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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.
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   

3.
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   

4.
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   

5.
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   

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.
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   

9.
The enumeration of binary cyclic self-orthogonal codes of length 63 is used to prove that any cyclic quasi-symmetric 2-(63,15,35)2-(63,15,35) design with block intersection numbers x=3x=3 and y=7y=7 is isomorphic to the geometric design having as blocks the three-dimensional subspaces in PG(5,2)PG(5,2).  相似文献   

10.
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   

11.
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   

12.
13.
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   

14.
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   

15.
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 xx a stochastic process M(x;t)M(x;t), 0<t<r0<t<r, is defined. Each mark process M(x;t)M(x;t) is compared with its expected value, say F(t;θ)F(t;θ), to produce a discrepancy measure at xx, where θθ 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   

16.
17.
For a loss distribution belonging to a location–scale family, Fμ,σFμ,σ, the risk measures, Value-at-Risk and Expected Shortfall are linear functions of the parameters: μ+τσμ+τσ where ττ is the corresponding risk measure of the mean-zero and unit-variance member of the family. For each risk measure, we consider a natural estimator by replacing the unknown parameters μμ and σσ by the sample mean and (bias corrected) sample standard deviation, respectively. The large-sample parametric confidence intervals for the risk measures are derived, relying on the asymptotic joint distribution of the sample mean and sample standard deviation. Simulation studies with the Normal, Laplace and Gumbel families illustrate that the derived asymptotic confidence intervals for Value-at-Risk and Expected Shortfall outperform those of Bahadur (1966) and Brazauskas et al. (2008), respectively. The method can also be effectively applied to Log-location-scale families whose supports are positive reals; an illustrative example is given in the area of financial credit risk.  相似文献   

18.
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   

19.
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   

20.
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   

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