Bayesian assessment of times to diagnosis in breast cancer screening

Breast cancer is one of the diseases with the most profound impact on health in developed countries and mammography is the most popular method for detecting breast cancer at a very early stage. This paper focuses on the waiting period from a positive mammogram until a confirmatory diagnosis is carried out in hospital. Generalized linear mixed models are used to perform the statistical analysis, always within the Bayesian reasoning. Markov chain Monte Carlo algorithms are applied for estimation by simulating the posterior distribution of the parameters and hyperparameters of the model through the free software WinBUGS.     

Exploring the number of groups in robust model-based clustering

Two key questions in Clustering problems are how to determine the number of groups properly and measure the strength of group-assignments. These questions are specially involved when the presence of certain fraction of outlying data is also expected.     

Order statistics from overlapping samples: bivariate densities and regression properties

In this paper, we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent distribution is absolutely continuous. We are also interested in the question to what extent conditional expectation of one of such order statistic given another determines the parent distribution. In particular, we provide a new characterization by linearity of regression of an order statistic from the extended sample given the one from the original sample, special case of which solves a problem explicitly stated in the literature. It appears that to describe the correct parent distribution it is convenient to use quantile density functions. In several other cases of regressions of order statistics we provide new results regarding uniqueness of the distribution in the sample.     

Distribution of cost inefficiency in stochastic frontier approach: evidence from Spanish banking

The aim of the paper is to demonstrate the appropriateness of an a priori analysis to determine the distributional assumption of the inefficiency term in a stochastic frontier model. To this end, theoretical distributions of estimated inefficiency were obtained when the inefficiency term is assumed to be distributed as a half normal and an exponential in a cost frontier model. Comparisons of such theoretical distributions with the respective cost inefficiency estimators using the goodness of fit test allow selecting the most appropriate distributional assumption. The application on three data sets of Spanish banking system in 2009 demonstrated the relevance of the research question. First, the results of estimated cost inefficiency with a half normal assumption are larger than with an exponential distribution significantly. Besides, half normal assumption was rejected and exponential was not rejected as the most appropriate distribution of inefficiency term in Spanish banking data set. However, the adjustment of saving banks data had been better with the former distribution than the latter. In the case of banks, any distribution results appropriate. To sum up, this work demonstrate that the distributional assumption on inefficiency term in Stochastic Frontier Approach must be established in a justified way, as it can significantly bias the results of estimated inefficiency and therefore, influences improving policies and strategies in the Spanish banking sector.     

Model Selection Using Conditional Densities

In this article we propose a new method to select a discrete model f(x; θ), based on the conditional density of a sample given the value of a sufficient statistic for θ. The main idea is to work with a broad family of discrete distributions, called the family of power series distribution, for which there is a common sufficient statistic for the parameter of interest. The proposed method uses the maximum conditional density in order to select the best model.

We compare our proposal with the usual methodology based on Bayes factors. We provide several examples that show that our proposal works fine in most instances. Bayes factors are strongly dependent on the prior information about the parameters. Since our method does not require the specification of a prior distribution, it provides a useful alternative to Bayes factors.     

A note on the moments of stochastic shrinkage parameters in ridge regression

The purpose of this note is to gain insight on the performance of two well known operational Ridge Regression estimators by deriving the moments of their stochastic shrinkage parameters. We also show that, under certain conditions, one of them has bounded moments.     

Optimal Method for Realizing Two-Sided Inferences About a Linear Combination of Two Proportions

In order to reach the inference about a linear combination of two independent binomial proportions, various procedures exist (Wald's classic method, the exact, approximate, or maximized score methods, and the Newcombe-Zou method). This article defines and evaluates 25 different methods of inference, and selects the ones with the best behavior. In general terms, the optimal method is the classic Wald method applied to the data to which z ² _α/2/4 successes and z ² _α/2/4 failures are added (≈1 if α = 5%) if no sample proportion has a value of 0 or 1 (otherwise the added increase may be different).

Supplemental materials are available for this article. Go to the publisher's online edition of Communications in Statistics - Simulation and Computation to view the free supplemental file.     

Another approach to inverting a covariance matrix when data are unbalanced

Searle and Rudan (1973) derive the inverse of a covariance matrix for unbalanced data in ANOVA. Their expression is highly complicated. This paper presents an alternative derivation and shows how unbalancedness enters in.     

CO-tucker: a new method for the simultaneous analysis of a sequence of paired tables

Relationships between species and their environment are a key component to understand ecological communities. Usually, this kind of data are repeated over time or space for communities and their environment, which leads to a sequence of pairs of ecological tables, i.e. multi-way matrices. This work proposes a new method which is a combined approach of STATICO and Tucker3 techniques and deals to the problem of describing not only the stable part of the dynamics of structure–function relationships between communities and their environment (in different locations and/or at different times), but also the interactions and changes associated with the ecosystems’ dynamics. At the same time, emphasis is given to the comparison with the STATICO method on the same (real) data set, where advantages and drawbacks are explored and discussed. Thus, this study produces a general methodological framework and develops a new technique to facilitate the use of these practices by researchers. Furthermore, from this first approach with estuarine environmental data one of the major advantages of modeling ecological data sets with the CO-TUCKER model is the gain in interpretability.