CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS IN ONE-WAY UNBALANCED DESIGNS

Consider the one way unbalanced components of variance model given by Yij = μ + Ai + Eij, (i = l, ... ,a, j = l, ... ,bi) where μ is an unknown constant parameter, Ai and Eij are independent normal random variables with zero means and variances σ2A and σ2E respectively, The problem is to obtain a confidence interval for σ2A with confidence coefficient greater than or equal to a specified 1 - α. Three new procedures for obtaining confidence intervals for σ2A are examined. These new methods are derived using unweighted means. These three methods are compared with a standard procedure based on confidence coefficients and expected widths .

On quadratic estimates of variance components

Quadratic estimates of variance components for various linear models were investigated;For the general balanced nested classification with no specific distributions assumed, it was shown that the quadratic estimate which was unbiased and which had minimum variance was given by the analysis of variance method of estimating the variance components;For the one fold classification with unequal numbers the model is yij=m+ai+bij where E ai2 = sigma a2; E bij2 = sigma 2;The best quadratic unbiased estimate of sigmaa2 depends on sigma2 and sigmaa2. Under the above model with the additional assumptions E ai 4 = 3 sigmaa4 and E bij 4 = 3 sigma4 the quadratic estimation of sigma a2 was investigated. Two methods of estimation were given, and a method of determining a lower bound on the efficiency of each method was given if w = sigmaa2/sigma2 is known. It is believed in most cases when w \u3e .01, that one of these two methods will give an efficiency above 80 percent;For the general balanced cross classification with normality assumptions it was shown that the best quadratic unbiased estimate of the variance components is given by the analysis of variance method of estimating variance components. It was also shown that the best quadratic unbiased estimate of any linear combination of variance components is given by the same linear combination of the best quadratic unbiased estimates of the individual variance components

Evaluation of Formulas for Predicting Various Components of Mixed Herd Milk

The Oklahoma Agricultural Experiment Station periodically issues revisions to its publications. The most current edition is made available. For access to an earlier edition, if available for this title, please contact the Oklahoma State University Library Archives by email at [email protected] or by phone at 405-744-6311

Comparison of the Mojonnier, Cenco Moisture Balance and Karl Fisher Titration as Methods of Determining the Total Solids in Fluid Milk

The Oklahoma Agricultural Experiment Station periodically issues revisions to its publications. The most current edition is made available. For access to an earlier edition, if available for this title, please contact the Oklahoma State University Library Archives by email at [email protected] or by phone at 405-744-6311

Introduction to the rheory of statistics

xv, 443 p.; 23 cm

Estimation Of Σ² In A Two-way Classification Model With Interaction

A method is given for estimating the error variance σ2 in a two-way classification model with interaction and with exactly one observation per cell. The method can also be used to help determine the pattern of interaction. © Taylor & Francis Group, LLC

Confidence Intervals On Individual Variances In Two-Way Models

Approximate confidence bounds on individual variances for unbalanced two-way crossed models are obtained. A simulation study was done to check the effectiveness of the approximate bounds, and to compare the proposed bounds with the cell mean procedure proposed by Srinivasan from the Colorado State Un. in her Ph.D. Thesis. Balanced incomplete block (BIB) designs are used as a special case of designs with empty cells, and confidence bounds on the variances are constructed for various design configurations. © 1992