半变系数模型PLS估计的渐近正态性

半变系数模型在统计建模中具有重要的应用．最近几年，人们提出了许多方法来估计其常系数和函数系数，但是估计的渐近性质还没有被系统的研究．本文介绍了半变系数模型的PLS估计，在Fan和Huang对常系数渐近性质研究的基础上，给出了函数系数的渐近正态性。     

Deconvolving compactly supported densities

This paper addresses the statistical problem of density deconvolution under the condition that the density to be estimated has compact support. We introduce a new estimation procedure, which establishes faster rates of convergence for smooth densities as compared to the optimal rates for smooth densities with unbounded support. This framework also allows us to relax the usual condition of known error density with non-vanishing Fourier transform, so that a nonparametric class of densities is valid; therefore, even the shape of the noise density need not be assumed. These results can also be generalized for fast decaying densities with unbounded support. We prove optimality of the rates in the underlying experiment and study the practical performance of our estimator by numerical simulations.      

Characterization of semiconductor laser frequency chirp based on signal distortion in dispersive optical fiber

In the paper, the simple method of laser chirp parameters estimation is presented. It is based on measuring time-domain distortions of chirped signal transmitted through dispersive fiber and finding laser chirp parameters by matching measured distortions to calculated ones. Experiments undertaken with 1.55 μm telecommunication grade distributed feedback (DFB) lasers and standard single-mode fiber are described, together with some practical remarks on measurement setup and main conclusions.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

A complete active-space self-consistent-field study on cubic N8

Summary Complete Active-Space Self-Consistent-Field (CAS-SCF) calculations for cubic N₈ are presented. We studied the N₈↔4N₂ reaction inD _4h symmetry and found its energy release and activation barrier with three different atomic basis sets. The energy release for this reaction is predicted to be around 526 kcal/mol, while the energy barrier to dissociation is estimated about 159 kcal/mol. These results are in substantial agreement with previousab initio estimates. The authors of this paper have agreed to not receive the proofs for correction.     

Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Let _l be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ₂=0.6240±0.0005±0.0011 and ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ₂=5/8 and ₃=35/24.     

Weber electrodynamics: part III. mechanics,gravitation

Weber electrodynamics predicts the Kaufmann-Bucherer experiments and the fine structure energy level splitting of the H-atom (neglecting spin) without mass change with velocity (i.e., mass ). The Weber potential for the gravitational case yields Newtonian mechanics, confirming Mach's principle. It provides a cosmological condition yielding an estimated radius of the universe of 8 × 10⁹ light years. Despite these successes, the independent evidence for Kaufmann mechanics, where mass changes with velocity (i.e., mass ) is convincing. Perhaps a slight alteration may make the Weber theory compatible with Kaufmann mechanics.     

Estimation of entropy and other functionals of a multivariate density

For a multivariate density f with respect to Lebesgue measure , the estimation of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGkbGaaiikaiaadAgacaGGPaGaamOzaiaadsgacqaH% 8oqBaSqabeqaniabgUIiYdaaaa!4404!\[\int {J(f)fd\mu } \], and in particular % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGMbWaaWbaaSqabeaacaaIYaaaaOGaamizaiabeY7a% TbWcbeqab0Gaey4kIipaaaa!41E4!\[\int {f^2 d\mu } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGMbGaciiBaiaac+gacaGGNbGaamOzaiaadsgacqaH% 8oqBaSqabeqaniabgUIiYdaaaa!44AC!\[\int {f\log fd\mu } \], is studied. These two particular functionals are important in a number of contexts. Asymptotic bias and variance terms are obtained for the estimators % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaacaWGkbGaaiikamaawagabeWcbeqaaiabgEIizdqdbaGaamOzaa% aakiaacMcacaWGKbGaamOramaaBaaaleaacaWGobaabeaaaeqabeqd% cqGHRiI8aaaa!4994!\[\mathop I\limits^ \wedge = \int {J(\mathop f\limits^ \wedge )dF_N } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaeSipIOdaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaacaWGkbGaaiikamaawagabeWcbeqaaiabgEIizdqdbaGaamOzaa% aakiaacMcadaGfGbqabSqabeaacqGHNis2a0qaaiaadAgaaaGccaWG% KbGaeqiVd0galeqabeqdcqGHRiI8aaaa!4C40!\[\mathop I\limits^ \sim = \int {J(\mathop f\limits^ \wedge )\mathop f\limits^ \wedge d\mu } \], where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGMbaaaaaa!3E9C!\[{\mathop f\limits^ \wedge }\] is a kernel density estimate of f and F _n is the empirical distribution function based on the random sample X ₁ ,..., X _n from f. For the two functionalsmentioned above, a first order bias term for Î can be made zero by appropriate choices of non-unimodal kernels. Suggestions for the choice of bandwidth are given; for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaadaGfGbqabSqabeaacqGHNis2a0qaaiaadAgaaaGccaWGKbGaam% OramaaBaaaleaacaWGobaabeaaaeqabeqdcqGHRiI8aaaa!476C!\[\mathop I\limits^ \wedge = \int {\mathop f\limits^ \wedge dF_N } \], a study of optimal bandwidth is possible.This research was supported by an NSERC Grant and a UBC Killam Research Fellowship.