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The meta-analysis of P-values is a widely used method in integrating information from multiple studies, and much research has focused on combining P-values. Among the established approaches, Fisher's test may be the most popular one. Many studies have been devoted to extending or modifying Fisher's statistic. For example, Lancaster's variation of Fisher's method may outperform the weighted Z-test and recently has drawn noteworthy attention. In this study, we first extend Lancaster's statistic by incorporating a weighting scheme. An approximation and an algorithm that are suitable for use under both independence and dependence assumptions are proposed for calculating the distribution of the weighted Lancaster statistic. The relationships between this method and existing ones are discussed. An application of the main results to a linkage test method in human gene mapping is then provided to show its use. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a new kernel regression estimators based on the two-time-scale stochastic approximation algorithm in the case of independent functional data. We study the properties of the proposed recursive estimators and compare them with the recursive estimators based on single-time-scale stochastic algorithm proposed by Slaoui and to the non-recursive estimator proposed by Slaoui. It turns out that, with an adequate choice of the parameters, the proposed two-time-scale estimators perform better than the recursive estimators constructed using single-time-scale stochastic algorithm. We corroborate these theoretical results through some simulations and two real datasets. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extension of the generalized class of recursive regression estimators to the case of strong mixing data. Then, we study the properties of these estimators and compare them with the well known Nadaraya-Watson estimator. The Bias, variance and Mean Integrated Square Error are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that the proposed recursive estimators allowed us to obtain quite better results compared to the non-recursive regression estimator under α-mixing condition in terms of estimation error and much better in terms of computational costs. [ABSTRACT FROM AUTHOR]

The correlational structure of a set of variables is often conveniently described by the pairwise partial correlations as they contain the same information as the Pearson correlations with the advantage of straightforward identifications of conditional linear independence. For mathematical convenience, multiple matrix representations of the pairwise partial correlations exist in the literature but their properties have not been investigated thoroughly. In this paper, we derive necessary and sufficient conditions for the eigenvalues of differently defined partial correlation matrices so that the correlation structure is a valid one. Equipped with these conditions, we will then emphasize the intricacies of algorithmic generations of correlation structures via partial correlation matrices. Furthermore, we examine the space of valid partial correlation structures and juxtapose it with the space of valid Pearson correlation structures. As these spaces turn out to be equal in volume for every dimension and equivalent with respect to rotation, a simple formula allows the creation of valid partial correlation matrices by the use of current algorithms for the generation and approximation of correlation matrices. Lastly, we derive simple conditions on the partial correlations for frequently assumed sparse structures. [ABSTRACT FROM AUTHOR]

This paper considers a new model in search theory to find a randomly located target in the 3-dimensional space. An approximation algorithm that facilitates searching procedures for searchers or robots is presented. The expected time to detect the target is also proved. The statistical analysis by calculating the optimal search strategy which minimizes the time to detect the target, assuming trivariate standard normal distribution is provided, and the technique by flowcharts is designed as well. The effectiveness of this strategy is illustrated by introducing an application from real world. [ABSTRACT FROM AUTHOR]

In this article we propose an automatic selection of the bandwidth of the recursive kernel density estimators for spatial data defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the MWISE (Mean Weighted Integrated Squared Error), the recursive estimator will be quite similar to the nonrecursive one in terms of estimation error and much better in terms of computational costs. In addition, we obtain the central limit theorem for the nonparametric recursive density estimator under some mild conditions. [ABSTRACT FROM AUTHOR]

To explore the operation characteristics of survival group sequential trials with a fixed follow-up period, the accrual time and total trial duration to ensure power and type I error rate requirements are explained and investigated for hazard ratios ranging from 1.3 to 3.0, with slow or high accrual rate, and in the presence or absence of censoring. Impacts of hazard rate, accrual rate, and competitive censoring on accrual time and subsequently on total trial duration are carefully illustrated. Real time for interim analyses, needed number of events, and recruited number of subjects at time of interim analyses are also tabulated. [ABSTRACT FROM AUTHOR]

Many mathematical and physical problems are led to find a root of a real functionf. This kind of equation is an inverse problem and it is difficult to solve it. Especially in engineering sciences, the analytical expression of the functionfis unknown to the experimenter, but it can be measured at each pointxkwithM(xk) as expected value and induced error ξk. The aim is to approximate the unique root θ under some assumptions on the functionfand errors ξk. We use a stochastic approximation algorithm that constructs a sequence (xk)k ⩾ 1. We establish the almost complete convergence of the sequence (xk)kto the exact root θ by considering the errors (ξk)kquasi-associated and we illustrate the method by numerical examples to show its efficiency. [ABSTRACT FROM AUTHOR]