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116
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 898 (35 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variation in the perturbed quantity. Up to the higherorder terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A. Two principal problems of matrix perturbation theory are the following. Given a matrix E, pr...
Analyzing Developmental Trajectories: A Semiparametric, GroupBased Approach
 Psychological Methods
, 1999
"... A developmental trajectory describes the course of a behavior over age or time. A groupbased method for identifying distinctive groups of individual trajectories within the population and for profiling the characteristics of group members is demonstrated. Such clusters might include groups of & ..."
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Cited by 216 (11 self)
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A developmental trajectory describes the course of a behavior over age or time. A groupbased method for identifying distinctive groups of individual trajectories within the population and for profiling the characteristics of group members is demonstrated. Such clusters might include groups of &quot;increasers. &quot; &quot;decreasers,&quot; and &quot;no changers. &quot; Suitably defined probability distributions are used to handle 3 data types—count, binary, and psychometric scale data. Four capabilities are demonstrated: (a) the capability to identify rather than assume distinctive groups of trajectories, (b) the capability to estimate the proportion of the population following each such trajectory group, (c) the capability to relate group membership probability to individual characteristics and circumstances, and (d) the capability to use the group membership probabilities for various other purposes such as creating profiles of group members. Over the past decade, major advances have been made in methodology for analyzing individuallevel developmental trajectories. The two main branches of methodology are hierarchical modeling (Bryk &
Least Squares Policy Evaluation Algorithms With Linear Function Approximation
 Theory and Applications
, 2002
"... We consider policy evaluation algorithms within the context of infinitehorizon dynamic programming problems with discounted cost. We focus on discretetime dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function ..."
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Cited by 90 (13 self)
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We consider policy evaluation algorithms within the context of infinitehorizon dynamic programming problems with discounted cost. We focus on discretetime dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function approximation. The first method is a new gradientlike algorithm involving leastsquares subproblems and a diminishing stepsize, which is based on the #policy iteration method of Bertsekas and Ioffe. The second method is the LSTD(#) algorithm recently proposed by Boyan, which for # =0coincides with the linear leastsquares temporaldifference algorithm of Bradtke and Barto. At present, there is only a convergence result by Bradtke and Barto for the LSTD(0) algorithm. Here, we strengthen this result by showing the convergence of LSTD(#), with probability 1, for every # [0, 1].
Interactions, Neighborhood Selection and Housing Demand
 J. Urban Econ
, 2008
"... This paper contributes to the growing literature that aims at identifying and measuring the impact of social context on individual economic behavior. We develop a model of housing structure demand with neighborhood effects and neighborhood choice. Modeling neighborhood choice is of fundamental impor ..."
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Cited by 39 (3 self)
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This paper contributes to the growing literature that aims at identifying and measuring the impact of social context on individual economic behavior. We develop a model of housing structure demand with neighborhood effects and neighborhood choice. Modeling neighborhood choice is of fundamental importance in estimating and understanding endogenous and contextual neighborhood effects. Controlling for nonrandom sorting into neighborhoods allows for unbiased estimates and provides a means for identifying endogenous neighborhood effects. Estimation of the model exploits a householdlevel data set that has been augmented with contextual information at two different levels (“scales”) of aggregation. One is at the neighborhood level, consisting of about ten neighbors, with the data coming from the neighborhood clusters subsample of the American Housing Survey. A second level is the census tract to which these dwelling units belong. These data were geocoded by means of privileged access to confidential US Census data. Our results for the neighborhood choice model indicate that individuals prefer to live near others like themselves. Our estimates of the housing structure demand equation confirm that neighborhood effects are important. In particular, one’s demand for housing depends on the mean of neighbors ’ demand for housing.
A theory of interactive parallel processing: new capacity measures and predictions for a response time inequality series
, 2004
"... The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of paral ..."
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Cited by 35 (10 self)
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The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of parallel channels ’ dependencies that incorporates standard independent and coactive parallel models as special cases. The metatheory is applied to OR and AND experimental paradigms, and the authors establish new theorems relating response time performance in these designs to earlier and novel issues. One notable outcome is the remarkable processing efficiency associated with linear parallelchannel systems that include mutually positive interactions. The results may offer insight into perceptual and cognitive configural–holistic processing systems.
Worstcase properties of the uniform distribution and randomized algorithms for robustness analysis
 Mathematics of Control, Signals, and Systems
, 1998
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An analysis of the alphabeta pruning algorithm
, 1973
"... The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or other reproductions of copyrighted material. Any copying of this document without permission of its author may be prohibited by law. ..."
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Cited by 16 (1 self)
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The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or other reproductions of copyrighted material. Any copying of this document without permission of its author may be prohibited by law.
A Markov Renewal Model for Rainfall Occurrences
, 1987
"... A probabilistic model for the temporal description of daily rainfall occurrences at a single location is presented. By defining an event as a day with measurable precipitation the model is cast into the discretetime point process framework. In the proposed model the sequence of times between events ..."
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Cited by 12 (0 self)
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A probabilistic model for the temporal description of daily rainfall occurrences at a single location is presented. By defining an event as a day with measurable precipitation the model is cast into the discretetime point process framework. In the proposed model the sequence of times between events is formed by sampling from two geometric distributions, according to transition probabilities specified by a Markov chain. The model belongs to the class of Markov renewal processes and exhibits clustering relative to the independent Bernoulli process. As a special case, it reduces to a renewal model with a mixture distribution for the interarrival times. The rainfall occurrence model coupled with a mixed exponential distribution for the nonzero daily rainfall amounts was applied to the daily rainfall series for Snoqualmie Falls, Washington, and was successful in preserving the shortterm structure of the occurrence process, as well as the distributional properties of the seasonal rainfall amounts.
Sequential estimation of a continuous probability density function and model
 Bulletin of Mathematical Statistics
, 1971
"... The purpose of this paper is to discuss statistical properties of an estimate of a probability density function based on the first n observations under the assumption of continuity or uniform continuity of the probability density function in case where we observe a sequence of random vectors which ..."
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Cited by 12 (0 self)
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The purpose of this paper is to discuss statistical properties of an estimate of a probability density function based on the first n observations under the assumption of continuity or uniform continuity of the probability density function in case where we observe a sequence of random vectors which come from a population