کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7548040 1489839 2018 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Schott's and Mao's test statistics for independence of normal random vectors
ترجمه فارسی عنوان
در آزمون شوات و مائو برای استقلال بردارهای معمول تصادفی
کلمات کلیدی
ابعاد بزرگ، استقلال کامل توزیع نرمال، محدود کردن توزیع،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
چکیده انگلیسی
Consider a random sample of n independently and identically distributed p-dimensional normal random vectors. A test statistic for complete independence of high-dimensional normal distributions, proposed by Schott (2005), is defined as the sum of squared Pearson's correlation coefficients. A modified test statistic has been proposed by Mao (2014). Under the assumption of complete independence, both test statistics are asymptotically normal if the limit limn→∞p∕n exists and is finite. In this paper, we investigate the limiting distributions for both Schott's and Mao's test statistics. We show that both test statistics, after suitably normalized, converge in distribution to the standard normal as long as both n and p tend to infinity. Furthermore, we show that the distribution functions of the test statistics can be approximated very well by a chi-square distribution function with p(p−1)∕2 degrees of freedom as n tends to infinity regardless of how p changes with n.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 140, September 2018, Pages 132-141
نویسندگان
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