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作者：KOO, JY
摘要：Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a class of functions having a smoothness measure p. Let T denote a known linear operator of order q which maps f to another function T(f) in a space G. Let T(n) denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let \\T(n)-T(f)\\G be a norm of T(n)-T(f). Under appropriate regularity conditions, it is shown that t...
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作者：SRIVASTAVA, MS; WU, YH
摘要：Pollak and Siegmund compared the Shiryayev-Roberts procedure with the CUSUM procedure for detecting a change in the drift of a Brownian motion based on the conditional average delay time. In this paper, the exponentially weighted moving average (EWMA) procedure proposed by Roberts is compared with the Shiryayev-Roberts and CUSUM procedures. The comparison is based on the stationary average delay time as advocated by Shiryayev. The optimal design for the EWMA procedure and its asymptotic proper...
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作者：JAMES, AT; VENABLES, WN
摘要：For small sample random effects models, results are derived which show in certain cases, and indicate in general, that an estimated random effects variance matrix may be used in the weight matrices without causing undue error in the empirically weighted mean. Exact error variances are derived mathematically for the empirically weighted mean for the two sample case in one and two dimensions. Simulation is used to determine errors for a practical example of six five-variate samples. For estimati...
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作者：FOSTER, DP; GEORGE, EI
作者单位：University of Texas System; University of Texas Austin
摘要：Consider the problem of estimating mu, based on the observation of Y0, Y1,...,Y(n), where it is assumed only that Y0, Y1,...,Y(kappa) iid N(mu, sigma2) for some unknown kappa. Unlike the traditional change-point problem, the focus here is not on estimating kappa, which is now a nuisance parameter. When it is known that kappa = k, the sample mean Y(k)BAR = SIGMA0(k)Y(i)/(k + 1), provides, in addition to wonderful efficiency properties, safety in the sense that it is minimax under squared error ...
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作者：HALL, P; LI, KC
作者单位：Commonwealth Scientific & Industrial Research Organisation (CSIRO); University of California System; University of California Los Angeles
摘要：This paper studies the shapes of low dimensional projections from high dimensional data. After standardization, let x be a p-dimensional random variable with mean zero and identity covariance. For a projection beta'x, \\beta\\ = 1, find another direction b so that the regression curve of b'x against beta'x is as nonlinear as possible. We show that when the dimension of x is large, for most directions beta even the most nonlinear regression is still nearly linear. Our method depends on the cons...
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作者：LI, G; DOSS, H
作者单位：Purdue University System; Purdue University; State University System of Florida; Florida State University
摘要：Suppose that X1,...,X(n) are i.i.d. approximately F, and we wish to test the null hypothesis that F is a member of the parametric family F = {F(theta)(x); theta is-an-element-of THETA} where THETA is-an-element-of R(q). The classical Pearson-Fisher chi-square test involves partitioning the real axis into k cells I1,...,I(k) and forming the chi-square statistic X2 = SIGMA(i=1)k(O(i)-nF(theta)(I(i)))2/nF(theta)(I(i)), where O(i) is the number of observations falling into cell i and theta is the ...
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作者：TRAN, LT
摘要：Let (X(t), Y(t)) be a stationary time series with X(t) being R(d)-valued and Y(t) real valued, and where Y(t) is not necessarily bounded. Let E(Y0\X0) be the conditional mean function. Under appropriate regularity conditions, local average estimators of this function can be chosen to achieve the optimal rate of convergence (n-1 log n)1/(d+2) in L(infinity) norm restricted to a compact. The result answers a question raised by Truong and Stone.
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作者：BARNDORFFNIELSEN, OE; BLAESILD, P
摘要：A variety of exponential models with affine dual foliations have been noted to possess certain rather similar statistical properties. To give a precise meaning to what has been conceived as ''similar'' we here propose a set of five conditions, of a differential geometric/statistical nature, that specify the class of what we term orthogeodesic models. It is discussed how these conditions capture the properties in question, and it is shown that some important nonexponential models turn out to sa...
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作者：LOW, MG
摘要：Renormalization arguments are used to derive optimal rates of convergence, under integrated squared error loss, for parameter spaces having a certain rectangular structure.
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作者：DETTE, H
摘要：In a recent paper Pukelsheim and Studden determined the E-optimal design for the polynomial regression model on the interval [-1, 1] where the variances of different observations are assumed to be constant. In this note we show that these results can be generalized for polynomial regression models with non constant variances proportional to specific functions.
