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1.
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   

2.
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   

3.
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   

4.
In this article we study the problem of classification of three-level multivariate data, where multiple qq-variate observations are measured on uu-sites and over pp-time points, under the assumption of multivariate normality. The new classification rules with certain structured and unstructured mean vectors and covariance structures are very efficient in small sample scenario, when the number of observations is not adequate to estimate the unknown variance–covariance matrix. These classification rules successfully model the correlation structure on successive repeated measurements over time. Computation algorithms for maximum likelihood estimates of the unknown population parameters are presented. Simulation results show that the introduction of sites in the classification rules improves their performance over the existing classification rules without the sites.  相似文献   

5.
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 XX. In particular, sample central moments of order 2k2k 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 XX.  相似文献   

6.
Collapsibility with respect to a measure of association implies that the measure of association can be obtained from the marginal model. We first discuss model collapsibility and collapsibility with respect to regression coefficients for linear regression models. For parallel regression models, we give simple and different proofs of some of the known results and obtain also certain new results. For random coefficient regression models, we define (average) AA-collapsibility and obtain conditions under which it holds. We consider Poisson regression and logistic regression models also, and derive conditions for collapsibility and AA-collapsibility, respectively. These results generalize some of the results available in the literature. Some suitable examples are also discussed.  相似文献   

7.
A representation of the transient probability functions of finite birth–death processes (with or without catastrophes) as a linear combination of exponential functions is derived using a recursive, Cayley–Hamilton approach. This method of solution allows practitioners to solve for these transient probability functions by reducing the problem to three calculations: determining eigenvalues of the QQ-matrix, raising the QQ-matrix to an integer power and solving a system of linear equations. The approach avoids Laplace transforms and permits solution of a particular transition probability function from state ii to jj without determining all such functions.  相似文献   

8.
The aim of an experiment is often to enable discrimination between competing forms for a response model. We investigate the selection of a continuous design for a non-sequential strategy when there are two competing generalized linear models for a binomial response, with a common link function and the linear predictor of one model nested within that of the other. A new criterion, TETE-optimality, is defined, based on the difference in the deviances from the two models, and comparisons are made with TT-, DsDs- and DD-optimality. Issues are raised through the study of two examples in which designs are assessed using simulation studies of the power to reject the null hypothesis of the smaller model being correct, when the data are generated from the larger model. Parameter estimation for discrimination designs is also discussed and a simple method is investigated of combining designs to form a hybrid design in order to achieve both model discrimination and estimation. This method has a computational advantage over the use of a compound criterion and the similar performance of the designs obtained from the two approaches is illustrated in an example.  相似文献   

9.
In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters ττ and θθ, which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for θθ and extreme quantiles are also proposed, but they both depend on the unknown parameter ττ, making them useless in practical situations. In this paper, we propose an estimator of ττ which is independent of θθ. Plugging our estimator of ττ 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   

10.
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   

11.
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   

12.
This paper deals with the distributions of test statistics for the number of useful discriminant functions and the characteristic roots in canonical discriminant analysis. These asymptotic distributions have been extensively studied when the number p   of variables is fixed, the number q+1q+1 of groups is fixed, and the sample size N tends to infinity. However, these approximations become increasingly inaccurate as the value of p increases for a fixed value of N. On the other hand, we encounter to analyze high-dimensional data such that p is large compared to n. The purpose of the present paper is to derive asymptotic distributions of these statistics in a high-dimensional framework such that q   is fixed, p→∞p, m=n-p+q→∞m=n-p+q, and p/n→c∈(0,1)p/nc(0,1), where n=N-q-1n=N-q-1. Numerical simulation revealed that our new asymptotic approximations are more accurate than the classical asymptotic approximations in a considerably wide range of (n,p,q)(n,p,q).  相似文献   

13.
Optimal symmetrical fractional factorial designs with nn runs and mm factors of ss levels each are constructed. We consider only designs such that no two factors are aliases. The minimum moment aberration criterion proposed by Xu (2003) is used to judge the optimality of the designs. The minimum moment aberration criterion is equivalent to the popular generalized minimum aberration criterion proposed by Xu and Wu (2001), but the minimum moment criterion is simpler to formulate and employ computationally. Some optimal designs are constructed by using generalized Hadamard matrices.  相似文献   

14.
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   

15.
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   

16.
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   

17.
18.
Suppose all events occurring in an unknown number (ν)(ν) of iid renewal processes, with a common renewal distribution F  , are observed for a fixed time ττ, where both νν and F   are unknown. The individual processes are not known a priori, but for each event, the process that generated it is identified. For example, in software reliability application, the errors (or bugs) in a piece of software are not known a priori, but whenever the software fails, the error causing the failure is identified. We present a nonparametric method for estimating νν and investigate its properties. Our results show that the proposed estimator performs well in terms of bias and asymptotic normality, while the MLE of νν derived assuming that the common renewal distribution is exponential may be seriously biased if that assumption does not hold.  相似文献   

19.
EE-optimal designs for comparing three treatments in blocks of size three are identified, where intrablock observations are correlated according to a first order autoregressive error process with parameter ρ∈(0,1)ρ(0,1). For number of blocks b   of the form b=3n+1b=3n+1, there are two distinct optimal designs depending on the value of ρρ, with the best design being unequally replicated for large ρρ. For other values of bb, binary, equireplicate designs with specified within-block assignment patterns are best. In many cases, the stronger majorization optimality is established.  相似文献   

20.
In Hedayat and Pesotan [1992, Two-level factorial designs for main effects and selected two-factor interactions. Statist. Sinica 2, 453–464.] the concepts of a g(n,e)g(n,e)-design and a g(n,e)g(n,e)-matrix are introduced to study designs of nn factor two-level experiments which can unbiasedly estimate the mean, the nn main effects and ee specified two-factor interactions appearing in an orthogonal polynomial model and it is observed that the construction of a g-design is equivalent to the construction of a g  -matrix. This paper deals with the construction of D-optimal g(n,1)g(n,1)-matrices. A standard form for a g(n,1)g(n,1)-matrix is introduced and some lower and upper bounds on the absolute determinant value of a D-optimal g(n,1)g(n,1)-matrix in the class of all g(n,1)g(n,1)-matrices are obtained and an approach to construct D-optimal g(n,1)g(n,1)-matrices is given for 2?n?82?n?8. For two specific subclasses, namely a certain class of g(n,1)g(n,1)-matrices within the class of g(n,1)g(n,1)-matrices of index one and the class C(H)C(H) of g(8t+2,1)g(8t+2,1)-matrices constructed from a normalized Hadamard matrix H   of order 8t+4(t?1)8t+4(t?1) two techniques for the construction of the restricted D-optimal matrices are given.  相似文献   

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