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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：FALK, M; MAROHN, F
摘要：Let (X1, Y1),..., (X(n), Y(n)) be independent replicates of the random vector (X, Y) is-an-element-of R(d+m), where X is R(d)-valued and Y is R(m)-valued. We assume that the conditional distribution P(Y is-an-element-of .\X = x) = Q(v)(.) of Y given X = x is a member of a parametric family, where the parameter space THETA is an open subset of R(k) with 0 is-an-element-of THETA. Under suitable regularity conditions we establish upper bounds for the power functions of asymptotic level-alpha test...
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作者：FAN, JQ
摘要：In this paper we introduce a smooth version of local linear regression estimators and address their advantages. The MSE and MISE of the estimators are computed explicitly. It turns out that the local linear regression smoothers have nice sampling properties and high minimax efficiency-they are not only efficient in rates but also nearly efficient in constant factors. In the nonparametric regression context, the asymptotic minimax lower bound is developed via the heuristic of the ''hardest one-...
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作者：HARDLE, W; HALL, P; ICHIMURA, H
作者单位：Universite Catholique Louvain; Australian National University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Single-index models generalize linear regression. They have applications to a variety of fields, such as discrete choice analysis in econometrics and dose response models in biometrics, where high-dimensional regression models are often employed. Single-index models are similar to the first step of projection pursuit regression, a dimension-reduction method. In both cases the orientation vector can be estimated root-n consistently, even if the unknown univariate function (or nonparametric link...
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作者：HE, XM; SIMPSON, DG
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We study how robust estimators can be in parametric families, obtaining a lower bound on the contamination bias of an estimator that holds for a wide class of parametric families. This lower bound includes as a special case the bound used to establish that the median is bias minimax among location equivariant estimators, and it is tight or nearly tight in a variety of other settings such as scale estimation, discrete exponential families and multiple linear regression. The minimum variation di...
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作者：TANG, SM; MACNEILL, IB
作者单位：Western University (University of Western Ontario)
摘要：It is shown that serial correlation can produce striking effects in distributions of change-point statistics. Failure to account for these effects is shown to invalidate change-point tests, either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process, or through diminution of the power of the tests when high frequency mass predominates. These effects are characterized by the expression (2pif(0)/integral-pi/-pi f(lambda)dlam...
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作者：NEUHAUS, G
摘要：For the two-sample problem with randomly censored data, there exists a general asymptotic theory of rank statistics which are functionals of stochastic integrals with respect to certain empirical martingales. In the present paper a conditional counterpart of this theory is developed. The conditional martingales are versions of the original ones reduced to the unit interval having their jumps at fixed lattice points. The resulting conditional tests are strictly distribution free under the null ...
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作者：GRUBEL, R; PITTS, SM
作者单位：University of London; University College London
摘要：We introduce a nonparametric estimator for the renewal function and discuss its properties, including consistency, asymptotic normality and asymptotic validity of bootstrap confidence regions. The underlying theme is that stochastic models can be regarded as functionals or nonlinear operators. This view leads to nonparametric estimators in a natural way and statistical properties of the estimators can be related to the local behaviour of the functionals.
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作者：STEIN, ML
摘要：Smoothing splines of a fixed order are commonly used as nonparametric regression estimates. The only parameter, then, that needs to be estimated is the smoothing parameter, which is often estimated using some form of cross validation. This work allows the order of the smoothing spline to be estimated using a model in which the order parameter is continuous. Within this setting, generalized cross validation and modified maximum likelihood estimates of the order and smoothing parameters are comp...
