共查询到20条相似文献,搜索用时 15 毫秒
1.
Consider the canonical-form MANOVA setup with X: n × p = (+ E, Xi ni × p, i = 1, 2, 3, Mi: ni × p, i = 1, 2, n1 + n2 + n3) p, where E is a normally distributed error matrix with mean zero and dispersion In (> 0 (positive definite). Assume (in contrast with the usual case) that M1i is normal with mean zero and dispersion In1) and M22 is either fixed or random normal with mean zero and different dispersion matrix In2 (being unknown. It is also assumed that M1 E, and M2 (if random) are all independent. For testing H0) = 0 versus H1: (> 0, it is shown that when either n2 = 0 or M2 is fixed if n2 > 0, the trace test of Pillai (1955) is uniformly most powerful invariant (UMPI) if min(n1, p)= 1 and locally best invariant (LBI) if min(n1 p) > 1 underthe action of the full linear group Gl (p). When p > 1, the LBI test is also derived under a somewhat smaller group GT(p) of p × p lower triangular matrices with positive diagonal elements. However, such results do not hold if n2 > 0 and M2 is random. The null, nonnull, and optimality robustness of Pillai's trace test under Gl(p) for suitable deviations from normality is pointed out. 相似文献
2.
N. Giri 《Revue canadienne de statistique》1979,7(1):53-60
Let X be a normally distributed p-dimensional column vector with mean μ and positive definite covariance matrix σ. and let X α, α = 1,…, N, be a random sample of size N from this distribution. Partition X as ( X 1, X (2)', X '(3))', where X1 is one-dimension, X(2) is p2- dimensional, and so 1 + p1 + p2 = p. Let ρ1 and ρ be the multiple correlation coefficients of X1 with X(2) and with ( X '(2), X '(3))', respectively. Write ρ2/2 = ρ2 - ρ2/1. We shall cosider the following two problems 相似文献
3.
Consider the problem of testing the composite null hypothesis that a random sample X1,…,Xn is from a parent which is a member of a particular continuous parametric family of distributions against an alternative that it is from a separate family of distributions. It is shown here that in many cases a uniformly most powerful similar (UMPS) test exists for this problem, and, moreover, that this test is equivalent to a uniformly most powerful invariant (UMPI) test. It is also seen in the method of proof used that the UMPS test statistic Is a function of the statistics U1,…,Un?k obtained by the conditional probability integral transformations (CPIT), and thus that no Information Is lost by these transformations, It is also shown that these optimal tests have power that is a nonotone function of the null hypothesis class of distributions, so that, for example, if one additional parameter for the distribution is assumed known, then the power of the test can not lecrease. It Is shown that the statistics U1, …, Un?k are independent of the complete sufficient statistic, and that these statistics have important invariance properties. Two examples at given. The UMPS tests for testing the two-parameter uniform family against the two-parameter exponential family, and for testing one truncation parameter distribution against another one are derived. 相似文献
4.
Franois Perron 《Revue canadienne de statistique》1991,19(1):103-108
Let X = (Xj : j = 1,…, n) be n row vectors of dimension p independently and identically distributed multinomial. For each j, Xj is partitioned as Xj = (Xj1, Xj2, Xj3), where pi is the dimension of Xji with p1 = 1,p1+p2+p3 = p. In addition, consider vectors Yji, i = 1,2j = 1,…,ni that are independent and distributed as X1i. We treat here the problem of testing independence between X11 and X13 knowing that X11 and X12 are uncorrected. A locally best invariant test is proposed for this problem. 相似文献
5.
Collings and Margolin(1985) developed a locally most powerful unbiased test for detecting negative binomial departures from a Poisson model, when the variance is a quadratic function of the mean. Kim and Park(1992) developed a locally most powerful unbiased test, when the variance is a linear function of the mean. It is found that a different mean-variance structure of a negative binomial derives a different locally optimal test statistic. In this paper Collings and Margolin's and Kim and Park's results are unified and extended by developing a test for overdispersion in Poisson model against Katz family of distributions, Our setup has two extensions: First, Katz family of distributions is employed as an extension of the negative binomial distribution. Second, the mean-variance structure of the mixed Poisson model is given by σ2 = μ+cμr for arbitrary but fixed r. We derive a local score test for testing H0 : c = 0. Superiority of a new test is proved by the asymtotic relative efficiency as well as the simulation study. 相似文献
6.
