On the recoding of continuous and bounded indexes to a binomial form: an application to quality-of-life scores

The statistical analysis of patient-reported outcomes (PROs) as endpoints has shown to be of great practical relevance. The resulting scores or indexes from the questionnaires used to measure PROs could be treated as continuous or ordinal. The goal of this study is to propose and evaluate a recoding process of the scores, so that they can be treated as binomial outcomes and, therefore, analyzed using logistic regression with random effects. The general methodology of recoding is based on the observable values of the scores. In order to obtain an optimal recoding, the evaluation of the recoding method is tested for different values of the parameters of the binomial distribution and different probability distributions of the random effects. We illustrate, evaluate and validate the proposed method of recoding with the Short Form-36 (SF-36) Survey and real data. The optimal recoding approach is very useful and flexible. Moreover, it has a natural interpretation, not only for ordinal scores, but also for questionnaires with many dimensions and different profiles, where a common method of analysis is desired, such as the SF-36.     

Identifying radon-prone building typologies by marginal modelling

Radon is a naturally occurring decay product of uranium known to be the main contributor to natural background radiation exposure. It has been established that the health risk related to radon exposure is lung cancer. In fact, radon is considered to be a major leading cause of lung cancer, second only to smoking. In this paper, we identified building typologies that affect the probability of detecting indoor radon concentration above reference values, using the data collected within two monitoring campaigns recently conducted in Northern Italy. This information is fundamental both in prevention, i.e. when the construction of a new building is planned and in mitigation, i.e. when a high concentration detected inside buildings has to be reduced. A spatial regression approach for binary data was adopted for this goal where some relevant covariates on the soil were retrieved by linking external spatial databases.     

On optimising the estimation of high quantiles of a probability distribution

One of the major aims of one-dimensional extreme-value theory is to estimate quantiles outside the sample or at the boundary of the sample. The underlying idea of any method to do this is to estimate a quantile well inside the sample but near the boundary and then to shift it somehow to the right place. The choice of this “anchor quantile” plays a major role in the accuracy of the method. We present a bootstrap method to achieve the optimal choice of sample fraction in the estimation of either high quantile or endpoint estimation which extends earlier results by Hall and Weissman (1997) in the case of high quantile estimation. We give detailed results for the estimators used by Dekkers et al. (1989). An alternative way of attacking problems like this one is given in a paper by Drees and Kaufmann (1998).     

Nonparametric comparison of curves with dependent errors

Suppose that data {(x _l,i,n , y _l,i,n ): l?=?1, …, k; i?=?1, …, n} are observed from the regression models: Y _l,i,n ?=?m _l (x _l,i,n )?+?? _l,i,n , l?=?1, …, k, where the regression functions {m _l } _l=1 ^k are unknown and the random errors {? _l,i,n } are dependent, following an MA(∞) structure. A new test is proposed for testing the hypothesis H ₀: m ₁?=?·?·?·?=?m _k , without assuming that {m _l } _l=1 ^k are in a parametric family. The criterion of the test derives from a Crámer-von-Mises-type functional based on different distances between {[mcirc]} _l and {[mcirc]} _s , l?≠?s, l, s?=?1, …, k, where {[mcirc] _l } _l=1 ^k are nonparametric Gasser–Müller estimators of {m _l } _l=1 ^k . A generalization of the test to the case of unequal design points, with different sample sizes {n _l } _l=1 ^k and different design densities {f _l } _l=1 ^k , is also considered. The asymptotic normality of the test statistic is obtained under general conditions. Finally, a simulation study and an analysis with real data show a good behavior of the proposed test.     

Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test

We study distributional properties of generalized order statistics (gos) related by a random shift or scaling scheme in the continuous and discrete case, respectively. In the continuous case, we obtain new characterizations of distributions relating non-neighbouring gos extending some results given in the literature for the neighbouring cases. On the other hand, in the discrete case, we investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose gos are related by a random translation.     

Random translation of discrete order statistics

We investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose order statistics are related by a random translation. We also provide some examples using the constructive method that we propose.     

A bibliography of statistical tolerance regions

The bibliography contains about 270 references dealing with statistical tolerance regions. These are classified according to the type of probability distribution concerned and according to some other criteria as well.     

Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

Percentile Related Bounds and Estimator for the Mean of the Negative Binomial Distribution

Upper and lower bounds are obtained for the mean of the negative binomial distribution. These bounds are simple functions of a percentile determined by the shape parameter. The result is then used to obtain a robust estimate of the mean when the shape parameter is known.     

An Exponential Model for Damage Accumulation

In this article, we present a general model for predicting the fatigue behavior for any stress level and amplitude using the exponential model. Based on the Wöhler field for fixed stress level, a compatibility functional equation enables us to derive the general model with eight parameters. The problem of parameter estimation is then discussed and some methods are described. Some examples are finally presented to illustrate the derived model and the proposed methods of estimation.