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作者：JIN, K
作者单位：State University System of Florida; Florida State University
摘要：We provide a solution to the smoothing parameter selection problem involved in the construction of adaptive estimates for the symmetric location model and the general linear model. Linear B-splines are used to give a simple form of the estimate of the score function of the underlying density. New empirical methods are proposed to locate the knots optimally and to select the number of knots. We also give asymptotic bounds for the empirical selection method and show that an estimate with an empi...
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作者：LEROUX, BG
摘要：A maximum-penalized-likelihood method is proposed for estimating a mixing distribution and it is shown that this method produces a consistent estimator, in the sense of weak convergence. In particular, a new proof of the consistency of maximum-likelihood estimators is given. The estimated number of components is shown to be at least as large as the true number, for large samples. Also, the large-sample limits of estimators which are constrained to have a fixed finite number of components are i...
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作者：LIU, RY; SINGH, K
摘要：Three notions of depth for directional data, angular simplicial depth (ASD), angular Tukey's depth (ATD) and arc distance depth (ADD), are developed and studied. The empirical versions of these depths give rise to center-outward rankings of angular data which may be regarded as extensions of the usual center-outward ranking on the line. Three medians derived from these depths are examined and compared. Applications in nonparametric classification and in implementing the bootstrap to construct ...
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作者：LOADER, CR
摘要：Many methods have been proposed for modelling nonhomogeneous Poisson processes, including change point models and log-linear models. In this paper, we use likelihood ratio tests to choose which of these models are necessary. Of particular interest is the test for the presence of a change point, for which standard asymptotic theory is not valid. Large deviation methods are applied to approximate the significance level, and power approximations are given. Confidence regions for the change point ...
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作者：EINMAHL, JHJ; MASON, DM
作者单位：University of Delaware
摘要：For random vectors taking values in R(d) we introduce a notion of multivariate quantiles defined in terms of a class of sets and study an associated process which we call the generalized quantile process. This process specializes to the well known univariate quantile process. We obtain functional central limit theorems for our generalized quantile process and show that both Gaussian and non-Gaussian limiting processes can arise. A number of interesting example are included.
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作者：KONING, AJ
摘要：In this paper stochastic integrals with respect to the basic martingale are approximated by Gaussian processes. The probability inequalities governing this approximation are used to study goodness-of-fit tests based on sublinear functionals of weighted versions of these stochastic integrals. As special cases of these tests, generalized rank and supremum-type tests are considered.
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作者：ROUSSAS, GG; TRAN, LT
作者单位：Purdue University System; Indiana University Purdue University Fort Wayne
摘要：For i = 1, 2,..., let X(i) and Y(i) be R(d)-valued (d greater-than-or-equal-to 1 integer) and R-valued, respectively, random variables, and let {(X(i), Y(i))}, i greater-than-or-equal-to 1, be a strictly stationary and alpha-mixing stochastic process. Set m(x) = E(Y1\X1 = x), x is-an-element-of R(d), and let m(n)(x) be a certain recursive kernel estimate of m(x). Under suitable regularity conditions and as n --> infinity, it is shown that m(n)(x), properly normalized, is asymptotically normal ...
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作者：DEVROYE, L
摘要：We consider the Akaike-Parzen-Rosenblatt density estimate f(nh) based upon any superkernel L (i.e., an absolutely integrable function with integral L = 1, whose characteristic function is 1 on [-1, 1]), and compare it with a kernel estimate g(nh) based upon an arbitrary kernel K. We show that for a given subclass of analytic densities, [GRAPHICS] where h > 0 is the smoothing factor. Thus, asymptotically, the class of superkernels is as good as any other class of kernels when certain analytic d...
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作者：MILBRODT, H
摘要：In this paper, we suggest tests of stationarity in the mean of autoregressive time series versus arbitrary trend alternatives. As an intermediate, though essential, step local asymptotic normality of autoregressive models with a nonparametric regression trend is established. Moreover, a functional central limit theorem for the underlying likelihood ratio processes is derived. These results then offer a general construction principle by which every goodness of fit test (case 0), which is based ...
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作者：ARCONES, MA; GINE, E
作者单位：University of Connecticut; City University of New York (CUNY) System
摘要：Bootstrap distributional limit theorems for U and V statistics are proved. They hold a.s., under weak moment conditions and without restrictions on the bootstrap sample size (as long as it tends to infinity), regardless of the degree of degeneracy of U and V. A testing procedure based on these results is outlined.
