共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper, we study a random field U?(t,x) governed by some type of stochastic partial differential equations with an unknown parameter θ and a small noise ?. We construct an estimator of θ based on the continuous observation of N Fourier coefficients of U?(t,x), and prove the strong convergence and asymptotic normality of the estimator when the noise ? tends to zero. 相似文献
2.
We consider the problem of estimating the mean θ of an Np(θ,Ip) distribution with squared error loss ∥δ−θ∥2 and under the constraint ∥θ∥≤m, for some constant m>0. Using Stein's identity to obtain unbiased estimates of risk, Karlin's sign change arguments, and conditional risk analysis, we compare the risk performance of truncated linear estimators with that of the maximum likelihood estimator δmle. We obtain for fixed (m,p) sufficient conditions for dominance. An asymptotic framework is developed, where we demonstrate that the truncated linear minimax estimator dominates δmle, and where we obtain simple and accurate measures of relative improvement in risk. Numerical evaluations illustrate the effectiveness of the asymptotic framework for approximating the risks for moderate or large values of p. 相似文献
3.
For a random sample of size n from an absolutely continuous random vector (X,Y), let Yi:n be ith Y-order statistic and Y[j:n] be the Y-concomitant of Xj:n. We determine the joint pdf of Yi:n and Y[j:n] for all i,j=1 to n, and establish some symmetry properties of the joint distribution for symmetric populations. We discuss the uses of the joint distribution in the computation of moments and probabilities of various ranks for Y[j:n]. We also show how our results can be used to determine the expected cost of mismatch in broken bivariate samples and approximate the first two moments of the ratios of linear functions of Yi:n and Y[j:n]. For the bivariate normal case, we compute the expectations of the product of Yi:n and Y[i:n] for n=2 to 8 for selected values of the correlation coefficient and illustrate their uses. 相似文献
4.
5.
We consider m×m covariance matrices, Σ1 and Σ2, which satisfy Σ2-Σ1=Δ, where Δ has a specified rank. Maximum likelihood estimators of Σ1 and Σ2 are obtained when sample covariance matrices having Wishart distributions are available and rank(Δ) is known. The likelihood ratio statistic for a test about the value of rank(Δ) is also given and some properties of its null distribution are obtained. The methods developed in this paper are illustrated through an example. 相似文献
6.
7.
Supersaturated designs (SSDs) offer a potentially useful way to investigate many factors with only few experiments in the preliminary stages of experimentation. This paper explores how to construct E(fNOD)-optimal mixed-level SSDs using k-cyclic generators. The necessary and sufficient conditions for the existence of mixed-level k-circulant SSDs with the equal occurrence property are provided. Properties of the mixed-level k -circulant SSDs are investigated, in particular, the sufficient condition under which the generator vector produces an E(fNOD)-optimal SSD is obtained. Moreover, many new E(fNOD)-optimal mixed-level SSDs are constructed and listed. The method here generalizes the one proposed by Liu and Dean [2004. k-circulant supersaturated designs. Technometrics 46, 32–43] for two-level SSDs and the one due to Georgiou and Koukouvinos [2006. Multi-level k-circulant supersaturated designs. Metrika 64, 209–220] for the multi-level case. 相似文献
8.
Consider the model where there are I independent multivariate normal treatment populations with p×1 mean vectors μi, i=1,…,I, and covariance matrix Σ. Independently the (I+1)st population corresponds to a control and it too is multivariate normal with mean vector μI+1 and covariance matrix Σ. Now consider the following two multiple testing problems. 相似文献
9.
10.
We determine a credible set A that is the “best” with respect to the variation of the prior distribution in a neighborhood Γ of the starting prior π0(θ). Among the class of sets with credibility γ under π0, the “optimally robust” set will be the one which maximizes the minimum probability of including θ as the prior varies over Γ. This procedure is also Γ-minimax with respect to the risk function, probability of non-inclusion. We find the optimally robust credible set for three neighborhood classes Γ, the ε-contamination class, the density ratio class and the density bounded class. A consequence of this investigation is that the maximum likelihood set is seen to be an optimal credible set from a robustness perspective. 相似文献
11.
