We show that quasi-every Brownian path in R (with respect to an Ornstein-Uhlenbeck process in the space of paths) has level sets of Hausdorff dimension 1 2 , for all levels, and quasi-every planar Brownian motion has ...
详细信息
We show that quasi-every Brownian path in R (with respect to an Ornstein-Uhlenbeck process in the space of paths) has level sets of Hausdorff dimension 1 2 , for all levels, and quasi-every planar Brownian motion has a set of r -multiple points of dimension 2 for arbitrary finite r .
作者：
STEELE, JMPrinceton University
Program in Statistics and Operations Research School of Engineering and Applied Science Princeton NJ 08544 USA
A bound is given for the cost of the spanning tree produced by the sequential minimal insertion procedure as applied to n points in the unit d -cube. The technique developed is reasonably general and can be applied to...
详细信息
A bound is given for the cost of the spanning tree produced by the sequential minimal insertion procedure as applied to n points in the unit d -cube. The technique developed is reasonably general and can be applied to several other problems of computational geometry, including the nearest neighbour heuristic for the traveling salesman problem. Attention is also given to bounding the sum of the powers of the edge lengths of sequentially constructed trees and paths. Examples illustrate that the bounds obtained are of best possible order as a function of the number of points.
Let X, Y and Z be independent random variables with common unknown distribution F. Using the Dirichlet process prior for F and squared erro loss function, the Bayes and empirical Bayes estimators of the parameters λ(...
详细信息
Let X, Y and Z be independent random variables with common unknown distribution F. Using the Dirichlet process prior for F and squared erro loss function, the Bayes and empirical Bayes estimators of the parameters λ(F). the probability that Z > X + Y, are derived. The limiting Bayes estimator of λ(F) under some conditions on the parameter of the process is shown to be asymptotically normal. The aysmptotic optimality of the empirical Bayes estimator of λ(F) is established. When X, Y and Z have support on the positive real line, these results are derived for randomly right censored data. This problem relates to testing whether than used discussed by Hollander and Proshcan (1972) and Chen, Hollander and Langberg (1983).
Letbe a Markov chain with state space inR+= (0,∞), an initial distributionμand a transition probabilityQ. For eachx∊R+the support ofis [0,x], which implies that. Setand put. We prove thatis a Markov renewal process ...
Letbe a Markov chain with state space inR+= (0,∞), an initial distributionμand a transition probabilityQ. For eachx∊R+the support ofis [0,x], which implies that. Setand put. We prove thatis a Markov renewal process and thatis a Markov process with a stationary transition probability function. Writeand suppose that. We give conditions under whichis relatively stable and show that, whereare stabilizing constants andZis exponentially distributed. We also show thatis asymptotically stationary and possesses a mixing property
Let X 1 , X 2 ,…, be i.i.d. random variables, which are uniformly distributed on [0,1]. Further let I 1 (0) = [0, 1] and let I k ( n ) denote the k th largest interval generated by the points 0, X 1 , X 2 ,…, X n −1...
详细信息
Let X 1 , X 2 ,…, be i.i.d. random variables, which are uniformly distributed on [0,1]. Further let I 1 (0) = [0, 1] and let I k ( n ) denote the k th largest interval generated by the points 0, X 1 , X 2 ,…, X n −1 , 1 (or equivalently, the interval corresponding to the k th largest spacing at the n th stage). This note studies the question for which classes of sequences k = k ( n ), will the interval I k ( n ) ( n ) be hit (a.s.) only finitely often, as well as infinitely often.
This note sharpens and generalizes an inequality of Platzman and Bartholdi on the ratio of the cost of the path provided by the spacefilling heuristic to the cost of the optimal path through n points in R d .
This note sharpens and generalizes an inequality of Platzman and Bartholdi on the ratio of the cost of the path provided by the spacefilling heuristic to the cost of the optimal path through n points in R d .
A rank test based on the number of ‘near-matches’ among within-block rankings is proposed for stochastically ordered alternatives in a randomized block design with t treatments and b blocks. The asymptotic relative ...
详细信息
A rank test based on the number of ‘near-matches’ among within-block rankings is proposed for stochastically ordered alternatives in a randomized block design with t treatments and b blocks. The asymptotic relative efficiency of this test with respect to the Page test is computed as number of blocks increases to infinity. A sequential analog of the above test procedure is also considered. A repeated significance test procedure is developed and average sample number is computed asymptotically under the null hypothesis as well as under a sequence of contiguous alternatives.
The problem of estimating the transition probabilities for the Markov chain associated to a Markov renewal process is considered. The estimators are to be based on censored observations of the Markov renewal process. ...
详细信息
The problem of estimating the transition probabilities for the Markov chain associated to a Markov renewal process is considered. The estimators are to be based on censored observations of the Markov renewal process. For a class of Markov renewal processes whose transition distributions factor, nonparametric estimators are defined. They are shown to be consistent and to converge weakly go Gaussian random variables. The result builds upon those in Gill (1980) for nonparametric estimation in this setting.
The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum informatio...
详细信息
This case study, involving a continuous processing operation of a plastic material, provides a simple, intuitively attractive evaluation of the potential reduction in variability that can be achieved by blending mater...
详细信息
This case study, involving a continuous processing operation of a plastic material, provides a simple, intuitively attractive evaluation of the potential reduction in variability that can be achieved by blending materials after production. The evaluation is based exclusively upon past data on unblended materials. The evaluations were complicated by the fact that measured variability was inflated by analytic error. The paper is not an endorsement of blending as a strategy for improving consistency. In fact, this evaluation showed that the blending that was practical in this application would provide only minimal improvements;thus the idea of blending was abandoned.
暂无评论