The problem of estimating the mean θ of a not necessarily normal p-variate (p > 3) distribution with unknown covariance matrix of the form σ2A (A a known diagonal matrix) on the basis of ni > 2 observations on each coordinate Xt (1 < i < p) is considered. It is argued that the class of scale (or variance) mixtures of normal distributions is a reasonable class to study. Assuming the loss function is quadratic, a large class of improved shrinkage estimators is developed in the case of a balanced design. We generalize results of Berger and Strawderman for one observation in the known-variance case. This methodology also permits the development of a new class of minimax shrinkage estimators of the mean of a p-variate normal distribution for an unbalanced design. Numerical calculations show that the improvements in risk can be substantial. 相似文献
7.
Let X1,…,Xn be exchangeable normal variables with a common correlation p, and let X(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 distributions. 相似文献
8.
Let X1 X2 … XN be independent normal p-vectors with common mean vector $$ = ($$) and common nonsingular covariance matrix $$ = Diag ($sGi) [(1–p) I + pE] Diag ($sGi), $sGi> 0, i = 1… p, 1>p>=1/p–1. Write rij = sample correlation between the i th and the j th variable i j = 1,… p. It has been proved that for testing the hypothesis H0 : p = 0 against the alternative H1 : p>0 where $$ and $sG1,…, $sGp are unknown, the test which rejects H0 for large value of $$ rij is locally best invariant for every $aL: 0 > $aL > 1 and locally minimax as p $$ 0 in the sense of Giri and Kiefer, 1964, for every $aL: 0 > $aL $$ $aL0 > 1 where$aL0 = Pp=0 $$. 相似文献
9.
Sam Efromovich 《Journal of nonparametric statistics》2014,26(3):555-573
‘?…?if we are prepared to assume that the unknown density has k derivatives, then?…?the optimal mean integrated squared error is of order n?2 k/(2 k+1)?…?’ The citation is from Silverman [(1986), Density Estimation for Statistics and Data Analysis, London: Chapman &; Hall] and its assertion is based on a classical minimax lower bound which is the pillar of the modern nonparametric statistics. This paper proposes a new minimax methodology that implies a faster decreasing minimax lower bound that is attainable by a data-driven estimator, and the same estimator is also minimax under the classical approach. The recommendation is to test performance of estimators via the new and classical minimax approaches. 相似文献
10.
S. Dahel 《统计学通讯:理论与方法》2013,42(6):1965-1972
Let X be a po-normal random vector with unknown µ and unknown covariance matrix ∑ and let X be partitioned as X = (X′ (1), …, X′ (r))′ where X(j)is a subvector of X with dimension pjsuch that ∑r j=1Pj = P0. Some admissible tests are derived for testing H0: μ = 0 versus H1: μ ¦0 based on a sample drawn from the whole vector X of dimension p and r additional samples drawn from X(1), X(2), …, X(r) respectively, All (r+1) samples are assumed to be independent. The distribution of some of the tests' statistics involved are also derived. 相似文献
11.
Alphonse K. A. Amey 《统计学通讯:模拟与计算》2013,42(4):1443-1457
The density of the multiple correlation coefficient is derived by direct integration when the sample covariance matrix has a linear non-central distribution. Using the density, we deduce the null and non-null distribution of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations with the same covariance matrix. We also compute actual significance levels of the test of the hypothesis Ho : ρ1·2…p = 0 versus Ha:ρ1·2…p > 0, given the mixture model. 相似文献
12.
Let π1,…,πp be p independent normal populations with means μ1…, μp and variances σ21,…, σ2p respectively. Let X(ni) be a simple random sample of size ni from πi, i = 1,…,p. Given the simple random samples X(n1),…, X(np) from π1,…,πp respectively, a test has been proposed for testing the homogeneity of variances H0: σ21=…σ2p, against the restricted alternative, H1: σ21≥…≥σ2p, with at least one strict inequality. Some properties of the test are discussed and critical values are tabulated. 相似文献
13.
