Likelihood ratio tests for covariance hypotheses generating commutative quadratic subspaces

We show that the likelihood ratio (LR) tests, for covariance hypotheses in multivariate normal models, take the form of a product of powers of independent beta variates whenever the covariance matrices generate a commutative quadratic subspace (CQS), See Seely (1971), under both the model and the hypothesis.     

A two-state markov model

Markov chains are used to model binary urine test results. Taking advantage of the transition mechanism of Markov chains, missing observations can be incorporated in the analysis. Maximum likelihood estimates of transition probabilities are computed. Formulas for empirical Bayes procedures are given.     

Nonparametric regression: An up–to–date bibliography

We attempt to give a complete list of references in non parametric regression estimation (including non parametric time series analysis), with a brief introduction of these works according a classification taking the diversity of problems or methods into account.     

Asymptotic bayesian inference in some nonstandard cases: Bernstein–von Mises Results and regular bayes' estimators

Asymptotically with probability close to one, the convergence in variation (also in distribution) to the multivariate normal, of the aposteriori density function of a parameter agains an apriori density, viz. the BERNSTEIN–VON MISES results are established when observations are not necessarily indenpendent or identically distributed but satisfy weak regularity assumptions on their joint density function. Regular BAYES' estimators are defined with respect to regular loss functions and a positive apriori density and proved consistent, asymptotically efficient and asymptotically normal. Examples and applications to conjugate families of densities, to inference in MARKOV Chains and other nonstandard cases illustrate results     

Bootstrap confidence intervals for smoothing splines and their comparison to bayesian confidence intervals

We construct bootstrap confidence intervals for smoothing spline estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from .exponential families. Several vari- ations of bootstrap confidence intervals are considered and compared. We find that the commonly used ootstrap percentile intervals are inferior to the T intervals and to intervals based on bootstrap estimation of mean squared errors. The best variations of the bootstrap confidence intervals behave similar to the well known Bayesian confidence intervals. These bootstrap confidence intervals have an average coverage probability across the function being estimated, as opposed to a pointwise property.     

Using bootstrap method to evaluate the estimates of nicotine equivalents from linear mixed model and generalized estimating equation

Twenty-four-hour urinary excretion of nicotine equivalents, a biomarker for exposure to cigarette smoke, has been widely used in biomedical studies in recent years. Its accurate estimate is important for examining human exposure to tobacco smoke. The objective of this article is to compare the bootstrap confidence intervals of nicotine equivalents with the standard confidence intervals derived from linear mixed model (LMM) and generalized estimation equation. We use percentile bootstrap method because it has practical value for real-life application and it works well with nicotine data. To preserve the within-subject correlation of nicotine equivalents between repeated measures, we bootstrap the repeated measures of each subject as a vector. The results indicate that the bootstrapped estimates in most cases give better estimates than the LMM and generalized estimation equation without bootstrap.     

On the partial autocorrelations of once integrated autoregressive-moving average processes

An observation, from practical experience with analysing univariate time series, suggests a simple relationship between the partial autocorrelations of a process realisation which requires first differencing, and those for that same sequence of differences. The asymptotic result is proved for a general once integrated autoregressive process, but an extension to twice integrated processes is shown not to be relevant for finite samples. The results are illustrated with examples from the literature.     

Gini index based goodness-of-fit test for the logistic distribution

To model growth curves in survival analysis and biological studies the logistic distribution has been widely used. In this article, we propose a goodness-of-fit test for the logistic distribution based on an estimate of the Gini index. The exact distribution of the proposed test statistic and also its asymptotic distribution are presented. In order to compute the proposed test statistic, parameters of the logistic distribution are estimated by approximate maximum likelihood estimators (AMLEs), which are simple explicit estimators. Through Monte Carlo simulations, power comparisons of the proposed test with some known competing tests are carried. Finally, an illustrative example is presented and analyzed.     

Male‐male sexual contact in the U.S.A.: Findings from five sample surveys, 1970–1990

Estimates of the prevalence of male‐male sexual contact are derived using data from five probability surveys conducted between 1970 and 1990. Estimated minimums of 5 to 7 percent of U.S. men report some same‐gender sexual contact during adulthood. Because of the likelihood of underreporting, these estimates might be considered lower bounds on the actual prevalence of such contact. Estimates show relatively little variation across social and demographic subgroups with the major exception that higher prevalence is reported among never‐married men, particularly those 35 and older. Some lesser variations are also found by service in the military, current residence, and current religious affiliation. Fragmentary evidence from these surveys suggests that some men may have episodic male‐male contact in adulthood while other men may have a relatively consistent and exclusive pattern of same‐gender contacts. Only one‐quarter to one‐half of the U.S. men who report male‐male contacts in adulthood also report having had such contacts during the preceding 12 months. In addition, the majority of men reporting same‐gender contacts in adulthood also report some male‐female contacts. Among men reporting same‐gender contacts in the preceding 12 months, however, the majority report exclusively male sexual contacts throughout adulthood. Potential implications of these findings for HIV prevention and research are discussed.     

An efficient procedure for computing minque of variance components and generalized least squares estimates of fixed effects

An efficient method for computing minimum norm quadratic unbiased estimates (MINQUE) of variance components and generalized least squares estimates of the fixed effects in the mixed model is developed. The computing algorithm uses a modification of the W transformation.