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Abstract: Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classic analysis and Bayesian analysis assuming no informative priors for the parameters of the model with cured fraction. A Bayesian approach is considered using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage are derived, analyzed and discussed in survival data with a cured fraction and covariates. The relevance of the approach is illustrated with a real data set, where it is shown that, by removing the most influential observations the decision about which model best fits the data is changed.
Keywords: cured fraction, local influence, generalized leverage, survival data.
Abstract: Flow cytometry scatter are ofen used in microbiology, and their measures are related to bacteria size and granulosity. We present an application of the skew-Laplace distribution to flow cytometry data. The goodness of fit is evaluated both graphically and numerically. We also study skewness and kurtosis values to assess usefulness of the skew-Laplace distribution.
Keywords: skew-Laplace distribution, goodness of fit, bacteria size.
Abstract: Equivalence testing is the natural approach to many statistical problems. First, its main application, bioequivalence testing, is reviewed. The basic concepts of bioequivalence testing (2×2 crossover designs, TOST, interval inclusion principle, etc.) and its problems (TOST biased character, the carryover problem, etc.) are considered. Next, equivalence testing is discussed more generally. Some applications and methods are reviewed and the relation of equivalence testing and distance-based inference is highlighted. A new distance-based method to determine whether two gene lists are equivalent in terms of their annotations in the Gene Ontology illustrates these ideas. We end with a general discussion and some suggestions for future research.
Keywords: Skew-normal distribution, maximum likelihood equations, moments.
Abstract: The main goal of this paper is to investigate how to estimate sampling design variances of model-based and model-assisted small area estimators in a complex survey sampling setup. For this sake, the Spanish Labour Force Survey is considered. Sample and aggregated data are taken from the Canary Islands in the second trimester of 2003 in order to obtain some small area estimators of ILO unemployment totals. Several problems arising from the application of standard small area estimation procedures to the survey are described. It is shown that standard variance estimators based on explicit formulas are not applicable in strict sense, since the assumptions under which they are derived do not hold. In addition two resampling techniques, bootstrap and jackknife are considered. These methods treat all the considered estimators in the same manner and therefore they can be used as performance measures to compare them. From the analysis of the obtained results, some recommendations are given.
Keywords: Labour Force Survey, small area estimation, linear models, mean square error, bootstrap, jackknife, unemployment totals, calibrated weights.
