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...
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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.
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. ...
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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.
A new method for obtaining an initial feasible interior-point solution to a linear program is presented. This method avoids the use of a "big-M", and is shown to work well on a standard set of test problems....
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A new method for obtaining an initial feasible interior-point solution to a linear program is presented. This method avoids the use of a "big-M", and is shown to work well on a standard set of test problems. Conditions are developed for obtaining a near-optimal solution that is feasible for an associated problem, and details of the computational testing are presented. Other issues related to obtaining and maintaining accurate feasible solutions to linear programs with an interior-point method are discussed. These issues are important to consider when solving problems that have no primal or dual interior-point feasible solutions.
A random sample size version of the central limit theorem is obtained for a general class of symmetric statistics based on uniform spacings. An important application to goodness of fit test for a Poisson process is di...
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A random sample size version of the central limit theorem is obtained for a general class of symmetric statistics based on uniform spacings. An important application to goodness of fit test for a Poisson process is discussed.
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...
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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.
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
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 ...
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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.
Version 5.1 of MINOS was used to analyze a set of linear programming test problems, which were run with different sets of options for scaling and partial pricing to illustrate the effects of these options on the perfo...
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Version 5.1 of MINOS was used to analyze a set of linear programming test problems, which were run with different sets of options for scaling and partial pricing to illustrate the effects of these options on the performance of the simplex method. Testing was performed on a DEC VAXstation II with 13 megabytes of main memory. The solution time was measured by timing the MINOS subroutine M5SOLV. The results demonstrate that the different options can significantly improve or degrade the performance of the simplex method. Scaling and partial pricing can improve the performance of the simplex method in most cases. However, options must be carefully chosen - a difficult task - in order not to degrade the performance of the simplex method.
The stability problem in queueing theory is concerned with the continuity of the mapping F from the set U of the input flows into the set V of the output flows. First, using the theory of probability metrics we estima...
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