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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   

2.
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   

3.
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)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)E(fNOD)-optimal SSD is obtained. Moreover, many new E(fNOD)E(fNOD)-optimal mixed-level SSDs are constructed and listed. The method here generalizes the one proposed by Liu and Dean [2004. kk-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   

4.
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   

5.
6.
In this article, we extended the empirical distribution function based test statistic IkIk of Skaug and Tjostheim [1993. Nonparametric test of serial independence based on the empirical distribution function. Biometrika 80, 591–602] in the time series setting to DnDn for spatial lattice data and derived the asymptotic distribution of the proposed test statistic DnDn under the null hypothesis of spatial independence. The size and power of the proposed test statistic under conditional autoregressive model (CAR) were simulated. We applied DnDn, Moran's I and Geary's c   to the transformed and well-studied sudden infant death syndrome data from North Carolina and found that DnDn produced a much smaller pp-value in testing spatial independence.  相似文献   

7.
In common with other non-linear models, the optimal design for a limiting dilution assay (LDA) depends on the value of the unknown parameter, θθ, in the model. Consequently optimal designs cannot be specified unless some assumptions are made about the possible values of θθ. 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 θθ is above or below a specified threshold, θ0θ0.  相似文献   

8.
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   

9.
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   

10.
We consider a regression of yy on xx given by a pair of mean and variance functions with a parameter vector θθ to be estimated that also appears in the distribution of the regressor variable xx. The estimation of θθ 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-yy unbiased estimating functions. Of special interest is the case where the distribution of xx depends only on a subvector αα of θθ, which may be considered a nuisance parameter. In general, αα must be estimated simultaneously together with the rest of θθ, but there are cases where αα 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   

11.
12.
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   

13.
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   

14.
15.
The probability function and binomial moments of the number NnNn of (upper) records up to time (index) n in a geometrically increasing population are obtained in terms of the signless q-Stirling numbers of the first kind, with q   being the inverse of the proportion λλ of the geometric progression. Further, a strong law of large numbers and a central limit theorem for the sequence of random variables NnNn, n=1,2,…,n=1,2,, are deduced. As a corollary the probability function of the time TkTk of the kth record is also expressed in terms of the signless q  -Stirling numbers of the first kind. The mean of TkTk is obtained as a q  -series with terms of alternating sign. Finally, the probability function of the inter-record time Wk=Tk-Tk-1Wk=Tk-Tk-1 is obtained as a sum of a finite number of terms of q  -numbers. The mean of WkWk is expressed by a q-series. As k   increases to infinity the distribution of WkWk converges to a geometric distribution with failure probability q. Additional properties of the q-Stirling numbers of the first kind, which facilitate the present study, are derived.  相似文献   

16.
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   

17.
An experimental design is said to be Schur optimal, if it is optimal with respect to the class of all Schur isotonic criteria, which includes Kiefer's criteria of ΦpΦp-optimality, distance optimality criteria and many others. In the paper we formulate an easily verifiable necessary and sufficient condition for Schur optimality in the set of all approximate designs of a linear regression experiment with uncorrelated errors. We also show that several common models admit a Schur optimal design, for example the trigonometric model, the first-degree model on the Euclidean ball, and the Berman's model.  相似文献   

18.
For the Weibull- and Richards-regression model robust designs are determined by maximizing a minimum of D  - or D1D1-efficiencies, taken over a certain range of the non-linear parameters. It is demonstrated that the derived designs yield a satisfactory solution of the optimal design problem for this type of model in the sense that these designs are efficient and robust with respect to misspecification of the unknown parameters. Moreover, the designs can also be used for testing the postulated form of the regression model against a simplified sub-model.  相似文献   

19.
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   

20.
In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter αα and a base probability measure G0G0. In problems where αα is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for αα. In this paper an approach is developed for computing a prior for the precision parameter αα that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.  相似文献   

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