共查询到20条相似文献,搜索用时 31 毫秒
1.
Tsukanov (Theor. Probab. Appl. 26 (1981) 173–177) considers the regression model , , where is a vector of measured values, contains the control variables, contains the observed values, and and are being estimated. Assuming that , where is non-random, and the rows of are i.i.d. , we extend Tsukanov's results by (i) computing E(detHp), where Hp is the covariance matrix of p?, the l.s.e. of p, (ii) considering ‘optimality in the mean’ for the largest root criterion, (iii) discussing these equations when the matrix R has a left-spherical distribution. 相似文献
2.
Carl Erik Särndal 《Journal of statistical planning and inference》1982,7(2):155-170
The paper presents a general randomization theory approach to point and interval estimation of Q linear functions Tq = ΣN1ckqYk(q = 1,…,Q), where Y1,…,YN are values of a variable of interest Y in a finite population. Such linear functions include population and domain means and totals, population regression coefficients, etc. We assume that some auxiliary information can be exploited. This suggests the generalized regression technique based on the fit of a linear model, whereby is created approximately design unbiased estimators T?q. The paper focuses on estimation of the variance-covariance matrix of the T?q for single stage and two stage designs. Two techniques based on Taylor expansions are compared. Results of Monte-Carlo experiments (not reported here) show that the coverage properties are good of normal-theory confidence intervals flowing from one or the other variance estimate. 相似文献
3.
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
4.
Asymptotic expansions for the percentiles and c.d.f., up to terms of order of the statistic , where mS1 and nS2 independently distributed W(m, p, Σ1) and W(n, p, Σ2) respectively, are obtained using methods similar to those of Ito [4], Chattopadhyay and Pillai [2]. These expansions hold when and. Tables of powers of T for p = 3 and p = 4 for m = 4 and various values of n are given and comparison made with the exact powers for p = 3. These powers are useful for the study of (i) the test of equality of covariance matrices in two p-variate normal populations and (ii) robustness of test of equality of mean vectors of l normal populations against the violation of the assumption of equality of covariance matrices. 相似文献
5.
Teruhiro Shirakura 《Journal of statistical planning and inference》1979,3(4):337-345
The norm of the alias matrix A of a design can be used as a measure for selecting a design. In this paper, an explicit expression for 6A6 will be given for a balanced fractional 2m factorial design of resolution 2l + 1 which obtained from a simple array with parameters (m; λ0, λ1,…, λm). This array is identical with a balanced array of strength m, m constraints and index set {λ0, λ1,…, λm}. In the class of the designs of resolution V (l = 2) obtained from S-arrays, ones which minimize 6A6 will be presented for any fixed N assemblies satisfying (i) m = 4, 11 ? N ? 16, (ii) m = 5, 16 ? N ? 32, and (iii) m = 6, 22 ? N ? 40. 相似文献
6.
Dieter Jungnickel 《Journal of statistical planning and inference》1979,3(3):273-278
Given any affine design with parameters v, b, r, k, λ and μ = k2/v and any design with parameters v′, b′, r′, k′, λ′ where r′ = tr for some natural number `t and k′?r, we construct a group divisible design with parameters v′' = vv′, m = v′, n = v, b′' = vb′, k′' = kk′, r′'= kr′, λ1 = tkλ and λ2 = μλ′. This is applied to some series of designs. As a lemma, we also show that any 0-1-matrix with row sums tr and column sums ?r may be written as the sum of r 0-1-matrices with row sums t and column sums ?1. 相似文献
7.
In this paper we study a situation where, instead of observing , we observe ; where the random variables in the vector d are called damage components. It is shown that A- and E-optimum designs minimize the effect of d in the mean square error (m.s.e.) of estimable linear functions of parameters under the ordinary linear model. 相似文献
8.
Geoffrey S. Watson 《Journal of statistical planning and inference》1983,8(3):245-256
The Langevin (or von Mises-Fisher) distribution of random vector x on the unit sphere ωq in q has a density proportional to exp κμ'x where μ'x is the scalar product of x with the unit modal vector μ and κ?0 is a concentration parameter. This paper studies estimation and tests for a wide variety of situations when the sample sizes are large. Geometrically simple test statistics are given for many sample problems even when the populations may have unequal concentration parameters. 相似文献
9.
