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作者：Spokoiny, VG
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.
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作者：Koltchinskii, VI
作者单位：University of New Mexico
摘要：Let {Y (j): j = 1,..., n} be independent observations in R-m, m greater than or equal to 1 with common distribution Q. Suppose that Y (j) = X (j) + xi (j), j = 1,...,n, where {X (j), xi (j), j = 1,...,n} are independent, X (j), j = 1,..., n have common distribution P and xi (j), j = 1,...,n have common distribution mu, so that Q = P * mu. The problem is to recover hidden geometric structure of the support of P based an the independent observations Y (j). Assuming that the distribution of the e...
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作者：Inglot, T; Kallenberg, WCM; Ledwina, T
作者单位：Wroclaw University of Science & Technology; University of Twente; Polish Academy of Sciences
摘要：The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly stronger than first-order...
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作者：Owen, AB
作者单位：Stanford University
摘要：Some standard numerical problems become intractable in high dimensions. Yet successes are often achieved in practice. This may be explained in terms of the underlying target function being somehow simpler than assumed in the intractability arguments. A prototypical form of simplicity is approximate linearity. In moderate dimensions, linearity can be investigated by linear regression. In very high dimensions, this becomes computationally inefficient and eventually infeasible, as the cost of reg...
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作者：Ossiander, M; Waymire, EC
作者单位：Oregon State University
摘要：The probability distribution of the cascade generators in a random multiplicative cascade represents a hidden parameter which is reflected in the fine scale limiting behavior of the scaling exponents (sample moments) of a single sample cascade realization as a.s. constants. We identify a large class of cascade generators uniquely determined by these scaling exponents. For this class we provide both asymptotic consistency and confidence intervals for two different estimators of the cumulant gen...
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作者：Stein, ML; Quashnock, JM; Loh, JM
作者单位：University of Chicago; University of Chicago
摘要：Motivated by the study of an important data set for understanding the large-scale structure of the universe, this work considers the estimation of the reduced second-moment function, or K function, of a stationary point process on R observed over a large number of segments of possibly varying lengths. Theory and simulation are used to compare the behavior of isotropic and rigid motion correction estimators and some modifications of these estimators. These results generally support the use of m...
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作者：Huang, JHZ; Kooperberg, C; Stone, CJ; Truong, YK
作者单位：University of Pennsylvania; Fred Hutchinson Cancer Center; University of California System; University of California Berkeley; University of North Carolina; University of North Carolina Chapel Hill; National University of Singapore
摘要：The logarithm of the relative risk function in a proportional hazards model involving one or more possibly time-dependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization is taken over a suitably chosen finite-dimensional estimation space, whose dimension increases with the sample size and which is constructed from linear spaces of functions of one covariate and their...
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作者：Zuo, YJ; Serfling, R
作者单位：Arizona State University; Arizona State University-Tempe; University of Texas System; University of Texas Dallas
摘要：Statistical depth Functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack thereof, of four key properties desirable for depth functions in general. Roughly speaking, these properties may be described as: affine invariance, maximality at center, monotonicity relative to deep...
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作者：Settimi, R; Smith, JQ
作者单位：University of Chicago; University of Warwick
摘要：We study the geometry of the parameter space for Bayesian directed graphical models with hidden variables that have a tree structure and where all the nodes are binary. We show that the conditional independence statements implicit in such models can be expressed in terms of polynomial relationships among the central moments. This algebraic structure will enable us to identify the inequality constraints on the space of the manifest variables that are induced by the conditional independence assu...
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作者：Kochar, SC; Mukerjee, H; Samaniego, FJ
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; University of California System; University of California Davis; Wichita State University
摘要：In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x, M(x), defined by M(x)= E[X - x\X > z], where X is a lifetime. EA is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (nondecreasing). There is some literature on empirical estimators of M and their properties. Although tests ...
