Tapered empirical likelihood for time series data in time and frequency domains

We investigate data tapering in two formulations of empiricallikelihood for time series. One empirical likelihood is formedfrom tapered data blocks in the time domain and a second isbased on the tapered periodogram in the frequency domain. Limitingdistributions are provided for both empirical likelihood versionsunder tapering. Theoretical and simulation evidence indicatesthat a data taper improves the coverage accuracy of empiricallikelihood confidence intervals for time series parameters,such as means and correlations.     

Unbiased Confidence Intervals for the Odds Ratio of Two Independent Binomial Samples with Application to Case–Control Data

The problem of confidence interval construction for the odds ratio of two independent binomial samples is considered. Two methods of eliminating the nuisance parameter from the exact likelihood, conditioning and maximization, are described. A conditionally exact tail method exists by putting together upper and lower bounds. A shorter interval can be obtained by simultaneous consideration of both tails. We present here new methods that extend the tail and simultaneous approaches to the maximized likelihood. The methods are unbiased and applicable to case-control data, for which the odds ratio is important. The confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability. A Bayesian confidence interval method and a large-sample chi2 procedure are included in the comparisons.     

Evaluation of the maximum likelihood estimate of the evolutionary tree topologies from DNA sequence data,and the branching order in hominoidea

Summary A maximum likelihood method for inferring evolutionary trees from DNA sequence data was developed by Felsenstein (1981). In evaluating the extent to which the maximum likelihood tree is a significantly better representation of the true tree, it is important to estimate the variance of the difference between log likelihood of different tree topologies. Bootstrap resampling can be used for this purpose (Hasegawa et al. 1988; Hasegawa and Kishino 1989), but it imposes a great computation burden. To overcome this difficulty, we developed a new method for estimating the variance by expressing it explicitly.The method was applied to DNA sequence data from primates in order to evaluate the maximum likelihood branching order among Hominoidea. It was shown that, although the orangutan is convincingly placed as an outgroup of a human and African apes clade, the branching order among human, chimpanzee, and gorilla cannot be determined confidently from the DNA sequence data presently available when the evolutionary rate constancy is not assumed.     

An Examination of the Conservative Nature of “Classical” Confidence Limits for a Proportion

The performance of the standard confidence limits for a proportion is studied over the entire range of proportions, and for various prescribed values of the nominal confidence coefficient. In the light of the conservative nature of these limits, modifications are suggested resulting in limits with average confidence coefficients close to the 95% nominal value. A comparison is made with a solution obtained from the application of Bayes's theorem to the problem.