Alignment of curves by nonparametric maximum likelihood estimation can be done when the individual transformations of the time axis is assumed to be of a parametric form, known up to some individual unobserved random parameters. We suggest a fast algorithm, based on a Laplace approximation, to find the nonparametric maximum likelihood estimator (NPMLE) for the shape function. We find smooth estimates for the shape functions without choosing any smoothing parameters or kernel function and we estimate realizations of the unobserved transformation parameters that align the curves to satisfy the eye. The method is applied to two data examples of electrophoretic spectra on feta cheese samples and on wheat samples, respectively. A small simulation study indicates reasonable robustness against assumptions regarding the error covariance function.

In this paper we investigate the use of a two-stage case-control design to test for linkage disequilibrium in a large sample with a large number of null makers and one potential candidate marker. The scores, or signals, obtained at the markers, at the same stage, are assumed to be independent. The aim is to reduce the cost due to the number of laboratory analyses. In the first stage, the test is carried out at all markers of a randomly selected proportion λ of the sample at hand. Then the markers showing a score over a specified threshold, say, the median score, along with an average random proportion p of the makers with scores below the median are selected for the second stage of the study. Combined scores are then computed at the second stage and these cross-stage scores are not assumed to be necessarily additive or independent. This, partially, extends Satagopan et al. (Biometrics 58 (2002) 163–170) analysis in the case of independent marker outcomes. The aim is to identify optimal values for p and λ that maximize the probability to detect association in the case of association. The transmission-disequilibrium test is considered in the analysis and analytical formulas for the underlying probabilities are derived throughout. Furthermore, simulation results on the performance of the two designs are presented.

Capture–recapture methods are largely used for estimating the size of some cetacean populations. The application of those methods for photo-identification data of recognizable individuals is very common. Poor quality photographs may lead the analyst to identify two sightings of the same individual as being different (false-negative errors). This kind of matching error inflates population size estimates. We develop a Bayesian approach to obtain bias corrected estimates of the population size N. The method can be used for M_t type capture–recapture models (Otis et al. Wildlife Monographs 62 (1978) 1–135) involving two or more sampling occasions. We used the methodology for simulated data.

A new class of discrete distributions is introduced by extending the generalized hypergeometric recast distribution; some of its properties are studied. It is shown that all its moments exist finitely. A genesis, probability mass function, mean and variance are obtained. Certain recurrence relations for probabilities, moments and factorial moments are derived. Certain mixtures and limiting cases are also considered.

In this paper, we derive the density and distribution functions of the estimator of the shrinkage parameters of the Liu and generalized Liu estimators associated with the normal linear regression model. We indicate how these distributions can be used in arriving at a confidence interval for the optimal value of the shrinkage parameter. Since the distributions are difficult to handle, we have carried out some numerical computations to illustrate them.

The sensitivity (S_e) and the specificity (S_p) are the two most common measures of the performance of a diagnostic test, where S_e is the probability of a diseased individual to be correctly identified by the test while S_p is the probability of a healthy individual to be correctly identified by the same test. A problem appears when all individuals cannot be verified by a gold standard. This occurs when there is not a definitive test for detection of the disease or the verification by a gold standard is an impracticable procedure according to its cost, accessibility or risks. In this paper we develop a Bayesian analysis to estimate the disease prevalence, the sensitivity and specificity of screening tests in the presence of a covariate and in the absence of a gold standard. We use the Metropolis–Hastings algorithm to obtain the posterior summaries of interest. We have as motivation for the investigation the LAMS (Latin American Screening) Study, an extensive project designed for comparing screening tools for cervical cancer in Brazil and Argentina. When applied to the analysis of data from LAMS Study, the proposed Bayesian method shows to be a useful alternative to estimate measures of performance of screening tests in the presence of covariates and when a gold standard is not available. An advantage of the method is the fact that the number of parameters to be estimated is not limited by the number of observations, as it happens with several frequentist approaches. However, it is important to point out that the Bayesian analysis requires informative priors in order for the parameters to be identifiable. The method can be easily extended for the analysis of other medical data sets.

In this paper stochastic expansions of the maximum likelihood estimator for location and for the asymptotic expansion of the distribution function of this estimator are derived. A Cornish–Fisher expansion is also given for the quantile function of the distribution function. All expansions are given in explicit expressions.

We study sequential infection spreading models on ℤ, where healthy particles stay inactive and infected particles have positive displacement rate. When one infected particle reaches a healthy site, all particles contained there become infected. The main focus of our study is the speed of infection spreading.