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1.
Consider the model where there are II independent multivariate normal treatment populations with p×1p×1 mean vectors μiμi, i=1,…,Ii=1,,I, and covariance matrix ΣΣ. Independently the (I+1)(I+1)st population corresponds to a control and it too is multivariate normal with mean vector μI+1μI+1 and covariance matrix ΣΣ. Now consider the following two multiple testing problems.  相似文献   

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We study a randomized adaptive design to assign one of the LL treatments to patients who arrive sequentially by means of an urn model. At each stage nn, a reward is distributed between treatments. The treatment applied is rewarded according to its response, 0?Yn?10?Yn?1, and 1-Yn1-Yn is distributed among the other treatments according to their performance until stage n-1n-1. Patients can be classified in K+1K+1 levels and we assume that the effect of this level in the response to the treatments is linear. We study the asymptotic behavior of the design when the ordinary least square estimators are used as a measure of performance until stage n-1n-1.  相似文献   

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We consider paths in the plane with (1,01,0), (0,10,1), and (a,ba,b)-steps that start at the origin, end at height nn, 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/ab/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 znzn is replaced by a power series of the form znφn(z),znφn(z), where φn(0)=1.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   

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Denote the integer lattice points in the N  -dimensional Euclidean space by ZNZN and assume that (Xi,Yi)(Xi,Yi), i∈ZNiZN is a mixing random field. Estimators of the conditional expectation r(x)=E[Yi|Xi=x]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?2N?2 cannot be linearly ordered. Our result applies to many situations where parametric methods cannot be adopted with confidence.  相似文献   

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For a random sample of size nn from an absolutely continuous random vector (X,Y)(X,Y), let Yi:nYi:n be iith YY-order statistic and Y[j:n]Y[j:n] be the YY-concomitant of Xj:nXj:n. We determine the joint pdf of Yi:nYi:n and Y[j:n]Y[j:n] for all i,j=1i,j=1 to nn, 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]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:nYi:n and Y[j:n]Y[j:n]. For the bivariate normal case, we compute the expectations of the product of Yi:nYi:n and Y[i:n]Y[i:n] for n=2n=2 to 8 for selected values of the correlation coefficient and illustrate their uses.  相似文献   

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We consider m×mm×m covariance matrices, Σ1Σ1 and Σ2Σ2, which satisfy Σ2-Σ1Σ2-Σ1=Δ, where ΔΔ has a specified rank. Maximum likelihood estimators of Σ1Σ1 and Σ2Σ2 are obtained when sample covariance matrices having Wishart distributions are available and rank(Δ)rank(Δ) is known. The likelihood ratio statistic for a test about the value of rank(Δ)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   

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Consider a sequence of independent and identically distributed random variables {Xi,i?1}{Xi,i?1} with a common absolutely continuous distribution function F  . Let X1:n?X2:n???Xn:nX1:n?X2:n???Xn:n be the order statistics of {X1,X2,…,Xn}{X1,X2,,Xn} and {Yl,l?1}{Yl,l?1} be the sequence of record values generated by {Xi,i?1}{Xi,i?1}. In this work, the conditional distribution of YlYl given Xn:nXn:n is established. Some characterizations of F   based on record values and Xn:nXn:n are then given.  相似文献   

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In this paper, we study a random field U?(t,x)U?(t,x) governed by some type of stochastic partial differential equations with an unknown parameter θθ and a small noise ??. We construct an estimator of θθ based on the continuous observation of N   Fourier coefficients of U?(t,x)U?(t,x), and prove the strong convergence and asymptotic normality of the estimator when the noise ?? tends to zero.  相似文献   

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This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models where errors form long memory moving average processes and designs are non-random. Unlike in the random design case, asymptotic null distribution of the likelihood ratio type test based on the Whittle quadratic form is shown to be non-standard and non-chi-square. Moreover, the rate of consistency of the minimum Whittle dispersion estimator of the slope parameter vector is shown to be n-(1-α)/2n-(1-α)/2, different from the rate n-1/2n-1/2 obtained in the random design case, where αα is the rate at which the error spectral density explodes at the origin. The proposed test is shown to be consistent against fixed alternatives and has non-trivial asymptotic power against local alternatives that converge to null hypothesis at the rate n-(1-α)/2n-(1-α)/2.  相似文献   

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We consider the problem of estimating the mean θθ of an Np(θ,Ip)Np(θ,Ip) distribution with squared error loss ∥δ−θ∥2δθ2 and under the constraint ∥θ∥≤mθm, for some constant m>0m>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 δmleδmle. We obtain for fixed (m,p)(m,p) sufficient conditions for dominance. An asymptotic framework is developed, where we demonstrate that the truncated linear minimax estimator dominates δmleδmle, 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   

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In this paper, we consider the following simple linear Errors-in-Variables (EV) regression model ηi=θ+βxi+?iηi=θ+βxi+?i, ξi=xi+δiξi=xi+δi, 1?i?n1?i?n. The moderate deviation principle for the least squares (LS) estimators of the unknown parameters θθ, ββ in the model are obtained.  相似文献   

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