Fixed Precision Estimate of Mean of a Gaussian Sequence with Unknown Covariance Structure

1980 ◽  
pp. 360-364
Author(s):  
Ryszard Zieliński
Keyword(s):  
Covariance Structure ◽  
Gaussian Sequence ◽  
Unknown Covariance

scholarly journals Capturing a Change in the Covariance Structure of a Multivariate Process

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 156
Author(s):  
Andriette Bekker ◽  
Johannes T. Ferreira ◽  
Schalk W. Human ◽  
Karien Adamski
Keyword(s):  
Covariance Matrix ◽  
Random Variables ◽  
Covariance Structure ◽  
Multivariate Normal ◽  
New Approach ◽  
Downward Shift ◽  
Consecutive Time ◽  
Time Periods ◽  
Unknown Covariance ◽  
Mean Vector

This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift.

A Bayesian approach to estimating linear mixtures with unknown covariance structure

2011 ◽  
Vol 38 (9) ◽  
pp. 1801-1817 ◽  
Author(s):  
Hannes Kazianka ◽  
Michael Mulyk ◽  
Jürgen Pilz
Keyword(s):  
Bayesian Approach ◽  
Covariance Structure ◽  
Linear Mixtures ◽  
Unknown Covariance

OPTIMAL QUADRATIC UNBIASED ESTIMATION FOR MODELS WITH LINEAR TOEPLITZ COVARIANCE STRUCTURE

Statistics ◽  
2003 ◽  
Vol 37 (1) ◽  
pp. 1-15
Author(s):  
JEAN-MICHEL MARIN ◽  
THIERRY DHORNE
Keyword(s):  
Covariance Structure ◽  
Unbiased Estimation

Power of Modified Brown-Forsythe and Mixed-Model Approaches in Split-Plot Designs

Methodology ◽  
2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Repeated Measures ◽  
Statistical Power ◽  
Mixed Model ◽  
Covariance Structure ◽  
Simulation Method ◽  
Future Research ◽  
Repeated Measures Design ◽  
Fixed And Random Effects ◽  
Split Plot ◽  
High Level

Abstract. Low precision of the inferences of data analyzed with univariate or multivariate models of the Analysis of Variance (ANOVA) in repeated-measures design is associated to the absence of normality distribution of data, nonspherical covariance structures and free variation of the variance and covariance, the lack of knowledge of the error structure underlying the data, and the wrong choice of covariance structure from different selectors. In this study, levels of statistical power presented the Modified Brown Forsythe (MBF) and two procedures with the Mixed-Model Approaches (the Akaike’s Criterion, the Correctly Identified Model [CIM]) are compared. The data were analyzed using Monte Carlo simulation method with the statistical package SAS 9.2, a split-plot design, and considering six manipulated variables. The results show that the procedures exhibit high statistical power levels for within and interactional effects, and moderate and low levels for the between-groups effects under the different conditions analyzed. For the latter, only the Modified Brown Forsythe shows high level of power mainly for groups with 30 cases and Unstructured (UN) and Autoregressive Heterogeneity (ARH) matrices. For this reason, we recommend using this procedure since it exhibits higher levels of power for all effects and does not require a matrix type that underlies the structure of the data. Future research needs to be done in order to compare the power with corrected selectors using single-level and multilevel designs for fixed and random effects.

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