Detecting homogeneous segments in DNA sequences by using hidden Markov models

In recent years there has been a rapid growth in the amount of DNA being sequenced and in its availability through genetic databases. Statistical techniques which identify structure within these sequences can be of considerable assistance to molecular biologists particularly when they incorporate the discrete nature of changes caused by evolutionary processes. This paper focuses on the detection of homogeneous segments within heterogeneous DNA sequences. In particular, we study an intron from the chimpanzee α-fetoprotein gene; this protein plays an important role in the embryonic development of mammals. We present a Bayesian solution to this segmentation problem using a hidden Markov model implemented by Markov chain Monte Carlo methods. We consider the important practical problem of specifying informative prior knowledge about sequences of this type. Two Gibbs sampling algorithms are contrasted and the sensitivity of the analysis to the prior specification is investigated. Model selection and possible ways to overcome the label switching problem are also addressed. Our analysis of intron 7 identifies three distinct homogeneous segment types, two of which occur in more than one region, and one of which is reversible.     

The Semiparametric Normal Variance-Mean Mixture Model

We study the normal variance-mean mixture model from a semiparametric point of view, i.e. we let the mixing distribution belong to a non-parametric family. The main results are consistency of the non-parametric maximum likelihood estimator and construction of an asymptotically normal and efficient estimator for the Euclidian part of the parameter. We study the model according to the theory outlined in the monograph by Bickel et al. (1993) and apply a general result (based on the theory of empirical processes) for semiparametric models from van der Vaart (1996) to prove asymptotic normality and efficiency of the proposed estimator.     

Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs

In this paper we consider the problem of estimating a coefficient of a strongly elliptic partial differential operator in stochastic parabolic equations. The coefficient is a bounded function of time. We compute the maximum likelihood estimate of the function on an approximating space (sieve) using a finite number of the spatial Fourier coefficients of the solution and establish conditions that guarantee consistency and asymptotic normality of the resulting estimate as the number of the coefficients increases. The equation is assumed diagonalizable in the sense that all the operators have a common system of eigenfunctions.     

Estimating the number of clusters

Hartigan (1975) defines the number q of clusters in a d ‐variate statistical population as the number of connected components of the set {f > c}, where f denotes the underlying density function on R^d and c is a given constant. Some usual cluster algorithms treat q as an input which must be given in advance. The authors propose a method for estimating this parameter which is based on the computation of the number of connected components of an estimate of {f > c}. This set estimator is constructed as a union of balls with centres at an appropriate subsample which is selected via a nonparametric density estimator of f. The asymptotic behaviour of the proposed method is analyzed. A simulation study and an example with real data are also included.     

Influence diagnostics in the capital asset pricing model under elliptical distributions

In this paper we consider the Capital Asset Pricing Model under Elliptical (symmetric) Distributions. This class of distributions, which contains the normal distribution, t, contaminated normal and power exponential, among others, offers a more flexible framework for modelling asset prices or returns. In order to analyze the sensibility to possible outliers and/or atypical returns of the maximum likelihood estimators, the local influence method was implemented. The results are illustrated by using a set of shares from companies who trade in the Chilean Stock Market. Our main conclusion is that symmetric distributions having heavier tails than those of the normal distribution, especially the t distribution with small degrees of freedom, show a better fit and allow the reduction of the influence of atypical returns in the maximum likelihood estimators.     

The analysis of age-specific fertility patterns via logistic models

In this paper, we introduce logistic models to analyse fertility curves. The models are formulated as linear models of the log odds of fertility and are defined in terms of parameters that are interpreted as measures of level, location and shape of the fertility schedule. This parameterization is useful for the evaluation, and interpretation of fertility trends and projections of future period fertility. For a series of years, the proposed models admit a state-space formulation that allows a coherent joint estimation of parameters and forecasting. The main features of the models compared with other alternatives are the functional simplicity, the flexibility, and the interpretability of the parameters. These and other features are analysed in this paper using examples and theoretical results. Data from different countries are analysed, and to validate the logistic approach, we compare the goodness of fit of the new model against well-known alternatives; the analysis gives superior results in most developed countries.     

Bootstrapping data with multiple levels of variation

The authors consider general estimators for the mean and variance parameters in the random effect model and in the transformation model for data with multiple levels of variation. They show that these estimators have different distributions under the two models unless all the variables have Gaussian distributions. They investigate the asymptotic properties of bootstrap procedures designed for the two models. They also report simulation results and illustrate the bootstraps using data on red spruce trees.     

Robust methods for generalized linear models with nonignorable missing covariates

The EM algorithm is often used for finding the maximum likelihood estimates in generalized linear models with incomplete data. In this article, the author presents a robust method in the framework of the maximum likelihood estimation for fitting generalized linear models when nonignorable covariates are missing. His robust approach is useful for downweighting any influential observations when estimating the model parameters. To avoid computational problems involving irreducibly high‐dimensional integrals, he adopts a Metropolis‐Hastings algorithm based on a Markov chain sampling method. He carries out simulations to investigate the behaviour of the robust estimates in the presence of outliers and missing covariates; furthermore, he compares these estimates to the classical maximum likelihood estimates. Finally, he illustrates his approach using data on the occurrence of delirium in patients operated on for abdominal aortic aneurysm.     

Inference in the presence of ranking error in ranked set sampling

The author proposes inference techniques for ranked set sample data in the presence of judgment ranking errors. He bases his analysis on the models of Bohn & Wolfe (1994) and Frey (2007a, b), of which parameters are estimated by minimizing a distance measure. He then uses the fitted models to calibrate confidence intervals and tests. He shows the validity of his approach through simulation and illustrates its application through the construction of distribution‐free confidence intervals for the median area of apple tree leaves covered by a spray.