共查询到20条相似文献,搜索用时 15 毫秒
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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
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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
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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
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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
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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
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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
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Alexander Kukush Andrii Malenko Hans Schneeweiss 《Journal of statistical planning and inference》2009
We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector θ to be estimated that also appears in the distribution of the regressor variable x. The estimation of θ is based on an extended quasi-score (QS) function. We show that the QS estimator is optimal within a wide class of estimators based on linear-in-y unbiased estimating functions. Of special interest is the case where the distribution of x depends only on a subvector α of θ, which may be considered a nuisance parameter. In general, α must be estimated simultaneously together with the rest of θ, but there are cases where α can be pre-estimated. A major application of this model is the classical measurement error model, where the corrected score (CS) estimator is an alternative to the QS estimator. We derive conditions under which the QS estimator is strictly more efficient than the CS estimator. 相似文献
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José Antonio Moler Fernando Plo Miguel San Miguel 《Journal of statistical planning and inference》2007
We study a randomized adaptive design to assign one of the L treatments to patients who arrive sequentially by means of an urn model. At each stage n, a reward is distributed between treatments. The treatment applied is rewarded according to its response, 0?Yn?1, and 1-Yn is distributed among the other treatments according to their performance until stage n-1. Patients can be classified in K+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-1. 相似文献
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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
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The generalized order-restricted information criterion (goric) is a model selection criterion which can, up to now, solely be applied to the analysis of variance models and, so far, only evaluate restrictions of the form Rθ≤0, where θ is a vector of k group means and R a cm×k matrix. In this paper, we generalize the goric in two ways: (i) such that it can be applied to t -variate normal linear models and (ii) such that it can evaluate a more general form of order restrictions: Rθ≤r, where θ is a vector of length tk, r a vector of length cm, and R a cm×tk matrix of full rank (when r≠0). At the end, we illustrate that the goric is easy to implement in a multivariate regression model. 相似文献
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A ridge function with shape function g in the horizontal direction is a function of the form g(x)h(y,0). Along each horizontal line it has the shape g(x), multiplied by a function h(y,0) which depends on the y-value of the horizontal line. Similarly a ridge function with shape function g in the vertical direction has the form g(y)h(x,π/2). For a given shape function g it may or may not be possible to represent an arbitrary function f(x,y) as a superposition over all angles of a ridge function with shape g in each direction, where h=hf=hf,g depends on the functions f and g and also on the direction, θ:h=hf,g(·,θ). We show that if g is Gaussian centered at zero then this is always possible and we give the function hf,g for a given f(x,y). For highpass or for odd shapes g , we show it is impossible to represent an arbitrary f(x,y), i.e. in general there is no hf,g. Note that our problem is similar to tomography, where the problem is to invert the Radon transform, except that the use of the word inversion is here somewhat “inverted”: in tomography f(x,y) is unknown and we find it by inverting the projections of f ; here, f(x,y) is known, g(z) is known, and hf(·,θ)=hf,g(·,θ) is the unknown. 相似文献
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We consider density estimation for a smooth stationary process Xt, t∈R, based on a discrete sample Yi=XΔi, i=0,…,n=T/Δ. By a suitable interpolation scheme of order p , we augment data to form an approximation Xp,t, t∈[0,T], of the continuous-time process and base our density estimate on the augmented sample path. Our results show that this can improve the rate of convergence (measured in terms of n) of the density estimate. Among other things, this implies that recording n observations using a small Δ can be more efficient than recording n independent observations. 相似文献
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In common with other non-linear models, the optimal design for a limiting dilution assay (LDA) depends on the value of the unknown parameter, θ, in the model. Consequently optimal designs cannot be specified unless some assumptions are made about the possible values of θ. If a prior distribution can be specified then a Bayesian approach can be adopted. A proper specification of the Bayesian approach requires the aim of the experiment to be described and quantified through an appropriate utility function. This paper addresses the problem of finding optimal designs for LDAs when the aim is to determine whether θ is above or below a specified threshold, θ0. 相似文献
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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
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We consider fixed-size estimation for a linear function of mean vectors from πi:Np(μi,Σi), i=1,…,k, when every Σi has some structure. The goal of inference is to construct a fixed-span confidence region with required accuracy. We find a sample size for each πi with the help of the ‘double shrink methodology’, that is introduced by this paper, via covariance structures of Σi, i=1,…,k. We estimate the sample size in a two-stage sampling and give a fixed-span confidence region that has the coverage probability approximately second-order consistent with the required accuracy. Some simulations are carried out to see moderate sample size performances of the proposed methodologies. 相似文献