首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider a linear regression model with regression parameter β=(β1,…,βp)β=(β1,,βp) and independent and identically N(0,σ2)N(0,σ2) distributed errors. Suppose that the parameter of interest is θ=aTβθ=aTβ where aa is a specified vector. Define the parameter τ=cTβ-tτ=cTβ-t where the vector cc and the number tt are specified and aa and cc are linearly independent. Also suppose that we have uncertain prior information that τ=0τ=0. We present a new frequentist 1-α1-α confidence interval for θθ 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-α1-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=0τ=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 ττ 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 2×22×2 factorial experiment with 20 replicates. Suppose that the parameter of interest θθ 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 θθ that utilizes this prior information.  相似文献   

2.
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   

3.
For fractional factorial (FF) designs, Zhang et al. (2008) introduced a new pattern for assessing regular designs, called aliased effect-number pattern (AENP), and based on the AENP, proposed a general minimum lower order confounding (denoted by GMC for short) criterion for selecting design. In this paper, we first have an overview of the existing optimality criteria of FF designs, and then propose a construction theory for 2n−m2nm GMC designs with 33N/128≤n≤5N/1633N/128n5N/16, where N=2n−mN=2nm is the run size and n is the number of factors, for all N's and n  's, via the doubling theory and SOS resolution IV designs. The doubling theory is extended with a new approach. By introducing a notion of rechanged (RC) Yates order for the regular saturated design, the construction result turns out to be quite transparent: every GMC 2n−m2nm design simply consists of the last n columns of the saturated design with a specific RC Yates order. This can be very conveniently applied in practice.  相似文献   

4.
5.
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   

6.
A popular measure to assess 2-level supersaturated designs is the E(s2)E(s2) criterion. In this paper, improved lower bounds on E(s2)E(s2) are obtained. The same improvement has recently been established by Ryan and Bulutoglu [2007. E(s2)E(s2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. However, our analysis provides more details on precisely when an improvement is possible, which is lacking in Ryan and Bulutoglu [2007. E(s2)E(s2)-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference 137, 2250–2262]. The equivalence of the bounds obtained by Butler et al. [2001. A general method of constructing E(s2)E(s2)-optimal supersaturated designs. J. Roy. Statist. Soc. B 63, 621–632] (in the cases where their result applies) and those obtained by Bulutoglu and Cheng [2004. Construction of E(s2)E(s2)-optimal supersaturated designs. Ann. Statist. 32, 1662–1678] is established. We also give two simple methods of constructing E(s2)E(s2)-optimal designs.  相似文献   

7.
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   

8.
9.
In this paper we revisit the classical problem of interval estimation for one-binomial parameter and for the log odds ratio of two binomial parameters. We examine the confidence intervals provided by two versions of the modified log likelihood root: the usual Barndorff-Nielsen's r*r* and a Bayesian version of the r*r* test statistic.  相似文献   

10.
In this paper, we study Lebesgue densities on (0,∞)d(0,)d that are non-increasing in each coordinate, while keeping all other coordinates fixed, from the perspective of local asymptotic minimax lower bound theory. In particular, we establish a local optimal rate of convergence of the order n−1/(d+2)n1/(d+2).  相似文献   

11.
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   

12.
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   

13.
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   

14.
15.
16.
A covering array  CA(N;t,k,v)CA(N;t,k,v) is an N×kN×k array, in which in every N×tN×t subarray, each of the vtvt possible t  -tuples over vv symbols occurs at least once. The parameter t is the strength   of the array. Covering arrays have a wide range of applications for experimental screening designs, particularly for software interaction testing. A compact representation of certain covering arrays employs “permutation vectors” to encode vt×1vt×1 subarrays of the covering array so that a covering perfect hash family whose entries correspond to permutation vectors yields a covering array. We introduce a method for effective search for covering arrays of this type using tabu search. Using this technique, improved covering arrays of strength 3, 4 and 5 have been found, as well as the first arrays of strength 6 and 7 found by computational search.  相似文献   

17.
The paper develops constrained Bayes and empirical Bayes estimators in the random effects ANOVA model under balanced loss functions. In the balanced normal–normal model, estimators of the Bayes risks of the constrained Bayes and constrained empirical Bayes estimators are provided which are correct asymptotically up to O(m-1)O(m-1), that is the remainder term is o(m-1)o(m-1), mm denoting the number of strata.  相似文献   

18.
Suppose that we have a linear regression model Y=Xβ+ν0(X)εY=Xβ+ν0(X)ε with random error εε, where X is a random design variable and is observed completely, and Y is the response variable and some Y-values are missing at random (MAR). In this paper, based on the ‘complete’ data set for Y after inverse probability weighted imputation, we construct empirical likelihood statistics on EY   and ββ which have the χ2χ2-type limiting distributions under some new conditions compared with Xue (2009). Our results broaden the applicable scope of the approach combined with Xue (2009).  相似文献   

19.
In this paper, we consider the multivariate normality test based on measure of multivariate sample skewness defined by Srivastava (1984). Srivastava derived asymptotic expectation up to the order N−1 for the multivariate sample skewness and approximate χ2χ2 test statistic, where N   is sample size. Under normality, we derive another expectation and variance for Srivastava's multivariate sample skewness in order to obtain a better test statistic. From this result, improved approximate χ2χ2 test statistic using the multivariate sample skewness is also given for assessing multivariate normality. Finally, the numerical result by Monte Carlo simulation is shown in order to evaluate accuracy of the obtained expectation, variance and improved approximate χ2χ2 test statistic. Furthermore, upper and lower percentiles of χ2χ2 test statistic derived in this paper are compared with those of χ2χ2 test statistic derived by Mardia (1974) which is used multivariate sample skewness defined by Mardia (1970).  相似文献   

20.
We determine a credible set A   that is the “best” with respect to the variation of the prior distribution in a neighborhood ΓΓ of the starting prior π0(θ)π0(θ). Among the class of sets with credibility γγ under π0π0, the “optimally robust” set will be the one which maximizes the minimum probability of including θθ as the prior varies over ΓΓ. This procedure is also Γ-minimaxΓ-minimax with respect to the risk function, probability of non-inclusion. We find the optimally robust credible set for three neighborhood classes ΓΓ, the ε-contaminationε-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   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号