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51.
In this paper, we consider simple random sampling without replacement from a dichotomous finite population. We investigate accuracy of the Normal approximation to the Hypergeometric probabilities for a wide range of parameter values, including the nonstandard cases where the sampling fraction tends to one and where the proportion of the objects of interest in the population tends to the boundary values, zero and one. We establish a non-uniform Berry–Esseen theorem for the Hypergeometric distribution which shows that in the nonstandard cases, the rate of Normal approximation to the Hypergeometric distribution can be considerably slower than the rate of Normal approximation to the Binomial distribution. We also report results from a moderately large numerical study and provide some guidelines for using the Normal approximation to the Hypergeometric distribution in finite samples. 相似文献
52.
One classical design criterion is to minimize the determinant of the covariance matrix of the regression estimates, and the designs are called D-optimal designs. To reflect the nature that the proposed models are only approximately true, we propose a robust design criterion to study response surface designs. Both the variance and bias are considered in the criterion. In particular, D-optimal minimax designs are investigated and constructed. Examples are given to compare D-optimal minimax designs with classical D-optimal designs. 相似文献
53.
The variance of the Horvitz–Thompson estimator for a fixed size Conditional Poisson sampling scheme without replacement and with unequal inclusion probabilities is compared to the variance of the Hansen–Hurwitz estimator for a sampling scheme with replacement. We show, using a theorem by Gabler, that the sampling design without replacement is more efficient than the sampling design with replacement. 相似文献
54.
Characterization of minimum aberration mixed factorials in terms of consulting designs 总被引:3,自引:0,他引:3
In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and
coding theory, we obtain combinatorial identities that relate the wordlength pattern of a regular mixed factorial design to
that of its consulting design. According to these identities, we further-more establish the general and unified rules for
identifying minimum aberration mixed factorial designs through their consulting designs. It is an improvement and generalization
of the results in Mukerjee and Wu (2001).
This paper is supported by NNSF of China grant No. 10171051 and RFDP grant No. 1999005512. 相似文献
55.
Y.P. Mack 《Journal of statistical planning and inference》1983,8(2):185-192
Let fn(x) be the univariate k-nearest neighbor (k-NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of fn(x) on some suitably chosen interval Jδ. Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size. 相似文献
56.
Recursive estimates of a probability density function (pdf) are known. This paper presents recursive estimates of a derivative of any desired order of a pdf. Let f be a pdf on the real line and p?0 be any desired integer. Based on a random sample of size n from f, estimators f(p)n of f(p), the pth order derivatives of f, are exhibited. These estimators are of the form , where δjp depends only on p and the jth observation in the sample, and hence can be computed recursively as the sample size increases. These estimators are shown to be asymptotically unbiased, mean square consistent and strongly consistent, both at a point and uniformly on the real line. For pointwise properties, the conditions on f(p) have been weakened with a little stronger assumption on the kernel function. 相似文献
57.
Marilena Barnabei 《Journal of statistical planning and inference》1979,3(3):279-286
In the present paper we start the study of arcs with weighted points in a finite projective plane, and we get some particular results about the existence or non-existence of these arcs. 相似文献
58.
Let X be a discrete random variable the set of possible values (finite or infinite) of which can be arranged as an increasing sequence of real numbers a1<a2<a3<…. In particular, ai could be equal to i for all i. Let X1n≦X2n≦?≦Xnn denote the order statistics in a random sample of size n drawn from the distribution of X, where n is a fixed integer ≧2. Then, we show that for some arbitrary fixed k(2≦k≦n), independence of the event {Xkn=X1n} and X1n is equivalent to X being either degenerate or geometric. We also show that the montonicity in i of P{Xkn = X1n | X1n = ai} is equivalent to X having the IFR (DFR) property. Let ai = i and . We prove that the independence of {X2n ? X1n ∈B} and X1n for all i is equivalent to X being geometric, where B = {m} (B = {m,m+1,…}), provided G(i) = qi?1, 1≦i≦m+2 (1≦i≦m+1), where 0<q<1. 相似文献
59.
K.A. Bush 《Journal of statistical planning and inference》1979,3(4):387-394
By a family of designs we mean a set of designs whose parameters can be represented as functions of an auxiliary variable t where the design will exist for infinitely many values of t. The best known family is probably the family of finite projective planes with υ = b = t2 + t + 1, r = k = t + 1, and λ = 1. In some instances, notably coding theory, the existence of families is essential to provide the degree of precision required which can well vary from one coding problem to another. A natural vehicle for developing binary codes is the class of Hadamard matrices. Bush (1977) introduced the idea of constructing semi-regular designs using Hadamard matrices whereas the present study is concerned mostly with construction of regular designs using Hadamard matrices. While codes constructed from these designs are not optimal in the usual sense, it is possible that they may still have substantial value since, with different values of λ1 and λ2, there are different error correcting capabilities. 相似文献
60.
Ching-Shui Cheng 《Journal of statistical planning and inference》1979,3(2):109-118
Youden hyperrectangles are higher-dimensional generalizations of balanced block designs and generalized Youden designs. This kind of design has been shown to be optimal for the elimination of multi-way heterogeneity. In this paper, patchwork and geometric methods are combined to construct Youden hyperrectangles for many parameter values. 相似文献