-
作者：SHEN, LZ
摘要：Bounded influence functions are used for robust estimation in semiparametric models. In this paper, we generalize Hampel's variational problem to semiparametric models and define the optimal B-robust influence function as the one solving the variational problem. We identify the lowest bounds for influence functions and establish the existence and uniqueness of the optimal influence functions in general semiparametric models. Explicit optimal influence functions are given for a special case. Ex...
-
作者：BIRGE, L; MASSART, P
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Let phi be a smooth function of k + 2 variables. We shall investigate in this paper the rates of convergence of estimators of T(f) = integral phi(f(x), f'(x),..., f((k))(x), x) dx when f belongs to some class of densities of smoothness s. We prove that, when s greater than or equal to 2k + 1/4, one can define an estimator (T) over cap(n) of T(f), based on n i.i.d. observations of density f on the real line, which converges at the semiparametric rate 1/root n. On the other hand, when s < 2k + 1...
-
作者：EGGERMONT, PPB; LARICCIA, VN
摘要：We consider the problem of estimating a pdf f from samples X(1), X(2), ..., X(n) of a random variable with pdf Kf, where K is a compact integral operator. We employ a maximum smoothed likelihood formalism inspired by a nonlinearly smoothed version of the EMS algorithm of Silverman, Jones, Wilson and Nychka. We show that this nonlinearly smoothed algorithm is itself an EM algorithm, which helps explain the strong convergence properties of the algorithm. For the case of(standard) density estimat...
-
作者：Falk, M
摘要：Consider an lid sample Y-1, ..., Y-n of random variables with common distribution function F, whose upper tail belongs to a neighborhood of the upper tail of a generalized Pareto distribution H-beta, beta is an element of R. We investigate the testing problem beta = beta(0) against a sequence beta = beta(n) of contiguous alternatives, based on the point processes N-n of the exceedances among Y-i over a sequence of thresholds t(n). It turns out that the (random) number of exceedances tau(n) ove...
-
作者：LEE, SMS; YOUNG, GA
作者单位：University of Cambridge
摘要：An iterated bootstrap confidence interval requires an additive correction to be made to the nominal coverage level of an uncorrected interval. Such correction is usually performed using a computationally intensive Monte Carlo simulation involving two nested levels of bootstrap sampling. Asymptotic expansions of the required correction and the iterated interval endpoints are used to provide two new computationally efficient methods for constructing an approximation to the iterated bootstrap con...
-
作者：LI, TH
摘要：A method is proposed to deal with the problem of blind deconvolution of a special non-Gaussian linear process, in which the input to the linear system is a real- or complex-valued multilevel random sequence that satisfies certain regularity conditions. The gist of the method is to apply a linear filter to the observed process and adjust the filter until a multilevel output is obtained. It is shown that the deconvolution problem can be solved (with only scale/rotation and shift ambiguities) if ...
-
作者：Doksum, K; Samarov, A
作者单位：Massachusetts Institute of Technology (MIT)
摘要：In a nonparametric regression setting with multiple random predictor variables, we give the asymptotic distributions of estimators of global integral functionals of the regression surface. We apply the results to the problem of obtaining reliable estimators for the nonparametric coefficient of determination. This coefficient, which is also called Pearson's correlation ratio, gives the fraction of the total variability of a response that can be explained by a given set of covariates. It can be ...
-
作者：MCCABE, BPM; TREMAYNE, AR
作者单位：University of Sydney
摘要：This paper addresses the problem of testing the hypothesis that an observed series is difference stationary. The alternative hypothesis is that the series is another nonstationary process; in particular, an autoregressive model with a random parameter is used. A locally best invariant test is developed assuming Gaussianity, and a representation of its asymptotic distribution as a mixture of Brownian motions is found. The performance of the test in finite samples is investigated by simulation. ...
-
作者：XU, JL; YANG, GL
作者单位：University System of Maryland; University of Maryland College Park
摘要：Let X((1)) less than or equal to X((2)) less than or equal to ...less than or equal to X((n)) be the order statistics of a random sample of n lifetimes. The total-time-on-test statistic at X((i)) is defined by S-i,S-n = Sigma(j=1)(i)(n - j + 1)(X((j)) - X((j-1))), 1 less than or equal to i less than or equal to n. A type II censored sample is composed of the r smallest observations and the remaining n - r Lifetimes which are known only to be at least as large as X((r)). Dufour conjectured that...
-
作者：SIEGMUND, D; VENKATRAMAN, ES
作者单位：Memorial Sloan Kettering Cancer Center
摘要：We study sequential detection of a change-point using the generalized likelihood ratio statistic. For the special case of detecting a change in a normal mean with known variance, we give approximations to the average run lengths and compare our procedure to standard CUSUM tests and combined CUSUM-Shewhart tests. Several examples indicating extensions to problems involving multiple parameters are discussed.
