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1.
Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index γγ. The class γ>0γ>0 corresponds to Pareto-type or heavy tailed distributions, while γ<0γ<0 indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with γ=0γ=0. The tail behaviour can then be specified using the Weibull tail index. Classical estimators of this index show severe bias. In this paper we present a new estimation approach based on the mean excess function, which exhibits improved bias and mean squared error. The asserted properties are supported by simulation experiments and asymptotic results. Illustrations with real life data sets are provided.  相似文献   

2.
This paper considered the estimation of the regression parameters of a general probit regression model. Accordingly, we proposed five ridge regression (RR) estimators for the probit regression models for estimating the parameters (β)(β) when the weighted design matrix is ill-conditioned and it is suspected that the parameter ββ may belong to a linear subspace defined by Hβ=hHβ=h. Asymptotic properties of the estimators are studied with respect to quadratic biases, MSE matrices and quadratic risks. The regions of optimality of the proposed estimators are determined based on the quadratic risks. Some relative efficiency tables and risk graphs are provided to illustrate the numerical comparison of the estimators. We conclude that when q≥3q3, one would uses PRRRE; otherwise one uses PTRRE with some optimum size αα. We also discuss the performance of the proposed estimators compare to the alternative ridge regression method due to Liu (1993).  相似文献   

3.
We consider Bayesian density estimation for compactly supported densities using Bernstein mixtures of beta-densities equipped with a Dirichlet prior on the distribution function. We derive the rate of convergence for αα-smooth densities for 0<α?20<α?2 and show that a faster rate of convergence can be obtained by using fewer terms in the mixtures than proposed before. The Bayesian procedure adapts to the unknown value of αα. The modified Bayesian procedure is rate-optimal if αα is at most one. This result can be extended to two dimensions.  相似文献   

4.
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   

5.
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   

6.
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   

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, a k  -step-stress accelerated life-testing is considered with an equal step duration ττ. For small to moderate sample sizes, a practical modification is made to the model previously considered by Gouno et al. [2004. Optimal step-stress test under progressive Type-I censoring. IEEE Trans. Reliability 53, 383–393] in order to guarantee a feasible k  -step-stress test under progressive Type-I censoring, and the optimal ττ is determined under this model. Next, we discuss the determination of optimal ττ under the condition that the step-stress test proceeds to the k  -th stress level, and the efficiency of this conditional inference is compared to that of the previous case. In all cases considered, censoring is allowed at each point of stress change (viz., iτiτ, i=1,2,…,ki=1,2,,k). The determination of optimal ττ is discussed under C-optimality, D-optimality, and A-optimality criteria. We investigate in detail the case of progressively Type-I right censored data from an exponential distribution with a single stress variable.  相似文献   

10.
We consider in this paper the regularization by projection of a linear inverse problem Y=Af+εξY=Af+εξ where ξξ denotes a Gaussian white noise, A   a compact operator and ε>0ε>0 a noise level. Compared to the standard unbiased risk estimation (URE) method, the risk hull minimization (RHM) procedure presents a very interesting numerical behavior. However, the regularization in the singular value decomposition setting requires the knowledge of the eigenvalues of AA. Here, we deal with noisy eigenvalues: only observations on this sequence are available. We study the efficiency of the RHM method in this situation. More generally, we shed light on some properties usually related to the regularization with a noisy operator.  相似文献   

11.
This paper deals with sparse K2×J(J>2)K2×J(J>2) tables. Projection-method Mantel–Haenszel (MH) estimators of the common odds ratios have been proposed for K2×JK2×J tables, which include Greenland's generalized MH estimator as a special case. The method projects log-transformed MH estimators for all K2×2K2×2 subtables, which were called naive MH estimators, onto a linear space spanned by log odds ratios. However, for sparse tables it is often the case that naive MH estimators are unable to be computed. In this paper we introduce alternative naive MH estimators using a graph that represents K2×JK2×J tables, and apply the projection to these alternative estimators. The idea leads to infinitely many reasonable estimators and we propose a method to choose the optimal one by solving a quadratic optimization problem induced by the graph, where some graph-theoretic arguments play important roles to simplify the optimization problem. An illustration is given using data from a case–control study. A simulation study is also conducted, which indicates that the MH estimator tends to have a smaller mean squared error than the MH estimator previously suggested and the conditional maximum likelihood estimator for sparse tables.  相似文献   

12.
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   

13.
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.
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   

16.
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   

17.
The problem of classifying all isomorphism classes of OA(N,k,s,t)OA(N,k,s,t)'s is shown to be equivalent to finding all isomorphism classes of non-negative integer solutions to a system of linear equations under the symmetry group of the system of equations. A branch-and-cut algorithm developed by Margot [2002. Pruning by isomorphism in branch-and-cut. Math. Programming Ser. A 94, 71–90; 2003a. Exploiting orbits in symmetric ILP. Math. Programming Ser. B 98, 3–21; 2003b. Small covering designs by branch-and-cut. Math. Programming Ser. B 94, 207–220; 2007. Symmetric ILP: coloring and small integers. Discrete Optim., 4, 40–62] for solving integer programming problems with large symmetry groups is used to find all non-isomorphic OA(24,7,2,2)OA(24,7,2,2)'s, OA(24,k,2,3)OA(24,k,2,3)'s for 6?k?116?k?11, OA(32,k,2,3)OA(32,k,2,3)'s for 6?k?116?k?11, OA(40,k,2,3)OA(40,k,2,3)'s for 6?k?106?k?10, OA(48,k,2,3)OA(48,k,2,3)'s for 6?k?86?k?8, OA(56,k,2,3)OA(56,k,2,3)'s, OA(80,k,2,4)OA(80,k,2,4)'s, OA(112,k,2,4)OA(112,k,2,4)'s, for k=6,7k=6,7, OA(64,k,2,4)OA(64,k,2,4)'s, OA(96,k,2,4)OA(96,k,2,4)'s for k=7,8k=7,8, and OA(144,k,2,4)OA(144,k,2,4)'s for k=8,9k=8,9. Further applications to classifying covering arrays with the minimum number of runs and packing arrays with the maximum number of runs are presented.  相似文献   

18.
Skew Dyck paths     
In this paper we study the class SS of skew Dyck paths, i.e. of those lattice paths that are in the first quadrant, begin at the origin, end on the x-axis, consist of up steps  U=(1,1)U=(1,1), down steps  D=(1,-1)D=(1,-1), and left steps  L=(−1,-1)L=(1,-1), and such that up steps never overlap with left steps. In particular, we show that these paths are equinumerous with several other combinatorial objects, we describe some involutions on this class, and finally we consider several statistics on SS.  相似文献   

19.
20.
In this note we provide a counterexample which resolves conjectures about Hadamard matrices made in this journal. Beder [1998. Conjectures about Hadamard matrices. Journal of Statistical Planning and Inference 72, 7–14] conjectured that if HH is a maximal m×nm×n row-Hadamard matrix then m is a multiple of 4; and that if n   is a power of 2 then every row-Hadamard matrix can be extended to a Hadamard matrix. Using binary integer programming we obtain a maximal 13×3213×32 row-Hadamard matrix, which disproves both conjectures. Additionally for n being a multiple of 4 up to 64, we tabulate values of m   for which we have found a maximal row-Hadamard matrix. Based on the tabulated results we conjecture that a m×nm×n row-Hadamard matrix with m?n-7m?n-7 can be extended to a Hadamard matrix.  相似文献   

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