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作者：HALL, P; PATIL, P
摘要：We provide an asymptotic formula for the mean integrated squared error (MISE) of nonlinear wavelet-based density estimators. We show that, unlike the analogous situation for kernel density estimators, this MISE formula is relatively unaffected by assumptions of continuity. In particular, it is available for densities which are smooth in only a piecewise sense. Another difference is that in the wavelet case the classical MISE formula is valid only for sufficiently small values of the bandwidth....
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作者：Wei, XY
摘要：We propose a conditional MLE of the index of regular variation when the functional form of a slowly varying function is assumed known in the tail, and we study its asymptotic properties. We prove asymptotic normality of P-theta(kn), a probability measure whose density is the product of the joint conditional density of the k(n) largest order statistics from F-theta(x) given Z(n - k), the (n - k)th order statistic, and a density of Z(n - k) with parameter theta. Based on this result, we shore th...
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作者：DAHLHAUS, R
摘要：In this paper we construct an efficient weighted least squares estimator for the mean and more generally for the regression parameters in certain Gaussian long range dependent regression models, including polynomial regression. The form of the estimator does not depend on the whole dependence structure of the residuals, but only on the local behaviour of the spectral density at zero. By using an estimator of the self-similarity parameter, we give a fully efficient estimator. Furthermore, we co...
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作者：KNEIP, A; ENGEL, J
作者单位：University of Bonn
摘要：Given data from a sample of noisy curves, we consider a nonlinear parametric regression model with unknown model function. An iterative algorithm for estimating individual parameters as well as the model function is introduced under the assumption of a certain shape invariance: the individual regression curves are obtained from a common shape function by Linear transformations of the axes. Our algorithm is based on least-squares methods for parameter estimation and on nonparametric kernel meth...
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作者：Hall, P; Lahiri, SN; Truong, YK
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Iowa State University
摘要：We address the empirical bandwidth choice problem in cases where the range of dependence may be virtually arbitrarily long. Assuming that the observed data derive from an unknown function of a Gaussian process, it is argued that, unlike more traditional contexts of statistical inference, in density estimation there is no clear role for the classical distinction between short- and long-range dependence. Indeed, the ''boundaries'' that separate different modes of behaviour for optimal bandwidths...
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作者：Pistone, G; Sempi, C
作者单位：University of Salento
摘要：Let M(mu) be the set of all probability densities equivalent to a given reference probability measure mu. This set is thought of as the maximal regular (i.e., with strictly positive densities) mu-dominated statistical model. For each f is an element of M(mu) We define (1) a Banach space L(f) with unit ball V-f and(2) a mapping sf from a subset U-f of M(mu) onto V-f, in such a way that the system (s(f), U-f, f is an element of M(mu)) is an affine atlas on M(mu). Moreover each parametric exponen...
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作者：GORDON, L; POLLAK, M
作者单位：Hebrew University of Jerusalem
摘要：We sequentially observe independent observations X(1),X(2),... such that initially they have distribution G(0); at some unknown time nu they become stochastically larger, having distribution G(1). Neither G(0) nor G(1) is fully specified. We wish to detect that a change has taken place as soon as possible after its occurrence, subject to a constraint on the rate of false alarms. We derive a family of nonparametric sequential procedures based on ranks, with noncontiguous alternatives in mind. L...
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作者：MYKLAND, PA
摘要：The paper develops a one-step triangular array Edgeworth expansion for multivariate martingales that are, essentially, asymptotically ergodic. Both discrete and continuous time are covered. The expansion is in a test function topology. We investigate when the expansion has the usual Edgeworth form, looking in particular at likelihood inference, including Cox regression, and at inference for stationary time series. The triangular array nature of the results make them useful for bootstrapping, a...
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作者：DAVIS, RA; HUANG, DW; YAO, YC
作者单位：Queensland University of Technology (QUT)
摘要：The problem of testing whether or not a change has occurred in the parameter values and order of an autoregressive model is considered. It is shown that if the white noise in the AR model is weakly stationary with finite fourth moments, then under the null hypothesis of no changepoint, the normalized Gaussian likelihood ratio test statistic converges in distribution to the Gumbel extreme value distribution. An asymptotically distribution-free procedure for testing a change of either the coeffi...
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作者：MURPHY, SA
摘要：The frailty model is a generalization of Cox's proportional hazards model which includes a random effect. Nielsen, Gill, Andersen and Sorensen (1992) proposed an EM algorithm to estimate the cumulative baseline hazard and the variance of the random effect. Here the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance.