Joseph P.S. Kung Anna de Mier Xinyu Sun Catherine Yan 《Journal of statistical planning and inference》2009
We consider paths in the plane with (1,0), (0,1), and (a,b)-steps that start at the origin, end at height n, and stay strictly to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at most b/a, then the ordinary generating function for the number of such paths ending at height n is algebraic. Our argument is in two parts. We use a simple combinatorial decomposition to obtain an Appell relation or “umbral” generating function, in which the power zn is replaced by a power series of the form znφn(z), where φn(0)=1. Then we convert (in an explicit way) the umbral generating function to an ordinary generating function by solving a system of linear equations and a polynomial equation. This conversion implies that the ordinary generating function is algebraic. We give several concrete examples, including an alternative way to solve the tennis ball problem. 相似文献
12.
13.
Let {Xn,n?1} be a sequence of independent identically distributed random variables, taking nonnegative integer values. An observation Xn is a tie for the maximum if Xn=max{X1,…,Xn-1}. In this paper, we obtain weak and strong laws of large numbers and central limit theorems for the cumulative number of ties for the maximum among the first n observations. 相似文献
14.
15.
We consider a linear regression model with regression parameter β=(β1,…,βp) and independent and identically N(0,σ2) distributed errors. Suppose that the parameter of interest is θ=aTβ where a is a specified vector. Define the parameter τ=cTβ-t where the vector c and the number t are specified and a and c are linearly independent. Also suppose that we have uncertain prior information that τ=0. We present a new frequentist 1-α confidence interval for θ that utilizes this prior information. We require this confidence interval to (a) have endpoints that are continuous functions of the data and (b) coincide with the standard 1-α confidence interval when the data strongly contradict this prior information. This interval is optimal in the sense that it has minimum weighted average expected length where the largest weight is given to this expected length when τ=0. This minimization leads to an interval that has the following desirable properties. This interval has expected length that (a) is relatively small when the prior information about τ is correct and (b) has a maximum value that is not too large. The following problem will be used to illustrate the application of this new confidence interval. Consider a 2×2 factorial experiment with 20 replicates. Suppose that the parameter of interest θ is a specified simple effect and that we have uncertain prior information that the two-factor interaction is zero. Our aim is to find a frequentist 0.95 confidence interval for θ that utilizes this prior information. 相似文献
16.
Let X={Xn}n?1 be a nonstationary random field satisfying a long range weak dependence for each coordinate at a time and a local dependence condition that avoids clustering of exceedances of high values. For these random fields, the probability of no exceedances of high values can be approximated by exp(−τ), where τ is the limiting mean number of exceedances. We present a class of nonstationary normal random fields for which this result can be applied. 相似文献
17.
18.
Denote the integer lattice points in the N -dimensional Euclidean space by ZN and assume that (Xi,Yi), i∈ZN is a mixing random field. Estimators of the conditional expectation r(x)=E[Yi|Xi=x] by nearest neighbor methods are established and investigated. The main analytical result of this study is that, under general mixing assumptions, the estimators considered are asymptotically normal. Many difficulties arise since points in higher dimensional space N?2 cannot be linearly ordered. Our result applies to many situations where parametric methods cannot be adopted with confidence. 相似文献
19.
Consider a mixture problem consisting of k classes. Suppose we observe an s-dimensional random vector X whose distribution is specified by the relations P(X∈A|Y=i)=Pi(A), where Y is an unobserved class identifier defined on {1,…,k}, having distribution P(Y=i)=pi. Assuming the distributions Pi having a common covariance matrix, elegant identities are presented that connect the matrix of Fisher information in Y on the parameters p1,…,pk, the matrix of linear information in X, and the Mahalanobis distances between the pairs of P 's. Since the parameters are not free, the information matrices are singular and the technique of generalized inverses is used. A matrix extension of the Mahalanobis distance and its invariant forms are introduced that are of interest in their own right. In terms of parameter estimation, the results provide an independent of the parameter upper bound for the loss of accuracy by esimating p1,…,pk from a sample of X′s, as compared with the ideal estimator based on a random sample of Y′s. 相似文献