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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：Nussbaum, M
摘要：Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam's deficiency distance Delta would make it precise. The models are then asymptotically equivalent for all purposes of statistical decision with bounded loss. In nonparametrics, a first result of this...
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作者：Brown, LD; Low, MG
摘要：The principal result is that, under conditions, to any nonparametric regression problem there corresponds an asymptotically equivalent sequence of white noise with drift problems, and conversely. This asymptotic equivalence is in a global and uniform sense. Any normalized risk function attainable in one problem is asymptotically attainable in the other, with the difference in normalized risks converging to zero uniformly over the entire parameter space. The results are constructive. A recipe i...
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作者：Stute, W
摘要：Let (F) over cap(n) be the Kaplan-Meier estimator of a distribution function F computed from randomly censored data. It is known that, under certain integrability assumptions on a function phi, the Kaplan-Meier integral integral phi d (F) over cap(n), when properly standardized, is asymptotically normal. In this paper it is shown that, with probability 1, the jackknife estimate of variance consistently estimates the (limit) variance.
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作者：Hossjer, O
摘要：Given data X(1),..., X(n) and a kernel h with m arguments, Serfling introduced the class of generalized L-statistics (GL-statistics), which is defined by taking linear combinations of the ordered h(X(i1),..., X(im)), where (i(1),...,i(m)) ranges over all n!/(n - m)! distinct m-tuples of (1,..., n). In this paper we derive a class of incomplete generalized L-statistics (IGL-statistics) by taking linear combinations of the ordered elements from a subset of {h(X(i1),..., X(im))} with size N(n). A...
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作者：Kleinberg, EM
摘要：We will introduce a generic approach for solving problems in pattern recognition based on the synthesis of accurate multiclass discriminators from large numbers of very inaccurate ''weak'' models through the use of discrete stochastic processes. Contrary to the standard expectation held for the many statistical and heuristic techniques normally associated with the field, a significant feature of this method of ''stochastic modeling'' is its resistance to so-called ''overtraining.'' The drop in...
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作者：Brown, LD; Low, MG
摘要：A general constrained minimum risk inequality is derived. Given two densities f(theta) and f(0) we find a lower bound for the risk at the point theta given an upper bound for the risk at the point 0. The inequality sheds new light on superefficient estimators in the normal location problem and also on an adaptive estimation problem arising in nonparametric functional estimation.
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作者：He, XM; Shao, QM
作者单位：University of Oregon
摘要：We obtain strong Bahadur representations for a general class of M-estimators that satisfies Sigma(i) psi(x(i), theta) = o(delta(n)), where the x(i)'s are independent but not necessarily identically distributed random variables. The results apply readily to M-estimators of regression with nonstochastic designs. More specifically, we consider the minimum L(p) distance estimators, bounded influence GM-estimators and regression quantiles. Under appropriate design conditions, the error rates obtain...
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作者：Breiman, L
摘要：In model selection, usually a ''best'' predictor is chosen from a collection {<(mu)over cap>(., s)} of predictors where <(mu)over cap>(., s) is the minimum least-squares predictor in a collection U-s of predictors. Here s is a complexity parameter; that is, the smaller s, the lower dimensional/smoother the models in U-s. If L is the data used to derive the sequence {<(mu)over cap>(., s)}, the procedure is called unstable if a small change in L can cause large changes in {<(mu)over cap>(., s)}....
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作者：Beran, R; Feuerverger, A; Hall, P
作者单位：University of Toronto; Australian National University
摘要：An experiment records stimulus and response for a random sample of cases. The relationship between response and stimulus is thought to be linear, the values of the slope and intercept varying by case. From such data, we construct a consistent, asymptotically normal, nonparametric estimator for the joint density of the slope and intercept. Our methodology incorporates the radial projection-slice theorem for the Radon transform, a technique for locally linear nonparametric regression and a taper...