A sorting-and-measuring machine (SMM) measures and sorts (classifies) on-line produced items into several groups according to their size. The measuring devices of the SMM perceive the actual item size with a random error ε and classify the item as being smaller than b iff z+ε<b. Here ε is a normal zero-mean r.v. with unknown standard deviation σ which is the main parameter characterizing the precision and technical condition of an SMM. The paper gives the following method of estimating σ. N0 items are measured and N1 of them are recognized by the SMM as belonging to the group a<z≤b. These N1 items are sorted again and N2 of them return to this group, these are sorted again, and so on. The estimation of σ is based on the statistics Nm/Nn. Moments of the ratio statistics Nm/Nn and their distributional properties are investigated. It turns out that the expected value of Nm/Nn depends almost linearly on σ which allows us to construct ‘almost’ unbiased estimators of type with good propert including robustness with respect to the distribution of item size. Convex combinations of statistics are considered to obtain an estimator with minimal variance. 相似文献
10.
In the usual two-way layout of ANOVA (interactions are admitted) let nij ? 1 be the number of observations for the factor-level combination(i, j). For testing the hypothesis that all main effects of the first factor vanish numbers are given such that the power function of the F-test is uniformly maximized (U-optimality), if one considers only designs (nij) for which the row-sums ni are prescribed. Furthermore, in the (larger) set of all designs for which the total number of observations is given, all D-optimum designs are constructed. 相似文献
11.
Jeremy E. Dawson 《Journal of statistical planning and inference》1985,11(1):103-110
We give a construction for a generalized Hadamard matrix GH(4q, EA(q)) as a 4 × 4 matrix of q × q blocks, for q an odd prime power other than 3 or 5. Each block is a GH(q, EA(q)) and certain combinations of 4 blocks form GH(2q, EA(q)) matrices. Hence a GH(4q, EA(q)) matrix exists for every prime power q. 相似文献
12.
We consider the signed linear rank statistics of the form where the cNi's are known real numbers, Δ∈[0,1] is an unknown real parameter,RΔNi is the rank of |YΔNi| among |YΔNj|, 1≤j≤N, ø is a score generating function, sgn y=1 or -1 according as y≥0 or <0, and YΔNj, 1≤j ≤N, are independent random variables with continuous cumulative distribution functions F(y?ΔdNj), 1≤ j≤N, respectively where the dfNi's are known real numbers. Under suitable assumptions on the c's, d's, φ and F, it is proved that the random process {SΔN?S0N?ESΔN, 0≤Δ≤1}, properly normalized, converges weakly to a Gaussian process, and this result is also true if ESΔN is replaced by ΔbN, where . As an application, we derive the asymptotic distribution of the properly normalized length of a confidence interval for Δ. 相似文献
13.
Rasul A. Khan 《Journal of statistical planning and inference》1981,5(3):243-251
Let X1,X2, … be iid random variables with the pdf f(x,θ)=exp(θx?b(θ)) relative to a σ-finite measure μ, and consider the problem of deciding among three simple hypotheses Hi:θ=θi (1?i?3) subject to P(acceptHi|θi)=1?α (1?i?3). A procedure similar to Sobel–Wald procedure is discussed and its asymptotic efficiency as compared with the best nonsequential test is obtained by finding the limit lima→0(EiN(a)/n(a)), where N (a) is the stopping time of the proposed procedure and n(a) is the sample size of the best non-sequential test. It is shown that the same asymptotic limit holds for the original Sobel–Wald procedure. Specializing to N(θ,1) distribution it is found that lima→0 (i=1,2) and lima→0 (E3N(α)n(α))=δ21/4δ, where δi=(θi+1?θi) with 0<δ1?δ2. Also, the asymptotic efficiency evaluated when the X's have an exponential distribution. 相似文献
14.
Consider the p-dimensional unit cube [0,1]p, p≥1. Partition [0, 1]p into n regions, R1,n,…,Rn,n such that the volume Δ(Rj,n) is of order n?1,j=1,…,n. Select and fix a point in each of these regions so that we have x(n)1,…,x(n)n. Suppose that associated with the j-th predictor vector x(n)j there is an observable variable Y(n)j, j=1,…,n, satisfying the multiple regression model , where g is an unknown function defined on [0, 1]pand {e(n)j} are independent identically distributed random variables with Ee(n)1=0 and Var e(n)1=σ2<∞. This paper proposes as an estimator of g(x), where k(u) is a known p-dimensional bounded density and {an} is a sequence of reals converging to 0 asn→∞. Weak and strong consistency of gn(x) and rates of convergence are obtained. Asymptoticnormality of the estimator is established. Also proposed is as a consistent estimate of σ2. 相似文献
15.
