摘要:

AbstractWe use the martingale approach to study large deviations and laws of the iterated logarithm for certain multidimensional diffusion processes. The criteria for the validity of these properties are expressed in terms of averaging properties of the coefficients of the infinitesimal generator. In particular we apply our results to diffusion processes with random coefficients.

ISSN:0319-5724    

DOI:10.2307/3315477

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractSuppose it is desired to obtain a large numberNsof items for which individual counting is impractical, but one can demand a batch to weigh at leastwunits so that the number of itemsNin the batch may be close to the desired numberNs. If the items have mean weight ωTH, it is reasonable to havewequal to ωTHNswhen ωTH is known. When ωTH is unknown, one can take a sample of sizen, not bigger thanNs, estimate ωTH by a good estimator ωn, and setwequal to ωnNs. LetRn=Kp2N2s/n+Ksnbe a measure of loss, whereKeandKsare the coefficients representing the cost of the error in estimation and the cost of the sampling respectively, and p is the coefficient of variation for the weight of the items. If one determines the sample size to be the integer closest to pCNswhen p is known, whereCis (Ke/Ks)1/2, thenRnwill be minimized. If p is unknown, a simple sequential procedure is proposed for which the average sample number is shown to be asymptotically equal to the optimal fixed sample size. When the weights are assumed to have a gamma distribution given ω and ω has a prior inverted gamma distribution, the optimal sample size can be found to be the nonnegative integer closest to pCNs+ p2A(pC– 1), whereAis a known constant given in the prior di

ISSN:0319-5724    

DOI:10.2307/3315478

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractThe problem of sequential sampling without recall from a Dirichlet process is studied. An individual observes a sequential samplep1,p2, … . At each stage the observer can either accept the current valuepior continue sampling. The total cost to the observer is the current value plus a cost for each observation taken after the first. A concrete context for the problem is provided by a shopper who must buy a particular item and can elicit price quotations sequentially but must pay for each quotation. Qualitative properties of optimal search rules are derived which establish that the problem is well behaved. In particular, the reservation‐price property is shown to hold. The results extend those in Christensen (19

ISSN:0319-5724    

DOI:10.2307/3315479

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractWe examine the behaviour of the sample autocorrelations of a seasonal time series for which the first difference of orders(s≥ 1) is stationary. The asymptotic distribution of the autocorrelations r'(k) based on uncentered data and of the autocorrelationsr(k) based on centered data are derived. In each case, the asymptotic distribution is characterized as a function of the lagkand the parameters of the process. A simulation study was conducted in order to investigate the rate of convergence of the finite sample distributions ofr(k) and r'(k) to their asymptotic counterparts and to evaluate the effect of centering or not centering the data on the distribution of autocorrelation

ISSN:0319-5724    

DOI:10.2307/3315480

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractGoodness‐of‐fit tests for the uniform distribution based on sums of smooth functions ofm‐spacings are studied. A limiting sum‐of‐weighted‐chi‐squareds approximation is shown to be accurate uniformly inmfor the special cases of analogues of Greenwooďs statistic and Moran's statistic. Asymptotic critical points are provided; theory and Monte Carlo studies show they are accurate for allmprovidednis mo

ISSN:0319-5724    

DOI:10.2307/3315481

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractThe problem of nonparametric estimation of a probability density function when the sample observations are contaminated with random noise is studied. A particular estimator f̌n(x) is proposed which uses kernel‐density and deconvolution techniques. The estimator f̌n(x) is shown to be uniformly consistent, and its appearance and properties are affected by constantsMnandhnwhich the user may choose. The optimal choices ofMnandhndepend on the sample sizen, the noise distribution, and the true distribution which is being estimated. Particular selections forMnandhnwhich minimize upper‐bound functions of the mean squared error for f̌n(x) are recom

ISSN:0319-5724    

DOI:10.2307/3315482

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractLetX1,…,Xnbe exchangeable normal variables with a common correlation p, and letX(1)>…>X(n)denote their order statistics. The random variable σni=n—k+1xi, called the selection differential by geneticists, is of particular interest in genetic selection and related areas. In this paper we give results concerning a conjecture of Tong (1982) on the distribution of this random variable as a function of ρ. The same technique used can be applied to yield more general results for linear combinations of order statistics from elliptical distri

ISSN:0319-5724    

DOI:10.2307/3315483

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY