scholarly journals Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix‐variate location mixture of normal distributions

2019 ◽  
Vol 46 (2) ◽  
pp. 636-660 ◽  
Author(s):  
Taras Bodnar ◽  
Stepan Mazur ◽  
Nestor Parolya
Keyword(s):  
Covariance Matrix ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Sample Covariance Matrix ◽  
Normal Distributions ◽  
Large Sample ◽  
Sample Covariance ◽  
Mixture Of Normal Distributions ◽  
Mean Vector

scholarly journals Central limit theorems for generalized Pólya urn models

2006 ◽  
Vol 43 (4) ◽  
pp. 938-951 ◽  
Author(s):  
I. Higueras ◽  
J. Moler ◽  
F. Plo ◽  
M. San Miguel
Keyword(s):  
Covariance Matrix ◽  
Central Limit ◽  
Limit Theorems ◽  
Lyapunov Equation ◽  
Central Limit Theorems ◽  
Random Trees ◽  
Urn Models ◽  
Pólya Urn ◽  
Polya Urn ◽  
Generalized Pólya Urn

In this paper we obtain central limit theorems for generalized Pólya urn models with L ≥ 2 colors where one out of K different replacements (actions) is applied randomly at each step. Each possible action constitutes a row of the replacement matrix, which can be nonsquare and random. The actions are chosen following a probability distribution given by an arbitrary function of the proportions of the balls of different colors present in the urn. Moreover, under the same hypotheses it is proved that the covariance matrix of the asymptotic distribution is the solution of a Lyapunov equation, and a procedure is given to obtain the covariance matrix in an explicit form. Some applications of these results to random trees and adaptive designs in clinical trials are also presented.

scholarly journals Central limit theorems for generalized Pólya urn models

2006 ◽  
Vol 43 (04) ◽  
pp. 938-951
Author(s):  
I. Higueras ◽  
J. Moler ◽  
F. Plo ◽  
M. San Miguel
Keyword(s):  
Covariance Matrix ◽  
Central Limit ◽  
Limit Theorems ◽  
Lyapunov Equation ◽  
Central Limit Theorems ◽  
Random Trees ◽  
Urn Models ◽  
Pólya Urn ◽  
Polya Urn ◽  
Generalized Pólya Urn

In this paper we obtain central limit theorems for generalized Pólya urn models with L ≥ 2 colors where one out of K different replacements (actions) is applied randomly at each step. Each possible action constitutes a row of the replacement matrix, which can be nonsquare and random. The actions are chosen following a probability distribution given by an arbitrary function of the proportions of the balls of different colors present in the urn. Moreover, under the same hypotheses it is proved that the covariance matrix of the asymptotic distribution is the solution of a Lyapunov equation, and a procedure is given to obtain the covariance matrix in an explicit form. Some applications of these results to random trees and adaptive designs in clinical trials are also presented.

scholarly journals On asymptotics of eigenvectors of large sample covariance matrix

2007 ◽  
Vol 35 (4) ◽  
pp. 1532-1572 ◽  
Author(s):  
Z. D. Bai ◽  
B. Q. Miao ◽  
G. M. Pan
Keyword(s):  
Covariance Matrix ◽  
Sample Covariance Matrix ◽  
Large Sample ◽  
Sample Covariance

SHRINKAGE ESTIMATION OF MEAN-VARIANCE PORTFOLIO

2016 ◽  
Vol 19 (01) ◽  
pp. 1650003 ◽  
Author(s):  
YAN LIU ◽  
NGAI HANG CHAN ◽  
CHI TIM NG ◽  
SAMUEL PO SHING WONG
Keyword(s):  
Covariance Matrix ◽  
Sample Covariance Matrix ◽  
Risk Level ◽  
Sample Mean ◽  
Expected Gain ◽  
Sample Covariance ◽  
Shrinkage Method ◽  
Gain Loss ◽  
Mean Variance Portfolio ◽  
Mean Vector

This paper studies the optimal expected gain/loss of a portfolio at a given risk level when the initial investment is zero and the number of stocks [Formula: see text] grows with the sample size [Formula: see text]. A new estimator of the optimal expected gain/loss of such a portfolio is proposed after examining the behavior of the sample mean vector and the sample covariance matrix based on conditional expectations. It is found that the effect of the sample mean vector is additive and the effect of the sample covariance matrix is multiplicative, both of which over-predict the optimal expected gain/loss. By virtue of a shrinkage method, a new estimate is proposed when the sample covariance matrix is not invertible. The superiority of the proposed estimator is demonstrated by matrix inequalities and simulation studies.

A Robust MEWMA Control Chart Based on FAST-MCD Algorithm

2012 ◽  
Vol 562-564 ◽  
pp. 1907-1911
Author(s):  
Zhe Li ◽  
Rui Miao ◽  
Chuan Qi Wei ◽  
Ze Feng Li ◽  
Zhi Bin Jiang
Keyword(s):  
Covariance Matrix ◽  
Control Chart ◽  
Robust Statistics ◽  
Sample Covariance Matrix ◽  
Initial Sample ◽  
Multivariate Process ◽  
Sample Covariance ◽  
Sample Data ◽  
Mewma Control Chart ◽  
Mean Vector

MEWMA control chart is generally used to monitor slight deviation of mean vector for multivariate process. Sample covariance matrix S is often applied to estimate population covariance . When the initial sample data contains outliers, the results may be impacted and then weak the probabilities of control chart signals since the conventional mean vector and covariance matrix are not robust statistics. In this paper, FAST-MCD algorithm is used to build a robust covariance matrix to improve the robustness of MEWMA control chart. From the analysis of samples, the robust MEMWA control chart based on FAST-MCD algorithm has better immunity to small amount of noise in the initial samples.

Sign in / Sign up

Export Citation Format

Share Document