Estimation in a linear regression model under the Kullback–Leibler loss and its application to model selection

This paper is concerned with the problem of constructing a good predictive distribution relative to the Kullback–Leibler information in a linear regression model. The problem is equivalent to the simultaneous estimation of regression coefficients and error variance in terms of a complicated risk, which yields a new challenging issue in a decision-theoretic framework. An estimator of the variance is incorporated here into a loss for estimating the regression coefficients. Several estimators of the variance and of the regression coefficients are proposed and shown to improve on usual benchmark estimators both analytically and numerically. Finally, the prediction problem of a distribution is noted to be related to an information criterion for model selection like the Akaike information criterion (AIC). Thus, several AIC variants are obtained based on proposed and improved estimators and are compared numerically with AIC as model selection procedures.     

高阶具正负系数中立型微分方程正解的存在性准则

考虑高阶具正负系数的中立型微分方程其中以及为奇数，通过对议程的讨论，得到了议程正解的存在准则。     

An Estimation Method of the Pair Potential Function for Gibbs Point Processes on Spheres

An estimation method for pairwise interaction potential of a stationary Gibbs point process is introduced by considering the case of observations located on a sphere. It is based both on Fourier decomposition of the potential and on minimum contrast estimation. It is defined when many independent realizations of the process are available. Consistency and asymptotic normality are proved for the resulting estimators. The method enables derivation of the choice of the potential function by embedded hypotheses testing. The method is applied to independent observations of root locations on internodes around stem of maize roots. The internodes are described as circles and we focus on the interaction function associated with the potential. Since a model with too many components seems to fail, we choose a sequential procedure based on embedded hypotheses testing to build a simpler model.     

规则区域上Helmholtz方程的一种快速算法

采用有限差分法对Ｈｅｌｍｈｏｌｔｚ 方程进行五点差分离散，在规则区域上引入快速傅里叶变换（ＦＦＴ） ， 将差分方程变换成一组三对角方程， 使求解规则子区域上 Ｈｅｌｍｈｏｌｔｚ 方程的计算量降为Ｏ（ Ｐｌｇ Ｐ） ，最后的数值结果证明了文中的算法是一种快速算法     

A bootstrap approximation to the joint distribution of sum and maximum of a stationary sequence

This paper establishes the asymptotic validity for the moving block bootstrap as an approximation to the joint distribution of the sum and the maximum of a stationary sequence. An application is made to statistical inference for a positive time series where an extreme value statistic and sample mean provide the maximum likelihood estimates for the model parameters. A simulation study illustrates small sample size behavior of the bootstrap approximation.     

Mixed inverse problems arising in the estimation of calibration factors in positron emission tomography

A penalized likelihood approach to the estimation of calibration factors in positron emission tomography (PET) is considered, in particular the problem of estimating the efficiency of PET detectors. Varying efficiencies among the detectors create a non-uniform performance and failure to account for the non-uniformities would lead to streaks in the image, so efficient estimation of the non-uniformities is desirable to reduce the propagation of noise to the final image. The relevant data set is provided by a blank scan, where a model may be derived that depends only on the sources affecting non-uniformities: inherent variation among the detector crystals and geometric effects. Physical considerations suggest a novel mixed inverse model with random crystal effects and smooth geometric effects. Using appropriate penalty terms, the penalized maximum likelihood estimates are derived and an efficient computational algorithm utilizing the fast Fourier transform is developed. Data-driven shrinkage and smoothing parameters are chosen to minimize an estimate of the predictive loss function. Various examples indicate that the approach proposed works well computationally and compares well with the standard method.     

二阶中立型无穷时滞微分方程的周期解

利用Fourier级数理论研究了二阶中立型无穷时滞微分方程的周期解,获得了周期解存在性和唯一性的充分必要条件.     

Testing regions with nonsmooth boundaries via multiscale bootstrap

A new class of approximately unbiased tests based on bootstrap probabilities is obtained for the multivariate normal model with unknown expectation parameter vector. The null hypothesis is represented as an arbitrary-shaped region with possibly nonsmooth boundary surfaces such as cones, which appear in, for example, multiple comparisons and hierarchical clustering. The size n^′$n^{\prime }$ of bootstrap samples is intentionally altered from the size n of the data. A scaling-law of the bootstrap probability leads to our bias corrected p  -values which are calculated by extrapolating the bootstrap probability back to n^′=-n$n^{\prime }=-n$. The new method approximates the bootstrap iteration applied to the bootstrap probability.     

重叠频分复用系统循环前缀的设计和分析

研究了在时变多径频率选择性衰落信道条件下,重叠频分复用/非正交频分复用系统的离散傅里叶变换实现,并对OvFDM-DFT系统的循环前缀进行了分析和设计,讨论了两种不同的循环前缀设计方法,即普通循环前缀和补零方式循环前缀对系统性能的影响。分析和仿真结果表明,在时变多径频率选择性衰落信道条件下补零方式的循环前缀远好于普通方式的循环前缀,仿真结果也验证了OvFDM符号具有明显的抗衰落性能。     

Semiparametric Mixtures of Symmetric Distributions

We consider in this paper the semiparametric mixture of two unknown distributions equal up to a location parameter. The model is said to be semiparametric in the sense that the mixed distribution is not supposed to belong to a parametric family. To insure the identifiability of the model, it is assumed that the mixed distribution is zero symmetric, the model being then defined by the mixing proportion, two location parameters and the probability density function of the mixed distribution. We propose a new class of M‐estimators of these parameters based on a Fourier approach and prove that they are ‐consistent under mild regularity conditions. Their finite sample properties are illustrated by a Monte Carlo study, and a benchmark real dataset is also studied with our method.