@bullet Estimation following a Robbins-monro Designed Experiment

Efficient Robbins-Monro Procedure for Binary Data

The Robbins-Monro procedure does not perform well in the estimation of extreme quantiles, because the procedure is implemented using asymptotic results, which are not suitable for binary data. Here we propose a modification of the Robbins-Monro procedure and derive the optimal procedure for binary data under some reasonable approximations. The improvement obtained by using the optimal procedure...

BUREAU OF THE CENSUS STATISTICAL RESEARCH DIVISION Statistical Research Report Series No. RR2001/02 Convergence of a Robbins-Monro Algorithm for Recursive Parameter Estimation with Non-Monotone Weights and Multiple Zeros

Convergence properties are established for the output of a deterministic Robbins-Monro recursion for functions that can have singularities and multiple zeros. Our analysis is built largely on adaptations of lemmas of Fradkov published in Russian. We present versions of these lemmas in English for the first time. A gap in Fradkov’s proof of the final lemma is fixed but only for the scalar case.

Stochastic Approximation and Modern Model-based Designs for Dose-Finding Clinical Trials.

In 1951 Robbins and Monro published the seminal paper on stochastic approximation and made a specific reference to its application to the "estimation of a quantal using response, non-response data". Since the 1990s, statistical methodology for dose-finding studies has grown into an active area of research. The dose-finding problem is at its core a percentile estimation problem and is in line wi...

Estimation of Contextual Effects through Nonlinear Multilevel Latent Variable Modeling with a Metropolis-Hastings Robbins-Monro Algorithm

The main purpose of this study is to improve estimation efficiency in obtaining fullinformation maximum likelihood (FIML) estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can produce FIML estimates and their standar...

The continuous dynamic Robbins-Monro procedure