Model Assisted Statistics and Applications

Recent renaming of the R.A. Fisher Award and Lectureship without official discussion among members of American Statistical Association (ASA), along with other events of similar type, was an important step in creating a new atmosphere in science in general. On the one hand, this is tightly related to such critical issues as freedom of speech, research and opinion, while on the other hand, it is related to conformity, yielding to irrelevant demand, and to denial of evidence as a first basic principle in science. The paper shows that a) all accusations against R. Fisher are factually groundless; b) the decision was motivated not by the facts, but by political and moral pressure, connected with allegedly “institutional racism” of the American society and the US police specifically; c) the decision was a natural consequence of the victimhood culture, which penetrates more and more into academia; d) this culture, in turn, is counter-scientific in a sense that it does not need any evidence; e) particularly, the most popular current thesis about “police bias against black people” – which seems a direct real trigger of the lecture renaming – cannot be confirmed by available data. Showing all that, the paper could be considered a warning against dangerous social tendencies in modern science in general and statistics in particular.

In this paper we revisit some issues related to the use of the Box-Cox transformation in censored and truncated regression models, which have been overlooked by the econometric and statistical literature. We first analyze the shape of the density function of the random variable which, rescaled by a Box-Cox transformation, leads to a normal random variable. Then, we identify the value ranges of the Box-Cox scale parameter for which a regular expectation of the derived random variable does not exist. This result calls for an extension of the concept of expectation, which can be computed regardless of the value of the scale parameter. For this purpose, we extend the concept of mean of a rescaled series of observations to the case of a random variable. Finally, we run estimates of censored and truncated Box-Cox standard Tobit models to determine the range of the scale parameter most relevant for empirical demand analyzes. These estimates highlight significant deviations from the assumption of normality of the dependent variable towards highly right skewed and leptokurtic distributions with no expectation.

The intentional killing of one human being by its own kind is considered the worst of the crimes. Therefore, homicide prevention is a major concern for policy makers in both developing and developed countries. We propose regression modeling for the homicide rates in Brazil along with appropriately chosen distributions for these responses that are in agreement with the restriction of values to the unit interval. We adopt the beta and simplex regression models with systematic components for the mean and dispersion parameters to explain the homicide rates in 27 state capitals of Brazil from the following explanatory variables: time, Gini coefficient, municipal human development index (MHDI), illiteracy and poverty rates. We employ standard likelihood techniques, perform influence and residual analysis and calculate goodness-of-fit statistics to select the best regression to explain homicides rates in these capitals. We perform the computations in the R package. The main results suggest the following: the mean homicide rate is increasing over time; there is a negative correlation between MHDI and murder rate; the poverty has a quite small negative impact on the mean homicide rates in the beta regression. The Gini coefficient and the illiteracy and poverty rates explain the dispersion of the homicide rates.

This paper deals with the problem of modelling time series data with structural breaks occur at multiple time points that may result in varying order of the model at every structural break. A flexible and generalized class of Autoregressive (AR) models with multiple structural breaks is proposed for modelling in such situations. Estimation of model parameters are discussed in both classical and Bayesian frameworks. Since the joint posterior of the parameters is not analytically tractable, we employ a Markov Chain Monte Carlo method, Gibbs sampling to simulate posterior sample. To verify the order change, a hypotheses test is constructed using posterior probability and compared with that of without breaks. The methodologies proposed here are illustrated by means of simulation study and a real data analysis.

Spatial panel data model captures spatial interactions across spatial units and over time. Lots of effort have been devoted to develop effective estimation methods for parametric and nonparametric spatial panel data models. Varying coefficient model has received a great deal of attention as an important tool for modeling panel data. In this paper we propose a kernel-based spatial error model for the purpose of analyzing spatial panel data. This model is based on the idea of fixed effect time-varying coefficient model and the kernel technique of support vector machine along with the technique of regularization. A generalized cross validation method is also considered for choosing the hyperparameters which affect the performance of the proposed model. The proposed model is evaluated through numerical studies.

This study introduces a measure called coefficient of within-cluster proximity (CWP) to evaluate the similarity of probability density functions (DFs) within clusters. After surveying the under and upper, and the computational problems of CWP, a fuzzy clustering algorithm for DFs is proposed. This algorithm can determine the suitable number of clusters and find the probability for each DF to belong to specific cluster. The convergence of the algorithm is considered in theory and illustrated by the numerical examples. The algorithm is applied to image recognition. The results show strong advantages of it in comparison to other algorithms. They also indicate the potential of the proposed approach in application to the data of different types.

Many researchers encounter the missing data problem. The phenomenon may be occasioned by data omission, non-response, death of respondents, recording errors, among others. It is important to find an appropriate data imputation technique to fill in the missing positions. In this study, the Expectation Maximization (EM) algorithm and two of its stochastic variants, stochastic EM (SEM) and Monte Carlo EM (MCEM), are employed in missing data imputation and parameter estimation in multivariate t distribution with unknown degrees of freedom. The imputation efficiencies of the three methods are then compared using mean square error (MSE) criterion. SEM yields the lowest MSE, making it the most efficient method in data imputation when the data assumes the multivariate t distribution. The algorithm’s stochastic nature enables it to avoid local saddle points and achieve global maxima; ultimately increasing its efficiency. The EM and MCEM techniques yield almost similar results. Large sample draws in the MCEM’s E-step yield more or less the same results as the deterministic EM. In parameter estimation, it is observed that the parameter estimates for EM and MCEM are relatively close to the simulated data’s maximum likelihood (ML) estimates. This is not the case in SEM, owing to the random nature of the algorithm.

In order to determine the potency of the test preparation relative to the standard preparation, it is often important to test parallelism between a pair of dose-response curves of reference standard and test sample. Optimal designs are known to be more powerful in testing parallelism as compared to classical designs. In this study, D-optimal design was implemented to study the parallelism and compare + its performance with a classical design. We modified D-optimal design to test the parallelism in the four-parameter logistic (4PL) model using Intersection-Union Test (IUT). IUT method is appropriate when the null hypothesis is expressed as a union of sets, and by using this method complicated tests involving several parameters are easily constructed. Since D-optimal design minimizes the variances of model parameters, it can bring more power to the IUT test. A simulation study will be presented to compare the empirical properties of the two different designs.