Radon is a natural radioactive gas known to be the main contributor to natural background radiation exposure and the major leading cause of lung cancer second to smoking. Indoor radon concentration levels of 200 and 400 Bq/m3 are reference values suggested by the 90/143/Euratom recommendation, above which mitigation measures should be taken in new and old buildings, respectively, to reduce exposure to radon. Despite this international recommendation, Italy still does not have mandatory regulations or guidelines to deal with radon in dwellings. Monitoring surveys have been undertaken in a number of western European countries in order to assess the exposure of people to this radioactive gas and to identify radon prone areas. However, such campaigns provide concentration values in each single dwelling included in the sample, while it is often necessary to provide measures of the pollutant concentration which refer to sub-areas of the region under study. This requires a realignment of the spatial data from the level at which they are collected (points) to the level at which they are necessary (areas). This is known as change of support problem.In this paper, we propose a methodology based on geostatistical simulations in order to solve this problem and to identify radon prone areas which may be suggested for national guidelines.

In this article we use Monte Carlo analysis to assess the small sample behaviour of the OLS, the weighted least squares (WLS) and the mixed effects meta-estimators under several types of effect size heterogeneity, using the bias, the mean squared error and the size and power of the statistical tests as performance indicators. Specifically, we analyse the consequences of heterogeneity in effect size precision (heteroskedasticity) and of two types of random effect size variation, one where the variation holds for the entire sample, and one where only a subset of the sample of studies is affected. Our results show that the mixed effects estimator is to be preferred to the other two estimators in the first two situations, but that WLS outperforms OLS and mixed effects in the third situation. Our findings therefore show that, under circumstances that are quite common in practice, using the mixed effects estimator may be suboptimal and that the use of WLS is preferable.

The present study deals with the method of estimation of the parameters of k-components load-sharing parallel system model in which each component’s failure time distribution is assumed to be geometric. The maximum likelihood estimates of the load-share parameters with their standard errors are obtained. (1 − γ) 100% joint, Bonferroni simultaneous and two bootstrap confidence intervals for the parameters have been constructed. Further, recognizing the fact that life testing experiments are time consuming, it seems realistic to consider the load-share parameters to be random variable. Therefore, Bayes estimates along with their standard errors of the parameters are obtained by assuming Jeffrey’s invariant and gamma priors for the unknown parameters. Since, Bayes estimators can not be found in closed form expressions, Tierney and Kadane’s approximation method have been used to compute Bayes estimates and standard errors of the parameters. Markov Chain Monte Carlo technique such as Gibbs sampler is also used to obtain Bayes estimates and highest posterior density credible intervals of the load-share parameters. Metropolis–Hastings algorithm is used to generate samples from the posterior distributions of the unknown parameters.

We consider a, discrete time, weakly stationary bidimensional process, for which the spectral measure is the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. In this paper we are interested in estimating the spectral density of the absolutely continuous measure and of the density on the lines. For this aim, by using the double kernel method, we construct consistent estimators of these densities and we study their asymptotic behaviors in term of the mean squared error with rate.

Robust Statistics considers the quality of statistical decisions in the presence of deviations from the ideal model, where deviations are modelled by neighborhoods of a certain size about the ideal model. We introduce a new concept of optimality (radius-minimaxity) if this size or radius is not precisely known: for this notion, we determine the increase of the maximum risk over the minimax risk in the case that the optimally robust estimator for the false neighborhood radius is used. The maximum increase of the relative risk is minimized in the case that the radius is known only to belong to some interval [r l ,r u ]. We pursue this minmax approach for a number of ideal models and a variety of neighborhoods. Also, the effect of increasing parameter dimension is studied for these models. The minimax increase of relative risk in case the radius is completely unknown, compared with that of the most robust procedure, is 18.1% versus 57.1% and 50.5% versus 172.1% for one-dimensional location and scale, respectively, and less than 1/3 in other typical contamination models. In most models considered so far, the radius needs to be specified only up to a factor $$\rho\le \frac{1}{3}$$ , in order to keep the increase of relative risk below 12.5%, provided that the radius–minimax robust estimator is employed. The least favorable radii leading to the radius–minimax estimators turn out small: 5–6% contamination, at sample size 100.

The main goal of the paper is to specify a suitable multivariate multilevel model for polytomous responses with a non-ignorable missing data mechanisminordertodeterminethefactorswhichinfluencethewayofacquisi- tion of the skills of the graduates and to evaluate the degree programmes on the basis of the adequacy of the skills they give to their graduates. The application is based on data gathered by a telephone survey conducted, about two years after the degree, on the graduates of year 2000 of the University of Florence. A multilevel multinomial logit model for the response of interest is fitted simul- taneously with a multilevel logit model for the selection mechanism by means of maximum likelihood with adaptive Gaussian quadrature. In the application the multilevel structure has a crucial role, while selection bias results negligible. The analysis of the empirical Bayes residuals allows to detect some extreme degree programmes to be further inspected.

The present paper proposes a PLS-based methodology for the study of so called “L” data-structures, where external information on both the rows and the columns of a dependent variable matrix is available. L-structures are frequently encountered in consumer preference analysis. In this domain it may be desirable to study the influence of both product and consumer descriptors on consumer preferences. The proposed methodology has been applied on data from the cosmetic industry. The preference scores from 142 consumers on 9 products were explained with respect to the products’ physico-chemical and sensory descriptors, and the consumers’ socio-demographic and behavioural characteristics.

In this paper we consider the inferential aspect of the nonparametric estimation of a conditional function \(g({\bf x};\phi)={\mathop{\mathbb E}\nolimits}[\phi(X_{t})|{\bf X}_{t,m}]\), where Xt,m represents the vector containing the m conditioning lagged values of the series. Here \(\phi\) is an arbitrary measurable function. The local polynomial estimator of order p is used for the estimation of the function g, and of its partial derivatives up to a total order p. We consider α-mixing processes, and we propose the use of a particular resampling method, the local polynomial bootstrap, for the approximation of the sampling distribution of the estimator. After analyzing the consistency of the proposed method, we present a simulation study which gives evidence of its finite sample behaviour.

This paper deals with the analysis of datasets, where the subjects are described by the estimated means of a p-dimensional variable. Classical statistical methods of data analysis do not treat measurements affected by intrinsic variability, as in the case of estimates, so that the heterogeneity induced among subjects by this condition is not taken into account. In this paper a way to solve the problem is suggested in the context of symbolic data analysis, whose specific aim is to handle data tables where single valued measurements are substituted by complex data structures like frequency distributions, intervals, and sets of values. A principal component analysis is carried out according to this proposal, with a significant improvement in the treatment of information.