Summary The classical likelihood ratio test based on the asymptotic chi-squared distribution of log-likelihood is one fundamental tools statistical inference. A recent universal approach sample splitting provides valid hypothesis tests and confidence sets in any setting for which we can compute split statistic, or, more generally, an upper bound null maximum likelihood. finite samples without r...

The method of maximum likelihood (ML), introduced by Fisher (1921), is widely used in human and quantitative genetics and we draw upon this approach throughout the book, especially in Chapters 13–16 (mixture distributions) and 26–27 (variance component estimation). Weir (1996) gives a useful introduction with genetic applications, while Kendall and Stuart (1979) and Edwards (1992) provide more ...

A generalization of the Half Logistic Distribution is developed through exponentiation of its survival function and named the Type II Generalized Half Logistic Distribution (GHLD). The distributional characteristics are presented and estimation of its parameters using maximum likelihood and modified maximum likelihood methods is studied with comparisons. Discrimination between Type II GHLD and ...

Previously, we have employed a program (Jtest) to test an hypothesis involving many parameters (multiple constraints). This test, which involves comparing parameter estimates with hypothesized values, is known as a Wald test. We also used the Jtest program to compare two di¤erent estimators in a Hausman test. There is an alternative method for conducting joint tests, which can be implemented ea...