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作者：VANDERVAART, A
摘要：Given a sample of size n from a distribution P-lambda, one wants to estimate a functional psi(lambda) of the (typically infinite-dimensional) parameter lambda. Lower bounds on the performance of estimators can be based on the concept of a differentiable functional P-lambda --> psi(lambda). In this paper we relate a suitable definition of differentiable functional to differentiability of lambda --> dP-lambda-1/2 and lambda --> psi(lambda). Moreover, we show that regular estimability of a functi...
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作者：SCHUMAKER, LL
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作者：YAJIMA, Y
摘要：We consider asymptotic properties of the least squares estimator (LSE) in a regression model with long-memory stationary errors. First we derive a necessary and sufficient condition that the LSE be asymptotically efficient relative to the best linear unbiased estimator (BLUE). Then we derive the asymptotic distribution of the LSE under a condition on the higher-order cumulants of the white-noise process of the errors.
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作者：DHAR, SK
摘要：In the additive effects outliers (A.O.) model considered here one observes Y(j,n) = X(j) + V(j,n), O less-than-or-equal-to j less-than-or-equal-to n, where {X(j)} is the first order autoregressive [AR(1)] process with the autoregressive parameter \rho\ < 1. The A.O.'s {V(j,n), O less-than-or-equal-to n} are i.i.d. with distribution function (d.f.) (1 - gamma-n)I[x greater-than-or-equal-to 0] + gamma-nL(n)(x), x epsilon R, 0 less-than-or-equal-to gamma-n less-than-or-equal-to 1, where the d.f.'...
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作者：LOPUHAA, HP; ROUSSEEUW, PJ
作者单位：University of Antwerp
摘要：Finite-sample replacement breakdown points are derived for different types of estimators of multivariate location and covariance matrices. The role of various equivariance properties is illustrated. The breakdown point is related to a measure of performance based on large deviations probabilities. Finally, we show that one-step reweighting preserves the breakdown point.
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作者：PRUITT, RC
摘要：Conditions under which the bivariate Kaplan-Meier estimate of Dabrowska is not a proper survival function are given. All points assigned negative mass are identified under the assumption that the observations follow an absolutely continuous distribution. The number of points assigned negative mass increases as n2 and the total amount of negative mass does not disappear as n --> infinity, where n is the sample size. A simulation study is reported which shows that large amounts of negative mass ...
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作者：BUJA, A; DUFFY, D; HASTIE, T; TIBSHIRANI, R
作者单位：Nokia Corporation; Nokia Bell Labs; AT&T; University of Toronto
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作者：BROWN, LD; LOW, MG
作者单位：University of California System; University of California Berkeley
摘要：This paper compares three methods for producing lower bounds on the minimax risk under quadratic loss. The first uses the bounds from Brown and Gajek. The second method also uses the information inequality and results in bounds which are always at least as good as those form the first method. The third method is the hardest-linear-family method described by Donoho and Liu. These methods are applied in four examples, the last of which relates to a frequently considered problem in nonparametric ...
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作者：EATON, ML; TYLER, DE
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：A relatively obscure eigenvalue inequality due to Wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix. The asymptotic distributions are obtained under a fairly general setting. An application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given.
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作者：GOLUBEV, GK; HASMINSKII, RZ
