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CLT for Sample Partial Correlation Coefficients

Author: ZhouShan
Tutor: BaiZhiDong
School: Northeast Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Partial correlation coefficient Law of large numbers Central limit theo-rein Double Expectations formula δmethod Non-normal distribution
CLC: O211.4
Type: Master's thesis
Year: 2011
Downloads: 35
Quote: 0
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Abstract


In the past several decades．a significant and constant advancement in the worldhas been in the rapid development and wide application of computer science Comput—ing speed and storage capability have increased a thousand％ld These computationaldevelopments have had strong impacts on every branch of science Although moderncomputer technology helps us in so many aspects．it also brings a new and urgent task tothe statisitcians However，the classical statistical methods are proved not valid in thosefields．which roots in the classicsl limit theorems are assumed on fixed dimension withinfinite sample sizeThis paper mainly studies the law"of large numbers and central limit theorem of thepartial correlation coefficient，namely sample partial correlation coefficient approximatelyconverges to population partial correlation coefficient，and after standardization，it has anormal limiting distribution The author deals with the normal samples and non—normalsamples，and considers the situation when the covariance matrix dimension and samplesize change synchronously，that is when(P q)／N Y∈(0，1)In normal distribu—tion condition．by deducing the distribution of a function of sample partial correlationcoefficient，the author derives its central limit theorem，then by useing the J method，theauthor solves the limit of partial correlation coefficient∥as the sample size approximatesinfinity，and constructs the confidence intervalIn non—normal distribution conditions．from a simple decomposition of sample covari—ante matrix：upper triangle matrix∑．the author finds out the limit of sample partialcorrelation coeffcient

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Limit theory
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