The set of distinct blocks of a block design is known as its support. We construct complete designs with parameters v(?7), k=3, λ=v ? 2 which contain a block of maximal multiplicity and with support size . Any complete design which contains such a block, and has parameters v, k, λ as above, must be supported on at most (v3) ? 4(v ? 2) blocks. Attention is given to complete designs because of their direct relationship to simple random sampling. 相似文献
16.
L. Pesotchinsky 《Journal of statistical planning and inference》1984,9(1):103-117
Unbiased linear estimators are considered for the model where ψ(x) is an unknown contamination. It is assumed that |ψ(x)|?φ(6x6) where φ is a convex function. Minimax analogues of Φp-optimality criteria are introduced. It is shown that, under certain (sufficient) conditions, the least squares estimators and corresponding designs are optimal in the class of all unbiased linear estimators and designs. It is also shown that, in the case when least squares estimators with symmetric design do not lead to an optimal solution, the relative efficiency of optimal least squares is not diminishing and has a uniform lower bound. 相似文献
17.
J.Q. Longyear 《Journal of statistical planning and inference》1981,5(2):181-187
A nest with parameters (r,k,λ)→(r′,k′,λ′) is a BIBD on (b,v,r,k,λ) where each block has a distinguished sublock of cardinality k, the sublocks forming a (b,v,r,k,λ)-design.These designs are ‘nested’ in the sense of W.T. Federer (1972), who recommended the use of these designs for the sequential addition of periods in marketing experiments in order to retain Youden design properties as rows are added. Note that for a Youden design, the b columns and v treatments are in an SBIBD arrangement with parameters v=b, k=r, and λ. 相似文献
18.
Saha and Mohanty (1970) presented a main effect fold-over design consisting of 14 treatment combinations of the 24×33 factorial, which had the nice property of being even balanced. Calling this design DSM, this paper establishes the following specific results: (i) DSM is not d-optimal in the subclass Δe of all 14 point even balanced main effect fold-over designs of the 24×33 factorial; (ii) DSM is not d-optimal in the subclass of all 14 point even and odd balanced main effect fold-over designs of the 24×33 factorial; (iii) DSM is even optimal in and Δe. In addition to these results two 14 point designs in are presented which are d-optimal and via a counter example it is shown that these designs are not odd optimal. Finally, several general matrix algebra results are given which should be useful in resolving d-optimality problems of fold-over designs of the kn11×kn22 factorial. 相似文献
19.
Yasunori Fujikoshi Tetsuto Himeno Hirofumi Wakaki 《Journal of statistical planning and inference》2008
This paper deals with the distributions of test statistics for the number of useful discriminant functions and the characteristic roots in canonical discriminant analysis. These asymptotic distributions have been extensively studied when the number p of variables is fixed, the number q+1 of groups is fixed, and the sample size N tends to infinity. However, these approximations become increasingly inaccurate as the value of p increases for a fixed value of N. On the other hand, we encounter to analyze high-dimensional data such that p is large compared to n. The purpose of the present paper is to derive asymptotic distributions of these statistics in a high-dimensional framework such that q is fixed, p→∞, m=n-p+q→∞, and p/n→c∈(0,1), where n=N-q-1. Numerical simulation revealed that our new asymptotic approximations are more accurate than the classical asymptotic approximations in a considerably wide range of (n,p,q). 相似文献
20.
The article deals with methods for computing the stationary marginal distribution in linear models of time series. Two approaches are described. First, an algorithm based on approximation of solution of the corresponding integral equation is briefly reviewed. Then, we study the limit behaviour of the partial sums c 1 η1+c 2 η2+···+c n η n where η i are i.i.d. random variables and c i real constants. We generalize procedure of Haiman (1998) [Haiman, G., 1998, Upper and lower bounds for the tail of the invariant distribution of some AR(1) processes. Asymptotic Methods in Probability and Statistics, 45, 723–730.] to an arbitrary causal linear process and relax the assumptions of his result significantly. This is achieved by investigating the properties of convolution of densities. 相似文献