《Journal of Statistical Computation and Simulation》2012,82(9):1311-1316
Exact unconditional tests for comparing two binomial probabilities are generally more powerful than conditional tests like Fisher's exact test. Their power can be further increased by the Berger and Boos confidence interval method, where a p-value is found by restricting the common binomial probability under H 0 to a 1?γ confidence interval. We studied the average test power for the exact unconditional z-pooled test for a wide range of cases with balanced and unbalanced sample sizes, and significance levels 0.05 and 0.01. The detailed results are available online on the web. Among the values 10?3, 10?4, …, 10?10, the value γ=10?4 gave the highest power, or close to the highest power, in all the cases we looked at, and can be given as a general recommendation as an optimal γ. 相似文献
14.
Consider the regression model Yi= g(xi) + ei, i = 1,…, n, where g is an unknown function defined on [0, 1], 0 = x0 < x1 < … < xn≤ 1 are chosen so that max1≤i≤n(xi-xi- 1) = 0(n-1), and where {ei} are i.i.d. with Ee1= 0 and Var e1 - s?2. In a previous paper, Cheng & Lin (1979) study three estimators of g, namely, g1n of Cheng & Lin (1979), g2n of Clark (1977), and g3n of Priestley & Chao (1972). Consistency results are established and rates of strong uniform convergence are obtained. In the current investigation the limiting distribution of &in, i = 1, 2, 3, and that of the isotonic estimator g**n are considered. 相似文献
15.
Let Sp × p have a Wishart distribution with parameter matrix Σ and n degrees of freedom. We consider here the problem of estimating the precision matrix Σ?1 under the loss functions L1(σ) tr (σ) - log |σ| and L2(σ) = tr (σ). James-Stein-type estimators have been derived for an arbitrary p. We also obtain an orthogonal invariant and a diagonal invariant minimax estimator under both loss functions. A Monte-Carlo simulation study indicates that the risk improvement of the orthogonal invariant estimators over the James-Stein type estimators, the Haff (1979) estimator, and the “testimator” given by Sinha and Ghosh (1987) is substantial. 相似文献
16.
Dayanand N. Naik 《统计学通讯:理论与方法》2013,42(6):2315-2321
Extensions of recent results for detection of mean slippage type outliers from i.i.d. multivariate normal and elliptically symmetric distributions are made to symmetric case, that is, when the observations are equicorrelated. The main tool used is Wijsman's (1967) representation theorem. The results obtained can be viewed as a robustness property of the use of Mardia's multivariate kurtosis as a locally optimal test statistic to detect outliers against equicorrelated distributions. 相似文献
17.
M. Ishaq Bhatti 《Statistical Papers》2000,41(3):345-352
Sen Gupta (1988) considered a locally most powerful (LMP) test for testing nonzero values of the equicorrelation coefficient
of a standard symmetric multivariate normal distribution. This paper constructs analogous tests for the symmetric multivariate
normal distribution. It shows that the new test is uniformly most powerful invariant even in the presence of a nuisance parameter,
σ2. Further applications of LMP invariant tests to several equicorrelated populations have been considered and an extension
to panel data modeling has been suggested. 相似文献
18.
19.
Let X1,…, Xn be random variables symmetric about θ from a common unknown distribution Fθ(x) =F(x–θ). To test the null hypothesis H0:θ= 0 against the alternative H1:θ > 0, permutation tests can be used at the cost of computational difficulties. This paper investigates alternative tests that are computationally simpler, notably some bootstrap tests which are compared with permutation tests. Of these the symmetrical bootstrap-f test competes very favourably with the permutation test in terms of Bahadur asymptotic efficiency, so it is a very attractive alternative. 相似文献
20.
Solomon W. Harrar 《Statistics》2013,47(5):405-414
The asymptotic null distribution of the locally best invariant (LBI) test criterion for testing the random effect in the one-way multivariable analysis of variance model is derived under normality and non-normality. The error of the approximation is characterized as O(1/n). The non-null asymptotic distribution is also discussed. In addition to providing a way of obtaining percentage points and p-values, the results of this paper are useful in assessing the robustness of the LBI criterion. Numerical results are presented to illustrate the accuracy of the approximation. 相似文献