We consider the Kiefer-Wolfowitz (KW) stochastic approximation algorithm and derive general upper bounds on its meansquared error. The bounds are established using an elementary induction argument and phrased directly in the terms of tuning sequences of the algorithm. From this we deduce the nonnecessity of one of the main assumptions imposed on the tuning sequences by Kiefer and Wolfowitz [Kie...

We consider the problem of calculating power and sample size for tests based on generalized estimating equations (GEE), that arise in studies involving clustered or correlated data (e.g., longitudinal studies and sibling studies). Previous approaches approximate the power of such tests using the asymptotic behavior of the test statistics under fixed alternatives. We develop a more accurate appr...

BACKGROUND The area under the receiver operating characteristic (ROC) curve, referred to as the AUC, is an appropriate measure for describing the overall accuracy of a diagnostic test or a biomarker in early phase trials without having to choose a threshold. There are many approaches for estimating the confidence interval for the AUC. However, all are relatively complicated to implement. Furthe...

The nexus between military expenditure and economic growth has been analyzed using different methods techniques in the literature, but most previous findings are indecisive, i.e., non-significant, positive, or negative. primary purpose of this article was to explain expenditure-economic Pakistan by capturing asymmetrical effects expenditures on non-linear autoregressive distribution lag-NARDL t...

This paper proposes a proof of the convergence distributed and asynchronous version Kiefer-Wolfowitz algorithm where agents do not exchange information with one another.

We address the classic problem of interval estimation of a binomial proportion. The Wald interval p̂ ± zα/2n−1/2(p̂(1 − p̂))1/2 is currently in near universal use. We first show that the coverage properties of the Wald interval are persistently poor and defy virtually all conventional wisdom. We then proceed to a theoretical comparison of the standard interval and four additional alternative inter...

We evaluate by simulation three model-based methods to test the influence of a single nucleotide polymorphism on a pharmacokinetic parameter of a drug: analysis of variance (ANOVA) on the empirical Bayes estimates of the individual parameters, likelihood ratio test between models with and without genetic covariate, and Wald tests on the parameters of the model with covariate. Analyses are perfo...