共查询到20条相似文献,搜索用时 21 毫秒
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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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Jonathan El Methni Laurent Gardes Stéphane Girard Armelle Guillou 《Journal of statistical planning and inference》2012
In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters τ and θ, which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for θ and extreme quantiles are also proposed, but they both depend on the unknown parameter τ, making them useless in practical situations. In this paper, we propose an estimator of τ which is independent of θ. Plugging our estimator of τ in the two previous ones allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unified way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a small simulation study and on a real data set. 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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In this paper, we consider the following simple linear Errors-in-Variables (EV) regression model ηi=θ+βxi+?i, ξi=xi+δi, 1?i?n. The moderate deviation principle for the least squares (LS) estimators of the unknown parameters θ, β in the model are obtained. 相似文献
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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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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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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 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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In this paper, we investigate the estimation problem of the mixture proportion λ in a nonparametric mixture model of the form λF(x)+(1-λ)G(x) using the minimum Hellinger distance approach, where F and G are two unknown distributions. We assume that data from the distributions F and G as well as from the mixture distribution λF+(1-λ)G are available. We construct a minimum Hellinger distance estimator of λ and study its asymptotic properties. The proposed estimator is chosen to minimize the Hellinger distance between a parametric mixture model and a nonparametric density estimator. We also develop a maximum likelihood estimator of λ. Theoretical properties such as the existence, strong consistency, asymptotic normality and asymptotic efficiency of the proposed estimators are investigated. Robustness properties of the proposed estimator are studied using a Monte Carlo study. Two real data examples are also analyzed. 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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This paper discusses a new perspective in fitting spatial point process models. Specifically the spatial point process of interest is treated as a marked point process where at each observed event x a stochastic process M(x;t), 0<t<r, is defined. Each mark process M(x;t) is compared with its expected value, say F(t;θ), to produce a discrepancy measure at x, where θ is a set of unknown parameters. All individual discrepancy measures are combined to define an overall measure which will then be minimized to estimate the unknown parameters. The proposed approach can be easily applied to data with sample size commonly encountered in practice. Simulations and an application to a real data example demonstrate the efficacy of the proposed approach. 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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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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Moments and central moments of a random variable X are expressed as integrals of functions of lower-order conditional moments and the cumulative distribution of X. In particular, sample central moments of order 2k are expressed as the sum of between groups variations, providing an analogue to the analysis of variance. Similar expressions are obtained for the expectations of real-valued and measurable functions of X. 相似文献
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This article considers sample size determination methods based on Bayesian credible intervals for θ, an unknown real-valued parameter of interest. We consider clinical trials and assume that θ represents the difference in the effects of a new and a standard therapy. In this context, it is typical to identify an interval of parameter values that imply equivalence of the two treatments (range of equivalence). Then, an experiment designed to show superiority of the new treatment is successful if it yields evidence that θ is sufficiently large, i.e. if an interval estimate of θ lies entirely above the superior limit of the range of equivalence. Following a robust Bayesian approach, we model uncertainty on prior specification with a class Γ of distributions for θ and we assume that the data yield robust evidence if, as the prior varies in Γ, the lower bound of the credible set inferior limit is sufficiently large. Sample size criteria in the article consist in selecting the minimal number of observations such that the experiment is likely to yield robust evidence. These criteria are based on summaries of the predictive distributions of lower bounds of the random inferior limits of credible intervals. The method is developed for the conjugate normal model and applied to a trial for surgery of gastric cancer. 相似文献