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作者：Spokoiny, VG
摘要：Let a function f be observed with a noise. We wish to test the null hypothesis that the function is identically zero, against a composite nonparametric alternative: functions from the alternative set are separated away from zero in an integral (e.g., L(2)) norm and also possess some smoothness properties. The minimax rate of testing for this problem was evaluated in earlier papers by Ingster and by Lepski and Spokoiny under different kinds of smoothness assumptions. It was shown that both the ...
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作者：Dette, H; Wong, WK
作者单位：University of California System; University of California Los Angeles
摘要：We consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model. This problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters. A Bayesian approach is adopted, and optimal Bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically. For some criteria, th...
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作者：Hjort, NL; Jones, MC
作者单位：Open University - UK
摘要：This paper develops a nonparametric density estimator with parametric overtones. Suppose f(x, theta) is some family of densities, indexed by a vector of parameters theta. We define a local kernel-smoothed likelihood function which, for each x, can be used to estimate the best local parametric approximant to the true density. This leads to a new density estimator of the form f(x, <(theta)over cap (x)>), thus inserting the best local parameter estimate for each new value of x. When the bandwidth...
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作者：Tran, L; Roussas, G; Yakowitz, S; Van, BT
作者单位：University of Arizona; University of California System; University of California Davis; Universite de Pau et des Pays de l'Adour
摘要：This investigation is concerned with recovering a regression function g(x(i)) on the basis of noisy observations taken at uniformly spaced design points x(i). It is presumed that the corresponding observations are corrupted by additive dependent noise, and that the noise is, in fact, induced by a general linear process in which the summand law can be discrete, as well as continuously distributed. Discreteness induces a complication because such noise is not known to be strong mixing, the postu...
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作者：Gustafson, P
摘要：We investigate the degree to which posterior expectations are sensitive to prior distributions, using a local method based on functional differentiation. Invariance considerations suggest a family of norms which can be used to measure perturbations to the prior. The sensitivity measure is seen to depend heavily on the choice of norm; asymptotic results suggest which norm will yield the most useful results in practice, We find that to maintain asymptotically sensible behaviour, it is necessary ...
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作者：Koch, I
摘要：For d-dimensional images and regression functions the true object is estimated by median smoothing. The mean square Error of the median smoother is calculated using the framework of M-estimation, and an expression for the asymptotic rate of convergence of the mean square error is given. It is shown that the median smoother performs asymptotically as well as the local mean. The optimal window size and the bandwidth of the median smoother are given in terms of the sample sire and the dimension o...
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作者：Kadane, JB; Wasserman, L
摘要：Choquet capacities are a generalization of probability measures that arise in robustness, decision theory and game theory. Many capacities that arise in robustness are symmetric or can be transformed into symmetric capacities. We characterize the extreme points of the set of upper distribution functions corresponding to coherent, symmetric Choquet capacities on [0, 1]. We also show that the set of 2-alternating capacities is a simplex and we give a Choquet representation of this set.
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作者：Morgan, JP; Uddin, N
作者单位：Tennessee Technological University
摘要：Optimal design is studied for factorial experiments in the nested row and column setting. The approach is analogous to that of orthogonal Latin squares: main effects plans are found by the superimposition of one nested row and column design upon another Conditions are stated for statistical orthogonality of the superimposed components, resulting in orthogonal main effects plans, and a number of constructions are given. Orthogonal collections of sets of Latin squares are introduced. All of the ...
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作者：Nobel, A
摘要：We establish general sufficient conditions for the L(2)-consistency of multivariate histogram regression estimates based on data-dependent partitions. These same conditions insure the consistency of partitioning regression estimates based on local polynomial fits, and, with an additional regularity assumption, the consistency of histogram estimates for conditional medians. Our conditions require shrinking cells, subexponential growth of a combinatorial complexity measure and sublinear growth o...
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作者：Efromovich, S; Low, M
作者单位：University of Pennsylvania
摘要：Bickel and Ritov suggested an optimal estimator for the integral of the square of the hth derivative of a density when the unknown density belongs to a Lipschitz class of a given order beta. In this context optimality means that the estimate is asymptotically efficient, that is, it has the best constant and rate of risk convergence, whenever beta > 2k + 1/4, and it is rate optimal otherwise. The suggested optimal estimator crucially depends on the value of beta which is obviously unknown. Bick...
