Quality of Fit Measures in the Framework of Quantile Regression

Abstract. In regression experiments, to learn about the strength of the relationship between a covariate vector and a dependent variable, we propose a ‘coefficient of determination’ based on the quantiles. Such a coefficient is a ‘local’ measure in the sense that the strength is measured at a prespecified quantile level. Once estimated, it can be used, for example, to measure the relative importance of a subset of covariates in the quantile regression context. Related to this coefficient, we also propose a new ‘local’ lack‐of‐fit measure of a given parametric model. We provide some asymptotic results of the proposed measures and carry out a Monte Carlo simulation study to illustrate their use and performance in practice.     

Inference for the Generalized Normal Laplace Distribution

The generalized normal Laplace distribution has been used in financial modeling because of its skewness and excess kurtosis. To estimate its parameters, we use a method based on minimizing the quadratic distance between the real and imaginary parts of the empirical and theoretical characteristic functions. The quadratic distance estimator (QDE) obtained is shown to be robust, consistent, and with an asymptotically normal distribution. The goodness-of-fit test statistics presented follow an asymptotic chi-square distribution. The performance of the QDE is illustrated by simulation results and an application to financial data.     

Polynomial Histograms for Multivariate Density and Mode Estimation

Abstract. We consider the problem of efficiently estimating multivariate densities and their modes for moderate dimensions and an abundance of data. We propose polynomial histograms to solve this estimation problem. We present first‐ and second‐order polynomial histogram estimators for a general d‐dimensional setting. Our theoretical results include pointwise bias and variance of these estimators, their asymptotic mean integrated square error (AMISE), and optimal binwidth. The asymptotic performance of the first‐order estimator matches that of the kernel density estimator, while the second order has the faster rate of O(n^?6/(d+6)). For a bivariate normal setting, we present explicit expressions for the AMISE constants which show the much larger binwidths of the second order estimator and hence also more efficient computations of multivariate densities. We apply polynomial histogram estimators to real data from biotechnology and find the number and location of modes in such data.     

Inequality restricted linear selection indices

The problem of construction of selection indices with arbitrary linear inequality constraints on covariances is considered. The selection indices suggested by Smith (1936), Kempthorne Nordskog (1959) Tall is (1962) are shown as special cases. A method of solution is presented and prediction errors of various indices are compared. The method is applied to the example given in Kempthorne Nordskog (1959).     

ISAR运动参数估计和补偿改进方法

在使用FFT距离多普勒算法进行ISAR成像处理时,回波相关性的减弱将加大运动补偿难度,带来较大的误差。该文在常规相邻相关法基础上,提出了一种改进的运动补偿方法。在距离向上,利用基准回波相关法与曲线拟合,克服了低回波相关性下包络对齐时出现的包络漂移、包络跳变等缺陷;在方位向上,利用DCFT变换,对目标的运动参数进行精确估计并加以补偿,减小了回波相关性降低对相位补偿的影响。仿真验证了该方法的有效性。     

转盘上单机排序问题的可解情形

文献[1]中证明,即使只有一台加工机器,带有转盘的流水作业问题的加工全长问题 T1也是强 NP 困难的。本文讨论问题 T1的几个多项式时间的可解情形。     

Minimum variance unbiased invariant estimation of variance components under normality

In a variance components model for normally distributed data, for a specified vector of linear combinations of the variance components, necessary and sufficient conditions are given under which the vector has a uniformly minimum variance unbiased translation-invariant estimator. The competing class of estimators is not restricted to those that are quadratic. For classification models, the conditions are translated into easy-to-check partial balance requirements on the incidence array.     

Inverse Problems of Matroid Intersection

In this paper we study the inverse problem of matroid intersection: Two matroids M ₁ = (E, ₁) and M ₂ = (E, ₂), their intersection B, and a weight function w on E are given. We try to modify weight w, optimally and with bounds, such that B becomes a maximum weight intersection under the modified weight. It is shown in this paper that the problem can be formulated as a combinatorial linear program and can be further transformed into a minimum cost circulation problem. Hence it can be solved by strongly polynomial time algorithms. We also give a necessary and sufficient condition for the feasibility of the problem. Finally we extend the discussion to the version of the problem with Multiple Intersections.     

Parametrically Guided Non-parametric Regression

We present a new approach to regression function estimation in which a non-parametric regression estimator is guided by a parametric pilot estimate with the aim of reducing the bias. New classes of parametrically guided kernel weighted local polynomial estimators are introduced and formulae for asymptotic expectation and variance, hence approximated mean squared error and mean integrated squared error, are derived. It is shown that the new classes of estimators have the very same large sample variance as the estimators in the standard non-parametric setting, while there is substantial room for reducing the bias if the chosen parametric pilot function belongs to a wide neighbourhood around the true regression line. Bias reduction is discussed in light of examples and simulations.     

On the Local Polynomial Estimators of the Counting Process Intensity Function and its Derivatives

Abstract. We consider the properties of the local polynomial estimators of a counting process intensity function and its derivatives. By expressing the local polynomial estimators in a kernel smoothing form via effective kernels, we show that the bias and variance of the estimators at boundary points are of the same magnitude as at interior points and therefore the local polynomial estimators in the context of intensity estimation also enjoy the automatic boundary correction property as they do in other contexts such as regression. The asymptotically optimal bandwidths and optimal kernel functions are obtained through the asymptotic expressions of the mean square error of the estimators. For practical purpose, we suggest an effective and easy‐to‐calculate data‐driven bandwidth selector. Simulation studies are carried out to assess the performance of the local polynomial estimators and the proposed bandwidth selector. The estimators and the bandwidth selector are applied to estimate the rate of aftershocks of the Sichuan earthquake and the rate of the Personal Emergency Link calls in Hong Kong.