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1.
Minimax optimal stopping times and minimax worst—case distributions are found for the problem of stopping a sequence of uniformly bounded i.i.d. random variables in a cost and a discount model when only the mean and/or the variance (and not the complete distribution) of the random variables is known  相似文献   

2.
This study provides sufficient conditions under which the uniform distance between the distribution of random sums of weighted random variables and the normal distribution is of order n-a(log n)a+b, for α <1/2, n-1/2(log n)b+3/2, for b > -3/2, and n-1/2log2n for b = -3/2. Extensions to one-sided linear processes are also discussed.  相似文献   

3.
In problems of optimal stopping for F((W(t)+x)+) -c(s + t) with W(t) denoting Brownian motion, bounds for the optimal stopping regions are derived which describe the growth of the optimal boundaries. This generalizes results by lrle (1988) where the case f(x) = x was treated. Extensions are given when positive part is replaced by absolute value and also when a random walk takes the place of Brownian motion.  相似文献   

4.
Abstract

A problem that often arises in the recruitment process is that the recruitment firms face possible loss of candidates. The loss of candidates can induce a loss cost to firms which need to restart the recruitment process. In this article, we model the recruitment process as a discrete-time stochastic optimal stopping problem with a finite planning horizon, where candidates may be hired by other firms during the period of waiting for employment with a loss probability. An optimal decision rule is presented to maximize the benefit of the recruitment firm. This decision rule demonstrates that the threshold of direct employment will be reduced as the loss probability (or the loss cost) is increasing. In addition, we find that new applicants are hardly being directly employed when the remaining time to the deadline is very long. Finally, a numerical example is given to illustrate the effectiveness of the proposed decision rule.  相似文献   

5.
An economical on-line quality control procedure is given for cases where measurement error u present.The unobservable quality characteristic procw is assumed to follow a normal random walk.model independent of the measurement error which is white noise. The off-target loss function used is proportional to the squared deviation from the target value.The procw is inspected at regular intervals of m time units and adjusted at the end of a cycle when the process goes out of the control limit d.The limning long-run average cost rate is evaluated.The optimum value of the control parameters,the inspection interval m,and the control limit d are obtained by minimlzlng the long-run average cost rate.When m is small and d is large, explicit expressions for the control parameters are given.  相似文献   

6.
Abstract.  In this paper, we consider the problem of testing for a parameter change in a first-order random coefficient integer-valued autoregressive [RCINAR(1)] model. We employ the cumulative sum (CUSUM) test based on the conditional least-squares and modified quasi-likelihood estimators. It is shown that under regularity conditions, the CUSUM test has the same limiting distribution as the supremum of the squares of independent Brownian bridges. The CUSUM test is then applied to the analysis of the monthly polio counts data set.  相似文献   

7.
Abstract

Assume that the probability of success is unimodal as a function of dose, such as may be the case when too much of a drug is toxic and too little is ineffective. We characterize a class of up-and-down designs, that is, treatment allocation methodologies, for identifying the dose that maximizes the patients' success probability. These designs are constructed to use accruing information to limit the number of patients that are exposed to doses with high probabilities of failure. This treatment allocation procedure is motivated by Kiefer–Wolfowitz's stochastic approximation procedure. However, we take the response to be binary and the possible treatment space to be a lattice. The procedure is shown to allocate treatments to pairs of subjects in a way that causes the treatment distribution to center around the treatment with maximum success probability. The procedure defines a nonhomogeneous random walk, so well-known theory is used to explicitly characterize the treatment distribution. As an estimator of the best dose, the mode of the empirical treatment distribution is shown to converge faster than does the last dose allocated, which is used as an estimator of the optimal dose in stochastic approximation procedures.  相似文献   

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