Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of them may negatively affect the inferences drawn. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to deal with missing data. The former assumes a normal distribution of the variables in the imputation model and the latter fills in missing values taking into account the distributional form of the variables to be imputed. This study examines the performance of these methods when data are missing at random on unordered categorical variables treated as predictors in the regression models. First, a survey data set with no missing values is used to generate a data set with missing at random observations on unordered categorical variables. Then, the two methods are separately used to impute the missing values of the generated data set. Their performance is compared in terms of bias and standard errors of the estimates from the regression models that determine the association between the woman’s contraceptive methods use status and her marital status, controlling for the region of origin. The baseline data used is the 2007 Demographic and Health Survey (DHS) data set from the Democratic Republic of Congo. The findings indicate that although the MVNI relies on the statistical parametric theory, it produces more accurate estimates than MICE for nonordered categorical variables.

The limiting tail behaviour of distributions is known to follow one of three possible limiting distributions, depending on the domain of attraction of the observational model under suitable regularity conditions. This work proposes a new approach for identification and analysis of the shape parameter of the GPD as a mixture distribution over the three possible regimes. This estimation is based on evaluation of posterior probabilities for each regime. The model-based approach uses a mixture at the observational level where a Generalized Pareto distribution (GPD) is assumed above the threshold, and mixture of Gammas distributions is used under a threshold. The threshold is also estimated. Simulation exercises were conducted to evaluate the accuracy of the model for various parameter settings and sample sizes, specifically in the estimation of high quantiles. They show an improved performance over existing approaches. The paper also compares inferences based on Bayesian regime choice against Bayesian averaging over the regimes. Results of environmental applications show the correctly identifying the GPD regime plays a vital role in these studies.

Asymptotic normality of density estimates often requires the continuity of the underlying density and assumptions on its derivatives. Recently, these assumptions have been weakened for some estimates using the less restrictive notion of regularity index. However, the particular definition of this index makes it unusable for many estimates. In this paper, we define a more general regularity concept: the $r$-regularity. This concept is used to obtain asymptotic law of the histogram without hypothesis on the continuity of the underlying density. As expected, when it does exist, the limit distribution is a standard Gaussian. Then, to illustrate the new definition of $r$-regularity, examples are studied.

Recently Dutta and Bhattacharya (Statistical Methodology 16 (2014) 100–116) introduced a novel Markov Chain Monte Carlo methodology that can simultaneously update all the components of high-dimensional parameters using simple deterministic transformations of a one-dimensional random variable drawn from any arbitrary distribution defined on a relevant support. The methodology, which the authors refer to as transformation-based Markov Chain Monte Carlo (TMCMC), greatly enhances computational speed and acceptance rate in high-dimensional problems. Two significant transformations associated with TMCMC are additive and multiplicative transformations. Combinations of additive and multiplicative transformations are also of much interest. In this work, we investigate geometric ergodicity associated with additive and multiplicative TMCMC, along with their combinations, assuming that the target distribution is multi-dimensional and belongs to the super-exponential family; we also illustrate their efficiency in practice with simulation studies.

Extraction of a signal in the presence of stochastic noise via wavelet shrinkage has been studied under assumptions that the noise is independent and identically distributed (IID) and that the samples are equispaced (evenly spaced in time). Previous work has relaxed these assumptions either to allow for correlated observations or to allow for random sampling, but very few papers have relaxed both together. In this paper we relax both assumptions by assuming the noise to be a stationary Gaussian process and by assuming a random sampling scheme dictated either by a uniform distribution or by an evenly spaced design subject to jittering. We show that, if the data are treated as if they were autocorrelated and equispaced, the resulting wavelet-based shrinkage estimator achieves an almost optimal convergence rate. We investigate the efficacy of the proposed methodology via simulation studies and illustrate it by the extraction of the light curve for a variable star.

This paper presents a spatiotemporal dynamic model which allows Bayesian inference of precipitation states in some Venezuelan meteorological stations. One of the limitations that are reported in digital databases is the reliability of the records and the lack of information for certain days, weeks, or months. To complete the missing data, the Gibbs algorithm, a Markov Chain Monte Carlo (MCMC) procedure, was used. A feature of precipitation series is that their distribution contains discrete and continuous components implying complicated dynamics. A model is proposed based on a discrete representation of a stochastic integro-difference equation. Given the difficulty of obtaining explicit analytical expressions for the predictive posterior distribution, approximations were obtained using a sequential Monte Carlo algorithm called the parallelized ensemble Kalman filter. The proposed method permits the completion of the missing data in the series where required and secondly allows the splitting of a large database into smaller ones for separate evaluation and eventual combination of the individual results. The objective is to reduce the dimension and computational cost in order to obtain models that are able to describe the reality in real time. It was shown that the obtained models are able to predict spatially and temporally the states of rainfall for at least three to four days quickly, efficiently and accurately. Three methods of statistical validation were used to evaluate the performance of the model and showed no significant discrepancies. Speedup and efficiency factors were calculated to compare the speed of calculation using the parallelized ensemble Kalman filter algorithm with the speed of the sequential version. The improvement in speed for four pthread executions was greatest.

Let $P(x)$ be a polynomial monotone increasing on $(-\infty,+\infty)$. The probability distribution possessing the distribution function

\[F(x)=\frac{1}{1+\exp\{-P(x)\}}\] is called the polynomial logistic distribution associated with polynomial $P$ and denoted by PL($P$). It has recently been introduced, as a generalization of the logistic distribution, by V. M. Koutras, K. Drakos, and M. V. Koutras who have also demonstrated the importance of this distribution in modeling financial data. In the present paper, for a random variable $X\sim\mathrm{PL}(P)$, the analytical properties of its characteristic function are examined, the moment-(in)determinacy for the powers $X^{m},\;m\in\mathbb{N}$ and $|X|^{p},\;p\in(0,+\infty)$ depending on the values of $m$ and $p$ is investigated, and exemplary Stieltjes classes for the moment-indeterminate powers of $X$ are constructed.

We study the consistency of a Bayesian variable selection procedure for generalized linear models. Specifically, we consider the consistency of a Bayes factor based on $g$-priors proposed by Sabanés Bové and Held [Bayesian Analysis 6 (2011) 387–410]. The integrals necessary for the computation of this Bayes factor are performed with Laplace approximation and Gaussian quadrature. We show that, under certain regularity conditions, the resulting Bayes factor is consistent. Furthermore, a simulation study confirms our theoretical results. Finally, we illustrate this model selection procedure with an application to a real ecological dataset.