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 ...
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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 .
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.
Given symmetric generalized inverses of A χ x′ c , where χ is a vector with n components, we obtain formulae for the corresponding generalized inverses (symmetric) of A . An application of such formulae in linear m...
Given symmetric generalized inverses of A χ x′ c , where χ is a vector with n components, we obtain formulae for the corresponding generalized inverses (symmetric) of A . An application of such formulae in linear models is suggested.
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(...
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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...
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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.
In applications, considerations on stochastic models often involve a Markov chain [formula omitted] with state space in R+, and a transition probability Q. For each x ε R+ the support of Q(x,) is [0, x]. This implies...
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A nonparametric formulation is set up for selecting the best one of k populations. “Best” is defined as the one with the smallest inter(a,e)-range, a measure of dispersion defined by the difference of the 6th quanti...
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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 ...
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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.
This paper discusses a sequential procedure to estimate an estimable parameter of the underlying unknown distribution function. The estimator is based on the corresponding U-statistic. Under appropriate regularity con...
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