On blocking rules for the bootstrap with dependent data

We address the issue of optimal block choice in applicationsof the block bootstrap to dependent data. It is shown that optimalblock size depends significantly on context, being equal ton^1/3, n^1/4 and n^1/5 in the cases of variance or bias estimation,estimation of a onesided distribution function, and estimationof a two-sided distribution function, respectively. A clearintuitive explanation of this phenomenon is given, togetherwith outlines of theoretical arguments in specific cases. Itis shown that these orders of magnitude of block sizes can beused to produce a simple, practical rule for selecting blocksize empirically. That technique is explored numerically.     

Modelling bivariate count series with excess zeros

Bivariate time series of counts with excess zeros relative to the Poisson process are common in many bioscience applications. Failure to account for the extra zeros in the analysis may result in biased parameter estimates and misleading inferences. A class of bivariate zero-inflated Poisson autoregression models is presented to accommodate the zero-inflation and the inherent serial dependency between successive observations. An autoregressive correlation structure is assumed in the random component of the compound regression model. Parameter estimation is achieved via an EM algorithm, by maximizing an appropriate log-likelihood function to obtain residual maximum likelihood estimates. The proposed method is applied to analyze a bivariate series from an occupational health study, in which the zero-inflated injury count events are classified as either musculoskeletal or non-musculoskeletal in nature. The approach enables the evaluation of the effectiveness of a participatory ergonomics intervention at the population level, in terms of reducing the overall incidence of lost-time injury and a simultaneous decline in the two mean injury rates.     

Multivariate elliptically contoured distributions for repeated measurements

The multivariate power exponential distribution, a member of the multivariate elliptically contoured family, provides a useful generalization of the multivariate normal distribution for the modeling of repeated measurements. Both light and heavy tailed distributions are included. The covariance matrix retains its interpretation so that it can easily be structured for serial dependence and several levels of variance components. A crossover trial on insulin applied to rabbits, with a series of repeated measurements within each period, is analyzed by means of this distribution using autocorrelation and two levels of variance components.     

A test of statistical techniques for detecting density dependence in sequential censuses of animal populations

Summary Principal and reduced major axes, and Bulmer's (1975) tests have been suggested as methods for detecting the presence of density dependence in a series of population censuses that are unsuitable for analysis by alternative means e.g. by k-factor analysis. These alternative methods are tested using census data, some of which are previously unpublished, from natural populations known from independent evidence to be subject to density dependent processes. All the methods fail to detect density dependence reliably, irrespective of sample size and the dynamics of the population. We conclude that none of the methods tested is sufficiently reliable to be useful as a test of density dependence in sequential censues of animal populations.