Statistical and computational tradeoff in genetic algorithm-based estimation

When a genetic algorithm (GA) is employed in a statistical problem, the result is affected by both variability due to sampling and the stochastic elements of algorithm. Both of these components should be controlled in order to obtain reliable results. In the present work we analyze parametric estimation problems tackled by GAs, and pursue two objectives: the first one is related to a formal variability analysis of final estimates, showing that it can be easily decomposed in the two sources of variability. In the second one we introduce a framework of GA estimation with fixed computational resources, which is a form of statistical and the computational tradeoff question, crucial in recent problems. In this situation the result should be optimal from both the statistical and computational point of view, considering the two sources of variability and the constraints on resources. Simulation studies will be presented for illustrating the proposed method and the statistical and computational tradeoff question.     

Bayesian comparative study on binary time series

In this paper, we consider the Bayesian analysis of binary time series with different priors, namely normal, Students' t, and Jeffreys prior, and compare the results with the frequentist methods through some simulation experiments and one real data on daily rainfall in inches at Mount Washington, NH. Among Bayesian methods, our results show that the Jeffreys prior perform better in most of the situations for both the simulation and the rainfall data. Furthermore, among weakly informative priors considered, Student's t prior with 7 degrees of freedom fits the data most adequately.     

Sharp bounds for the mean of the total time on test for distributions with increasing generalized failure rate

The results of this paper are the continuation of the research presented by Bieniek [Optimal bounds for the mean of the total time on test for distributions with decreasing generalized failure rate. Statistics. 2016;50:1206–1220]. We consider the remaining total time on test after a given failure in a life test experiment. We derive sharp upper bounds on the mean of the total time on test optimal in the class of distributions with increasing generalized failure rate with respect to generalized Pareto distributions. Specific results are obtained for distributions with increasing density and increasing failure rate. We also provide exemplary numerical values of the obtained bounds and we compare them with the corresponding bounds for distributions with decreasing generalized failure rate.     

Ordering results on extremes of scaled random variables with dependence and proportional hazards

This study deals with random variables equipped with Archimedean copulas and following scale proportional hazards (SPHs) or revered hazards models. We build the usual stochastic order both between minimums of two SPHs samples with Archimedean survival copulas and between maximums from two scale proportional reversed hazards (PRHs) samples with Archimedean copulas. The hazard rate order between minimums of independent SPHs samples and the reversed hazard rate order between maximums of independent scale PRHs samples are both derived. Also we have a discussion on the dispersive order between minimums from samples with a common Archimedean survival copula. The present results either generalize or improve some related ones in the recent literature.     

Verification in biometric systems: problems and modern methods of their solution

The paper deals with the problem of electronic verification of people on the basis of measurement information of a fingerprint reader and new approaches to its solution. The offered method guaranties the restriction of error probabilities of both type at the desired level at making a decision about permitting or rejecting the request on service in the system. On the basis of investigation of real data obtained in the real biometrical system, the choice of distribution laws is substantiated and the proper estimations of their parameters are obtained. Using chosen distribution laws, the normal distribution for measurement results of characteristics of the people having access to the system and the beta distribution for the people having no such access, the optimal rule based on the Constrained Bayesian Method (CBM) of making a decision about giving a permission of access to the users of the system is justified. The CBM, the Neyman–Pearson and classical Bayes methods are investigated and their good and negative points are examined. Computation results obtained by direct computation, by simulation and using real data completely confirm the suppositions made and the high quality of verification results obtained on their basis.     

Allocation strategies of standby redundancies in series/parallel system

This article deals with the topic of optimal allocation of two standby redundancies in a two-component series/parallel system. There are two original components C₁ and C₂ which can be used to construct a series/parallel system, and two spares R₁ (same as C₁) and R₂ (different from both C₁ and C₂) at hand with them being standby redundancies so as to enhance the reliability level of the system. The goal for an engineer is to seek after the optimal allocation policy in this framework. It is shown that, for the series structure, the engineer should allocate R₂ to C₁ and R₁ to C₂ provided that C₁ (or R₁) performs either the best or worst among all the units; otherwise, the allocation policy should be reversed. For the parallel structure, the optimal allocation strategy is just opposed to that of series case. We also provide some numerical examples for illustrating the theoretical results.     

An introduction to copula-based bivariate reliability Concepts

Several attempts were made in the literature to generalize the notions based on univariate quantiles to higher dimensions. As quantile-based reliability concepts are receiving much attention, it is important to address these problems in the field of Reliability theory. In this paper, bivariate reliability concepts using the dependence structure are introduced. The properties and characterizations of the bivariate reliability concepts are presented; it includes the characterization based on the relationship between bivariate hazard rate and bivariate mean residual life. The bivariate reliability concepts in reversed time are also studied.     

A note on stable limit theory for the OLSE with non usual rates and the heteroskedasticity robust Wald test

We are occupied with an example concerning the limit theory of the ordinary least squares estimator (OLSE) when the innovation process of the regression has the form of a martingale transform the iid part of which lies in the domain of attraction of an α-stable distribution, the scaling sequence has a potentially diverging truncated α-moment, and the regressor process has a potentially divergent truncated second moment. We obtain matrix rates that reflect the stability parameter as well as the slow variations present in the aforementioned sequences, and stable limits. We also derive asymptotic exactness, consistency, and local asymptotic unbiasedness under appropriate local alternatives for a heteroskedasticity robust Wald test based on subsampling. The results could be useful for inference on the factor loadings in an instance of the APT model.     

On the mean L1-error in the heteroscedastic deconvolution problem with compactly supported noises

We study the heteroscedastic deconvolution problem when random noises have compactly supported densities. In this context, the Fourier transforms of the densities can vanish on the real line. We propose a truncated type of estimator for target density and derive the convergence rate of the mean L¹-error uniformly over a class of target densities. A lower bound for the mean L¹-error is also established. Some simulations will be given to illustrate the performance of the proposed estimator.     

A unified approach to stochastic comparisons of multivariate mixture models

In this paper, we consider a unified approach to stochastic comparisons of random vectors corresponding to two general multivariate mixture models. These stochastic comparisons are made with respect to multivariate hazard rate, reversed hazard rate and likelihood ratio orders. As an application, results are presented for stochastic comparisons of generalized multivariate frailty models.