The asymptotic covariance matrix of sample correlation coefficients under general conditions

Asymptotic Theory for Sample Covariance Matrix under Cross – Sectional Dependence

where X = (Xij)p×n consists of independent and identically distributed real random variables and T is a symmetric nonnegative definite nonrandom matrix. When p → ∞ and n → ∞ with p n → 0, it is shown that its empirical spectral distribution converges to a fixed distribution under the fourth moment condition. It is then discussed that such an asymptotic distribution can be used to derive an asym...

Covariance Selection by Thresholding the Sample Correlation Matrix

This article shows that when the nonzero coefficients of the population correlation matrix are all greater in absolute value than (C1 log p/n) 1/2 for some constant C1, we can obtain covariance selection consistency by thresholding the sample correlation matrix. Furthermore, the rate (log p/n) is shown to be optimal.

Two-Sample Quantile Tests Under General Conditions

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Honey, I Shrunk the Sample Covariance Matrix

The central message of this paper is that nobody should be using the sample covariance matrix for the purpose of portfolio optimization. It contains estimation error of the kind most likely to perturb a mean-variance optimizer. In its place, we suggest using the matrix obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coeff...