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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：YING, ZL
摘要：We study in detail asymptotic properties of maximum likelihood estimators of parameters when observations are taken from a two-dimensional Gaussian random field with a multiplicative Ornstein-Uhlenbeck covariance function. Under the complete lattice sampling plan, it is shown that the maximum likelihood estimators are strongly consistent and asymptotically normal. The asymptotic normality here is normalized by the fourth root of the sample size and is obtained through higher order expansions o...
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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：BOSE, A; BOUKAI, B
作者单位：Purdue University System; Purdue University; Purdue University in Indianapolis
摘要：We consider the problem of sequentially estimating one parameter in a class of two-parameter exponential family of distributions. We assume a weighted squared error loss with a fixed cost of estimation error. The stopping rule, based on the maximum likelihood estimate of the nuisance parameter, is shown to be independent of the terminal estimate. The asymptotic normality of the stopping variable is established and approximations to its mean and to the regret associated with it are also provide...
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作者：SIEGMUND, D; ZHANG, HP
作者单位：Yale University
摘要：Using an expression for the expected number of local maxima of a random field, we derive an upper bound for the volume of a tube about a manifold in the unit sphere and show that under certain conditions our bound agrees with the evaluation of the tube volume in Weyl's formula. Applications to tests and confidence regions in nonlinear regression are discussed.
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作者：CRITCHLEY, F; MARRIOTT, P; SALMON, M
作者单位：University of Surrey; European University Institute
摘要：A new mathematical object called a preferred point geometry is introduced in order to (a) provide a natural geometric framework in which to do statistical inference and (b) reflect the distinction between homogeneous aspects (e.g., any point theta may be the true parameter) and preferred point ones (e.g., when theta0 is the true parameter). Although preferred point geometry is applicable generally in statistics, we focus here on its relationship to statistical manifolds, in particular to Amari...
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作者：SEIDENFELD, T; WASSERMAN, L
摘要：Suppose that a probability measure P is known to lie in a set of probability measures M. Upper and lower bounds on the probability of any event may then be computed. Sometimes, the bounds on the probability of an event A conditional on an event B may strictly contain the bounds on the unconditional probability of A. Surprisingly, this might happen for every B in a partition B. If so, we say that dilation has occurred. In addition to being an interesting statistical curiosity, this counterintui...
