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作者：Wellner, JA; Zhang, Y
作者单位：University of Washington; University of Washington Seattle; State University System of Florida; University of Central Florida
摘要：We study two estimators of the mean function of a counting process based on panel count data. The setting for panel count data is one in which n independent subjects, each with a counting process with common mean function, are observed at several possibly different times during a study. Following a model proposed by Schick and Yu, we allow the number of observation times, and the observation times themselves, to be random variables. Our goal is to estimate the mean function of the counting pro...
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作者：Bühlmann, P; Yu, B
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of California System; University of California Berkeley; AT&T; University of California System; University of California Berkeley
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作者：Romano, JP; Wolf, M
作者单位：Stanford University; Universidad Carlos III de Madrid
摘要：Given a sample X-1,...,X-n from a distribution F, the problem of constructing nonparametric confidence intervals for the mean mu (F) is considered. Unlike bootstrap procedures or those based on normal approximations, we insist an any procedure being truly nonparametric in the sense that the probability that the confidence interval contains mu (F) based on a sample of size n from F be at least 1 - alpha for all F and all n. Bahadur and Savage proved it is impossible to find an effective (or bou...
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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...
