共查询到20条相似文献,搜索用时 31 毫秒
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In this paper, we investigate the estimation problem of the mixture proportion λ in a nonparametric mixture model of the form λF(x)+(1-λ)G(x) using the minimum Hellinger distance approach, where F and G are two unknown distributions. We assume that data from the distributions F and G as well as from the mixture distribution λF+(1-λ)G are available. We construct a minimum Hellinger distance estimator of λ and study its asymptotic properties. The proposed estimator is chosen to minimize the Hellinger distance between a parametric mixture model and a nonparametric density estimator. We also develop a maximum likelihood estimator of λ. Theoretical properties such as the existence, strong consistency, asymptotic normality and asymptotic efficiency of the proposed estimators are investigated. Robustness properties of the proposed estimator are studied using a Monte Carlo study. Two real data examples are also analyzed. 相似文献
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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)/2, different from the rate n-1/2 obtained in the random design case, where α 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)/2. 相似文献
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Trimmed U -statistics can be constructed in two different ways: by basing the statistic on a trimmed sample or by averaging the trimmed set of kernel values. Mild conditions are given to ensure the rate of convergence to normality is O(n-1/2) in both cases. 相似文献
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Jean-Claude Fort Thierry Klein Agnès Lagnoux Béatrice Laurent 《Journal of statistical planning and inference》2013
We consider a functional linear model where the explicative variables are known stochastic processes taking values in a Hilbert space, the main example is given by Gaussian processes in L2([0,1]). We propose estimators of the Sobol indices in this functional linear model. Our estimators are based on U-statistics. We prove the asymptotic normality and the efficiency of our estimators and we compare them from a theoretical and practical point of view with classical estimators of Sobol indices. 相似文献
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The paper studies the three-parameter generalization of the logarithmic distribution that is obtained as the cluster distribution for the generalized Euler distribution. The diagnostic statistic, R(x)=xpx/[(x-1)px-1], is constant for the logarithmic distribution. For the new distribution it can decrease, stay constant, or increase as x increases. The relative values of the extra parameters determine the flatness/hollowness of the distribution and its tail behaviour. Kemp's q-logarithmic distribution and the Euler cluster distribution are special cases. Fitted data sets illustrate the properties of the distribution and its limiting forms. 相似文献
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C. Radhakrishna Rao Damodar N. Shanbhag Theofanis Sapatinas M. Bhaskara Rao 《Journal of statistical planning and inference》2009
In the course of studying the moment sequence {nn:n=0,1,…}, Eaton et al. [1971. On extreme stable laws and some applications. J. Appl. Probab. 8, 794–801] have shown that this sequence, which is, indeed, the moment sequence of a log-extreme stable law with characteristic exponent γ=1, corresponds to a scale mixture of exponential distributions and hence to a distribution with decreasing failure rate. Following essentially the approach of Shanbhag et al. [1977. Some further results in infinite divisibility. Math. Proc. Cambridge Philos. Soc. 82, 289–295] we show that, under certain conditions, log-extreme stable laws with characteristic exponent γ∈[1,2) are scale mixtures of exponential distributions and hence are infinitely divisible and have decreasing failure rates. In addition, we study the moment problem associated with the log-extreme stable laws with characteristic exponent γ∈(0,2] and throw further light on the existing literature on the subject. As a by-product, we show that generalized Poisson and generalized negative binomial distributions are mixed Poisson distributions. Finally, we address some relevant questions on structural aspects of infinitely divisible distributions, and make new observations, including in particular that certain results appearing in Steutel and van Harn [2004. Infinite Divisibility of Probability Distributions on the Real Line. Marcel Dekker, New York] have links with the Wiener–Hopf factorization met in the theory of random walk. 相似文献
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Super-simple cyclic designs are useful on constructing codes and designs such as superimposed codes, perfect hash families and optical orthogonal codes with index two. In this paper, we show that there exists a super-simple cyclic (v,4,λ) for 7?v?41 and all admissible λ with two definite exceptions of (v,λ)=(9,3),(13,5) and one possible exception of (v,λ)=(39,18). Some useful algorithms are explained for computer search and new designs are displayed. 相似文献
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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)-design and a g(n,e)-matrix are introduced to study designs of n factor two-level experiments which can unbiasedly estimate the mean, the n main effects and e 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)-matrices. A standard form for a g(n,1)-matrix is introduced and some lower and upper bounds on the absolute determinant value of a D-optimal g(n,1)-matrix in the class of all g(n,1)-matrices are obtained and an approach to construct D-optimal g(n,1)-matrices is given for 2?n?8. For two specific subclasses, namely a certain class of g(n,1)-matrices within the class of g(n,1)-matrices of index one and the class C(H) of g(8t+2,1)-matrices constructed from a normalized Hadamard matrix H of order 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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The problem of classifying all isomorphism classes of 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)'s, OA(24,k,2,3)'s for 6?k?11, OA(32,k,2,3)'s for 6?k?11, OA(40,k,2,3)'s for 6?k?10, OA(48,k,2,3)'s for 6?k?8, OA(56,k,2,3)'s, OA(80,k,2,4)'s, OA(112,k,2,4)'s, for k=6,7, OA(64,k,2,4)'s, OA(96,k,2,4)'s for k=7,8, and OA(144,k,2,4)'s for k=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
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In this paper, we study a random field U?(t,x) governed by some type of stochastic partial differential equations with an unknown parameter θ and a small noise ?. We construct an estimator of θ based on the continuous observation of N Fourier coefficients of U?(t,x), and prove the strong convergence and asymptotic normality of the estimator when the noise ? tends to zero. 相似文献
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In this paper, we study Lebesgue densities on (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). 相似文献
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Consider a sequence of independent and identically distributed random variables {Xi,i?1} with a common absolutely continuous distribution function F . Let X1:n?X2:n???Xn:n be the order statistics of {X1,X2,…,Xn} and {Yl,l?1} be the sequence of record values generated by {Xi,i?1}. In this work, the conditional distribution of Yl given Xn:n is established. Some characterizations of F based on record values and Xn:n are then given. 相似文献