共查询到10条相似文献,搜索用时 15 毫秒
1.
In order to construct a fixed-size confidence region for the mean vector of an unknown distribution functionF, a new purely sequential sampling strategy is proposed first. For this new procedure, under some regularity conditions onF, the coverage probability is shown (Theorem 2.1) to be at least (1−α)−Bα2d2+o(d2) asd→0, where (1−α) is the preassigned level of confidence,Bis an appropriate functional ofF, and 2dis the preassigned diameter of the proposed spherical confidence region for the mean vector ofF. An accelerated version of the stopping rule is also provided with the analogous second-order characteristics (Theorem 3.1). In the special case of ap-dimensional normal random variable, analogous purely sequential and accelerated sequential procedures as well as a three-stage procedure are briefly introduced together with their asymptotic second-order characteristics. 相似文献
2.
Srivastava gave an asymptotically efficient and consistent sequential procedure to obtain a fixed-width confidence region for the mean vector of any p-dimensional random vector with finite second moments. For normally distributed random vectors, Srivastava and Bhargava showed that the specified coverage probability is attained independent of the width, the mean vector, and the covariance matrix by taking a finite number of observations over and above T prescribed by the sequential rule. However, the problem of showing that E(T−n0) is bounded, where n0 is the sample size required if the covariance matrix were known, has not been available. In this paper, we not only show that it is bounded but obtain sharper estimates of E(T) on the lines of Woodroofe. We also give an asymptotic expansion of the coverage probability. Similar results have recently been obtained by Nagao under the assumption that the covariance matrix Σ=∑ki=1 σiAi and ∑ki=1 Ai=I, where Ai's are known matrices. We obtain the results of this paper under the sole assumption that the largest latent root of Σ is simple. 相似文献
3.
Yoshikazu Takada 《Journal of multivariate analysis》1998,64(2):118-130
We consider confidence sets for the mean of a multivariate normal distribution with unknown covariance matrix of the formσ2I. The coverage probability of the usual confidence set is shown to be improved asymptotically by centering at a shrinkage estimator. 相似文献
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An exact asymptotic formula for the tail probability of a multivariate normal distribution is derived. This formula is applied to establish two asymptotic results for the maximum deviation from the mean: the weak convergence to the Gumbel distribution of a normalized maximum deviation and the precise almost sure rate of growth of the maximum deviation. The latter result gives rise to a diagnostic tool for checking multivariate normality by a simple graph in the plane. Some simulation results are presented. 相似文献
6.
Yasunori Fujikoshi 《Journal of multivariate analysis》1997,61(2):187-193
In this paper we obtain an asymptotic expansion for the distribution of Hotelling'sT2-statisticT2under nonnormality when the sample size is large. In the derivation we find an explicit Edgeworth expansion of the multivariatet-statistic. Our method is to use the Edgeworth expansion and to expand the characteristic function ofT2. 相似文献
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In the univariate case it is well known that the one sided t test is uniformly most powerful for the null hypothesis against all one sided alternatives. Such a property does not easily extend to the multivariate case. In this paper, a test derived for the hypothesis that the mean of a vector random variable is zero against specified alternatives, when the covariance matrix is unknown. This test depends on the given alternatives and is more powerful than Hotelling's T2. The results are derived both for real and complex vector observations and under normal and spherical distributions. The properties of the proposed tests are investigated in detail when a single alternative is specified. 相似文献
9.
Jein-Shan Chen 《Journal of Global Optimization》2006,36(4):565-580
This paper is a follow-up of the work [Chen, J.-S.: J. Optimiz. Theory Appl., Submitted for publication (2004)] where an NCP-function and a descent method were proposed for the nonlinear complementarity problem. An unconstrained reformulation was formulated due to a merit function based on the proposed NCP-function. We continue to explore properties of the merit function in this paper. In particular, we show that the gradient of the merit function is globally Lipschitz continuous which is important from computational aspect. Moreover, we show that the merit function is SC
1 function which means it is continuously differentiable and its gradient is semismooth. On the other hand, we provide an alternative proof, which uses the new properties of the merit function, for the convergence result of the descent method considered in [Chen, J.-S.: J. Optimiz. Theory Appl., Submitted for publication (2004)]. 相似文献