the prime objective of the study is to identify the long-run and short-run relationship between indian stock price viz., bse sensex (hereafter named as bse) and gold price (gold) in india. the daily closing price data were collected for the period of ten years ranging from 1st april 2004 to 31st march 2014 with 2490 observations. the study employed two models: model one used gold as dependent v...

We study the convergence of two stochastic approximation algorithms with randomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer–Wolfowitz algorithm. We establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms, and these conditions demonstrate the effect of the “ra...

We study the convergence of two stochastic approximation algorithms with randomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer–Wolfowitz algorithm. We establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms, and these conditions demonstrate the effect of the “ra...

Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein (2009), introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting Bayes rule. The second, motivated by Ji...

Multivariate generalizations of the Wald-Wolfowitz runs statistic and the Smirnov maximum deviation statistic for the two-sample problem are presented. They are based on the minimal spanning tree of the pooled sample points. Some null distribution results are derived, and a simulation study of power is reported. (To be published in Annals of Statistics) *Supported by Department of Energy **Supp...