44 research outputs found
Optimal sampling strategies for multiscale stochastic processes
In this paper, we determine which non-random sampling of fixed size gives the
best linear predictor of the sum of a finite spatial population. We employ
different multiscale superpopulation models and use the minimum mean-squared
error as our optimality criterion. In multiscale superpopulation tree models,
the leaves represent the units of the population, interior nodes represent
partial sums of the population, and the root node represents the total sum of
the population. We prove that the optimal sampling pattern varies dramatically
with the correlation structure of the tree nodes. While uniform sampling is
optimal for trees with ``positive correlation progression'', it provides the
worst possible sampling with ``negative correlation progression.'' As an
analysis tool, we introduce and study a class of independent innovations trees
that are of interest in their own right. We derive a fast water-filling
algorithm to determine the optimal sampling of the leaves to estimate the root
of an independent innovations tree.Comment: Published at http://dx.doi.org/10.1214/074921706000000509 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Brief history of the Lehmann Symposia: Origins, goals and motivation
The idea of the Lehmann Symposia as platforms to encourage a revival of
interest in fundamental questions in theoretical statistics, while keeping in
focus issues that arise in contemporary interdisciplinary cutting-edge
scientific problems, developed during a conversation that I had with Victor
Perez Abreu during one of my visits to Centro de Investigaci\'{o}n en
Matem\'{a}ticas (CIMAT) in Guanajuato, Mexico. Our goal was and has been to
showcase relevant theoretical work to encourage young researchers and students
to engage in such work. The First Lehmann Symposium on Optimality took place in
May of 2002 at Centro de Investigaci\'{o}n en Matem\'{a}ticas in Guanajuato,
Mexico. A brief account of the Symposium has appeared in Vol. 44 of the
Institute of Mathematical Statistics series of Lecture Notes and Monographs.
The volume also contains several works presented during the First Lehmann
Symposium. All papers were refereed. The program and a picture of the
participants can be found on-line at the website
http://www.stat.rice.edu/lehmann/lst-Lehmann.html.Comment: Published at http://dx.doi.org/10.1214/074921706000000347 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multiscale smoothing error models
Caption title.Includes bibliographical references (p. 9-10).Supported by the Air Force Office of Scientific Research. AFOSR-92-J-0002 Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Army Research Office. DAAL03-92-G-0115Mark R. Luettgen, Alan S. Willsky
Analysis, estimation and control for perturbed and singular systems and for systems subject to discrete events.
Annual technical report for grant AFOSR-88-0032.Investigators: Alan S. Willsky, George C. Verghese.Includes bibliographical references (p. [10]-[15]).Research supported by the AFOSR. AFOSR-88-003
Multiscale Riccati equations and a two-sweep algorithm for the optimal fusion of multiresolution data
Cover title.Includes bibliographical references (p. 48-49).Research supported by the National Science Foundation. ECS-8700903 Research supported by the Air Force Office of Scientific Research. AFOSR-88-0032 Research supported by the US Army Research Office. DAAL03-86-K-0171K.C. Chou, A.S. Willsky
Analysis, estimation and control for perturbed and singular systems for systems subject to discrete events.
"The principle investigator for this effort is Professor Alan S. Willsky, and Professor George C. Verghese is co-principal investigator."--P. [3].Includes bibliographical references (p. [20]-[25]).Final technical report for grant AFOSR-88-0032.Supported by the AFOSR. AFOSR-88-003