The effects of data input errors on subsequent statistical inference

Data input errors can potentially affect statistical inferences, but little research has been published to date on this topic. In the present paper, we report the effect of data input errors on the statistical inferences drawn about population parameters in an empirical study involving 280 students from two Polish universities, namely the Warsaw University of Life Sciences – SGGW and the University of Information Technology and Management in Rzeszow. We found that 28% of the students committed at least one data error. While some of these errors were small and did not have any real effect, a few of them had substantial effects on the statistical inferences drawn about the population parameters.     

Exact Likelihood Inference for k Exponential Populations Under Joint Type-II Censoring

In this paper, when a jointly Type-II censored sample arising from k independent exponential populations is available, the conditional MLEs of the k exponential mean parameters are derived. The moment generating functions and the exact densities of these MLEs are obtained using which exact confidence intervals are developed for the parameters. Moreover, approximate confidence intervals based on the asymptotic normality of the MLEs and credible confidence regions from a Bayesian viewpoint are also discussed. An empirical comparison of the exact, approximate, bootstrap, and Bayesian intervals is also made in terms of coverage probabilities. Finally, an example is presented in order to illustrate all the methods of inference developed here.     

Some Results Based on a Version of the Generalized Dynamic Entropies

We propose new dynamic measures of uncertainty based on the notion of generalized dynamic entropy introduced in Di Crescenzo and Longobardi (2006). These can uniquely determine distribution functions in continuous and discrete cases, and the characterizations of some well-known distributions are provided. We also define some orderings and aging notions based on the generalized dynamic measures, and prove some of their properties, obtaining as corollaries results that have recently appeared in the literature.     

Construction of Fuzzy Control Charts Based on Weighted Possibilistic Mean

The problem of constructing control charts for fuzzy data has been considered in literature. The proposed transformation approaches and direct fuzzy approaches have their advantages and disadvantages. The representative values charts based on transformation methods are often recommended in practical application. For representing a fuzzy set by a crisp value, the weight of importance of the members assigned with some membership levels in a fuzzy set should be considered, and the possibility theory can be employed to deal with such problem. In this article, we propose to employ the weighted possibilistic mean (WPM), weighted interval valued possibilistic mean (WIVPM) of fuzzy number as a sort of representative values for the fuzzy attribute data, and establish new fuzzy control charts with WPM and WIVPM. The performance of the charts is compared to the existing fuzzy charts with a fuzzy c-chart example via newly defined average number of inspection for variation of control state.     

Bayesian optimal sequential design for nonparametric regression via inhomogeneous evolutionary MCMC

We develop a novel computational methodology for Bayesian optimal sequential design for nonparametric regression. This computational methodology, that we call inhomogeneous evolutionary Markov chain Monte Carlo, combines ideas of simulated annealing, genetic or evolutionary algorithms, and Markov chain Monte Carlo. Our framework allows optimality criteria with general utility functions and general classes of priors for the underlying regression function. We illustrate the usefulness of our novel methodology with applications to experimental design for nonparametric function estimation using Gaussian process priors and free-knot cubic splines priors.     

Generating synthetic data to produce public-use microdata for small geographic areas based on complex sample survey data with application to the National Health Interview Survey

Small area statistics obtained from sample survey data provide a critical source of information used to study health, economic, and sociological trends. However, most large-scale sample surveys are not designed for the purpose of producing small area statistics. Moreover, data disseminators are prevented from releasing public-use microdata for small geographic areas for disclosure reasons; thus, limiting the utility of the data they collect. This research evaluates a synthetic data method, intended for data disseminators, for releasing public-use microdata for small geographic areas based on complex sample survey data. The method replaces all observed survey values with synthetic (or imputed) values generated from a hierarchical Bayesian model that explicitly accounts for complex sample design features, including stratification, clustering, and sampling weights. The method is applied to restricted microdata from the National Health Interview Survey and synthetic data are generated for both sampled and non-sampled small areas. The analytic validity of the resulting small area inferences is assessed by direct comparison with the actual data, a simulation study, and a cross-validation study.     

Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes

We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.     

The Gamma-count distribution in the analysis of experimental underdispersed data

Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of counts by Gaussian regression models ignores the discreteness, asymmetry and heteroscedasticity and is inefficient, providing unrealistic standard errors or possibly negative predictions of the expected number of events. The Poisson regression is the standard model for count data with underlying assumptions on the generating process which may be implausible in many applications. Statisticians have long recognized the limitation of imposing equidispersion under the Poisson regression model. A typical situation is when the conditional variance exceeds the conditional mean, in which case models allowing for overdispersion are routinely used. Less reported is the case of underdispersion with fewer modeling alternatives and assessments available in the literature. One of such alternatives, the Gamma-count model, is adopted here in the analysis of an agronomic experiment designed to investigate the effect of levels of defoliation on different phenological states upon the number of cotton bolls. Data set and code for analysis are available as online supplements. Results show improvements over the Poisson model and the semi-parametric quasi-Poisson model in capturing the observed variability in the data. Estimating rather than assuming the underlying variance process leads to important insights into the process.     

Transect-spacing design of ice cores on the Antarctic continent

Chemical analyses of ice cores, drilled deep into an ice sheet, provide a historical record of the earth's atmosphere that dates back as far as 400,000–500,000 years. Although the atmosphere mixes quite well, it is recognized that spatial variability associated with ice-core locations should be allowed for. In this article, spatial statistical methodology is applied to the design question of finding the best spacing of ice-core locations on a partial transect of Antarctica.     

Acute Middle Ear Infection in Small Children: A Bayesian Analysis Using Multiple Time Scales

The study is based on a sample of 965 children living in Oulu region (Finland), who were monitored for acute middle ear infections from birth to the age of two years. We introduce a nonparametrically defined intensity model for ear infections, which involves both fixed and time dependent covariates, such as calendar time, current age, length of breast-feeding time until present, or current type of day care. Unmeasured heterogeneity, which manifests itself in frequent infections in some children and rare in others and which cannot be explained in terms of the known covariates, is modelled by using individual frailty parameters. A Bayesian approach is proposed to solve the inferential problem. The numerical work is carried out by Monte Carlo integration (Metropolis-Hastings algorithm).