LOCAL POLYNOMIAL QUASI-LIKELIHOOD REGRESSION ON RANDOM FIELDS

In this paper, local quasi‐likelihood regression is considered for stationary random fields of dependent variables. In the case of independent data, local polynomial quasi‐likelihood regression is known to have several appealing features such as minimax efficiency, design adaptivity and good boundary behaviour. These properties are shown to carry over to the case of random fields. The asymptotic normality of the regression estimator is established and explicit formulae for its asymptotic bias and variance are derived for strongly mixing stationary random fields. The extension to multi‐dimensional covariates is also provided in full generality. Moreover, evaluation of the finite sample performance is made through a simulation study.     

A New Characterization and Estimation of the Zero–bias Bandwidth

It is well established that bandwidths exist that can yield an unbiased non–parametric kernel density estimate at points in particular regions (e.g. convex regions) of the underlying density. These zero–bias bandwidths have superior theoretical properties, including a 1/n convergence rate of the mean squared error. However, the explicit functional form of the zero–bias bandwidth has remained elusive. It is difficult to estimate these bandwidths and virtually impossible to achieve the higher–order rate in practice. This paper addresses these issues by taking a fundamentally different approach to the asymptotics of the kernel density estimator to derive a functional approximation to the zero–bias bandwidth. It develops a simple approximation algorithm that focuses on estimating these zero–bias bandwidths in the tails of densities where the convexity conditions favourable to the existence of the zerobias bandwidths are more natural. The estimated bandwidths yield density estimates with mean squared error that is O(n^–4/5), the same rate as the mean squared error of density estimates with other choices of local bandwidths. Simulation studies and an illustrative example with air pollution data show that these estimated zero–bias bandwidths outperform other global and local bandwidth estimators in estimating points in the tails of densities.     

Kernel smoothing for finite populations

We identify a role for smooth curve provision in the finite population context. The performance of kernel density estimates in this scenario is explored, and they are tailored to the finite population situation especially by developing a method of data-based selection of the smoothing parameter appropriate to this problem. Simulated examples are given, including some from the particular context of permutation distributions which first motivated this investigation.     

一种固定帧长的EPON MAC算法

提出了一种固定大小帧结构的EPON MAC协议,采用固定的帧长,提高了以太网交换机速率。将一帧周期分成三段,光网络单元不仅报告队列长度信息,而且报告帧到达分布信息,降低了高优先级业务时延抖动,授权采取高优先级优先授权的原则,降低了高优先级业务的接入时延,满足了对时延和时延抖动敏感语音业务的要求。     

Automatic repeated-loess decomposition of data consisting of sums of oscillatory curves

Repeated loess is a nonparametric procedure that uses progressive smoothing and differencing to decompose data consisting of sums of curves. Smoothing is by locally weighted polynomial regression. Here the procedure was developed so that the decomposition into components was controlled automatically by the number of maxima in each component. The level of smoothing of each component was chosen to maximize the estimated probability of the observed number of maxima. No assumptions were made about the periodicity of components and only very weak assumptions about their shapes. The automatic procedure was applied to simulated data and to experimental data on human visual sensitivity to line orientation.An erratum to this article can be found at     

The Penalized Analytic Center Estimator

In a linear regression model, the Dantzig selector (Candès and Tao, 2007 Candès, E., Tao, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics 35:2313–2351.[Crossref], [Web of Science ®] , [Google Scholar]) minimizes the L₁ norm of the regression coefficients subject to a bound λ on the L_∞ norm of the covariances between the predictors and the residuals; the resulting estimator is the solution of a linear program, which may be nonunique or unstable. We propose a regularized alternative to the Dantzig selector. These estimators (which depend on λ and an additional tuning parameter r) minimize objective functions that are the sum of the L₁ norm of the regression coefficients plus r times the logarithmic potential function of the Dantzig selector constraints, and can be viewed as penalized analytic centers of the latter constraints. The tuning parameter r controls the smoothness of the estimators as functions of λ and, when λ is sufficiently large, the estimators depend approximately on r and λ via r/λ².     

Testing for structural changes in linear regressions with time-varying variance

Abstract

This article proposes a nonparametric test for structural changes in linear regression models that allows for serial correlation, autoregressive conditional heteroskedasticity and time-varying variance in error terms. The test requires no trimming of the boundary region near the end points of the sample period, and requires no prior information on the alternative, what it requires is the transformed OLS residuals under the null hypothesis. We show that the test has a limiting standard normal distribution under the null hypothesis, and is powerful against single break, multiple breaks and smooth structural changes. The Monte Carlo experiment is conducted to highlight the merits of the proposed test relative to other popular tests for structural changes.     

Reducing data dimension for cluster detection

Clustering high-dimensional data is often a challenging task both because of the computational burden required to run any technique, and because the difficulty in interpreting clusters generally increases with the data dimension. In this work, a method for finding low-dimensional representations of high-dimensional data is discussed, specifically conceived to preserve possible clusters in data. It is based on the critical bandwidth, a nonparametric statistic to test unimodality, related to kernel density estimation. Some useful properties of the aforementioned statistic are enlightened and an adjustment to use it as a basis for reducing dimensionality is suggested. The method is illustrated by simulated and real data examples.     

Adaptive smoothing in associated kernel discrete functions estimation using Bayesian approach

This paper demonstrates that cross-validation (CV) and Bayesian adaptive bandwidth selection can be applied in the estimation of associated kernel discrete functions. This idea is originally proposed by Brewer [A Bayesian model for local smoothing in kernel density estimation, Stat. Comput. 10 (2000), pp. 299–309] to derive variable bandwidths in adaptive kernel density estimation. Our approach considers the adaptive binomial kernel estimator and treats the variable bandwidths as parameters with beta prior distribution. The best variable bandwidth selector is estimated by the posterior mean in the Bayesian sense under squared error loss. Monte Carlo simulations are conducted to examine the performance of the proposed Bayesian adaptive approach in comparison with the performance of the Asymptotic mean integrated squared error estimator and CV technique for selecting a global (fixed) bandwidth proposed in Kokonendji and Senga Kiessé [Discrete associated kernels method and extensions, Stat. Methodol. 8 (2011), pp. 497–516]. The Bayesian adaptive bandwidth estimator performs better than the global bandwidth, in particular for small and moderate sample sizes.     

Information,measure shifts and distribution metrics

Reflexive shifting of a given distribution, using its own distribution function, can reveal information. The shifts are changes in measure such that the separation of the resulting left and right unit shifted distributions reveals the binary entropy of position, called locational or partition entropy. This can be used for spread and asymmetry functions. Alternatively, summary metrics for distributional asymmetry and spread can be based on the relative strengths of left- and right-hand shifts. Such metrics are applicable even for long tail densities where distributional moments may not exist.