of Pennsylvania. $b Applied Mathematics and Computational Science. $3 2094759
773 0 $t Dissertation Abstracts International $g 74-10B(E).
790 $a 0175
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3566481