Approximation of sampling variances and confidence intervals for maximum likelihood estimates of variance components

1992 ◽  
Vol 109 (1-6) ◽  
pp. 264-280 ◽  
Author(s):  
K. Meyer ◽  
W. G. Hill
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Variance Components ◽  
Maximum Likelihood Estimates

Likelihood-based confidence intervals of relative fitness for a common experimental design

2005 ◽  
Vol 62 (3) ◽  
pp. 693-699 ◽  
Author(s):  
Steven T Kalinowski ◽  
Mark L Taper
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimates ◽  
Relative Fitness ◽  
Literature Analysis ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Statistical Inferences ◽  
Different Types

Statistical inferences concerning the relative fitness of different types of individuals in a population have not been well developed. We present a method for calculating confidence intervals for maximum likelihood estimates of relative fitness obtained from an experimental design that is common in the fisheries literature. Analysis and simulation show that these confidence limits are reliable. We also show that the bias of the estimates is low for realistic sample sizes.

Asymptotic Optimality of Restricted Maximum Likelihood Estimates for the Mixed Model

1979 ◽  
Vol 28 (1-4) ◽  
pp. 125-142 ◽  
Author(s):  
Kalyan Das
Keyword(s):  
Maximum Likelihood ◽  
Conceptual Design ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Mixed Model ◽  
Asymptotic Optimality ◽  
Restricted Maximum Likelihood ◽  
Maximum Likelihood Estimates ◽  
Asymptotically Normal ◽  
Reasonable Sense

In this paper we study the asymptotic optimality of the restricted maximum likelihood estimates of variance components in the mixed model of analysis of variance. Using conceptual design sequences of Miller (1977), under slightly stronger conditions, we show that the restricted maximum likelihood estimates are not only asymptotically normal, but also asymptotically equivalent to the maximum likelihood estimates in a reasonable sense.

Infinite Parameter Estimates in Logistic Regression: Opportunities, Not Problems

2002 ◽  
Vol 27 (2) ◽  
pp. 147-161 ◽  
Author(s):  
David Rindskopf
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Strict Sense ◽  
Hypothesis Tests ◽  
Infinite Slope ◽  
Alternative Method

Infinite parameter estimates in logistic regression are commonly thought of as a problem. This article shows that in principle an analyst should be happy to have an infinite slope in logistic regression, because it indicates that a predictor is perfect. Using simple approaches, hypothesis tests may be performed and confidence intervals calculated even when a slope is infinite. Some functions of parameters that are infinite are still well defined, and reasonable estimates of these quantities (in particular, LD50) may be obtained even when the maximum likelihood estimates do not, in a strict sense, exist. Surprisingly, these techniques can provide more reasonable and useful results than the most popular alternative method, exact logistic regression.

scholarly journals The Type I Generalized Half-Logistic Distribution Based on Upper Record Values

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Devendra Kumar ◽  
Neetu Jain ◽  
Shivani Gupta
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Record Values ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Type I ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
First Four Moments

We consider the type I generalized half-logistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.

Combining Aggregate and Individual Level Data to Estimate an Individual Level Correlation Coefficient

2003 ◽  
Vol 28 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Trivellore E. Raghunathan ◽  
Paula K. Diehr ◽  
Allen D. Cheadle
Keyword(s):  
Maximum Likelihood ◽  
Correlation Coefficient ◽  
Confidence Intervals ◽  
Method Of Moments ◽  
Aggregate Data ◽  
Maximum Likelihood Estimates ◽  
Regression Coefficients ◽  
Individual Level ◽  
Level Data ◽  
The Individual

Methods are developed that use aggregate data, possibly based on a large number of individuals, and individual level data, from a small fraction of individuals from the same or similar population, to eliminate ecological bias inherent in the analysis of aggregate data. The primary focus is on estimating the individual level correlation coefficient but the proposed methodology can be extended to estimate regression coefficients. Two approaches, the method of moments and the maximum likelihood, are developed for a bivariate distribution, but can be extended to a multivariate distribution. The method of moments develops a corrected estimate of the within-group covariance matrix, which is then used to estimate the individual level correlation and regression coefficients. The second method assumes bivariate normality and maximizes the combined likelihood function based on the two data sets. The maximum likelihood estimates are obtained using the EM-algorithm. A simulation study investigates the repeated sampling properties of these procedures in terms of bias and the mean square error of the point estimates and the actual coverage of the confidence intervals. The maximum likelihood estimates are almost unbiased and the confidence intervals are well calibrated for simulation conditions considered. The method of moments estimates have the same desirable properties for some simulation conditions. Under all conditions, the correlation coefficient between aggregate variables is severely biased as an estimate of the individual level correlation coefficient.

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