### A Festschrift for Herman Rubin

Editor: Anirban DasGupta

Lecture Notes--Monograph Series, Volume 45
Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004.
417 pp.

#### Abstract:

This volume is a collection of 32 original papers and two biographical accounts put together as a Festschrift to Herman Rubin to honor his diverse and many deep contributions to mathematical sciences over more than 50 years. The topics of the original articles touch on the main themes in which Professor Rubin has contributed, as well as other topics of intense current activity. This volume contains innovative new methodological articles on cluster analysis, goodness of fit, likelihood inference, classification algorithms, and meta analysis. On the purely theoretical side, there are a number of comprehensive review articles on fractional Brownian motion, stochastic integration, de Finetti theorems, admissibility, and estimation under constraints. Each of these review articles provides readable glimpses into the current state of the art. Some notable classic unsolved problems in number theory and random permutations provide attractive additions to the interesting landscape of this volume.

#### Subjects:

Mathematical statistics
Bayesian statistical decision theory
Estimation theory
Set theory
Probabilities
62-06 (primary)
00A30 (secondary)
Permanent link to this monograph: http://projecteuclid.org/euclid.lnms/1196285369
ISBN:0-940600-61-7
Mathmatical Reviews number (MathSciNet): MR2126881
Zentralblatt Math Identifier: 1066.62002

iii-iv

Preface

Anirban DasGupta; v

Contributor's List

vi-vii

List of Publications

viii-xvi

Some reminiscences of my friendship with Herman Rubin

Herman Chernoff; 1-4

Evaluating improper priors and the recurrence of symmetric Markov chains: an overview

Morris L. Eaton; 5-20

Estimation in restricted parameter spaces: a review

Eric Marchand, and William E. Strawderman; 21-44

A Rubinesque theory of decision

J. B. Kadane, Mark J. Schervish, and Teddy Seidenfeld; 45-55

On the distribution of the greatest common divisor

Persi Diaconis, and Paul Erdös; 56-61

Versions of de Finetti’s Theorem with applications to damage models

C. R. Rao, and D. N. Shanbhag; 62-74

A short history of stochastic integration and mathematical finance: the early years, 1880–1970

Robert Jarrow, and Philip Protter; 75-91

Non-linear filtering with Gaussian martingale noise: Kalman filter with fBm noise

L. Gawarecki, and V. Mandrekar; 92-97

Self-similar processes, fractional Brownian motion and statistical inference

B. L. S. Prakasa Rao; 98-125

Some properties of the arc-sine law related to its invariance under a family of rational maps

Jim Pitman, and Marc Yor; 126-137

On time changing continuous martingales to Brownian motion

Burgess Davis; 138-139

On counts of Bernoulli strings and connections to rank orders and random permutations

Jayaram Sethuraman, and Sunder Sethuraman; 140-152

Chebyshev polynomials and $G$-distributed functions of $F$-distributed variables

Anirban DasGupta, and L. Shepp; 153-163

Zeroes of infinitely differentiable characteristic functions

Herman Rubin, and Thomas M. Sellke; 164-170

On the characteristic function of Pearson type IV distributions

Wei-Liem Loh; 171-179

Characterizations, Sub and resampling, and goodness of fit

L. Brown, Anirban DasGupta, John Marden, and Dimitris Politis; 180-206

Notes on the bias-variance trade-off phenomenon

Jeesen Chen; 207-217

Combining correlated unbiased estimators of the mean of a normal distribution

Timothy Keller, and Ingram Olkin; 218-227

An asymptotic minimax determination of the initial sample size in a two-stage sequential procedure

Michael Woodroofe; 228-236

Ming-Yen Cheng, Peter Hall, and John A. Hartigan; 237-249

Conservative bounds on extreme P-values for testing the equality of two probabilities based on very large sample sizes

Herman Chernoff; 250-254

Detecting a target in very noisy data from multiple looks

Jiashun Jin; 255-286

$r$-scan extremal statistics of inhomogeneous Poisson processes

Samuel Karlin, and Chingfer Chen; 287-290

On the strong consistency, weak limits and practical performance of the ML estimate and Bayesian estimates of a symmetric domain in $R^k$

Wen-Chi Tsai, and Anirban DasGupta; 291-308

Maximum likelihood estimation for the contact process

Marta Fiocco, and Willem R. van Zwet; 309-318

On the "Poisson boundaries" of the family of weighted Kolmogorov statistics

Leah Jager, and Jon A. Wellner; 319-331

A theorem on compatibility of systems of sets with applications

A. Goswami, and B. V. Rao; 332-336

A question of geometry and probability

Richard A. Vitale; 337-341

Generalized Accept-Reject sampling schemes

George Casella, Christian P. Robert, and Martin T. Wells; 342-347

Scalable mining for classification rules in relational databases

Min Wang, Bala Iyer, and Jeffrey Scott Vitter; 348-377

A simple proof of a condition for cointegration

T. W. Anderson; 378-384

Forecasting NBA basketball playoff outcomes using the weighted likelihood

Feifang Hu, and James V. Zidek; 385-395

Distributions of failure times associated with non-homogeneous compound Poisson damage processes

S. Zacks; 396-407

Conversations with Herman Rubin

Mary Ellen Bock; 408-417