A Selective Overview and Comparison of Robust Mixture Regression Estimators

Mixture regression models have been widely used in business, marketing and social sciences to model mixed regression relationships arising from a clustered and thus heterogeneous population. The unknown mixture regression parameters are usually estimated by maximum likelihood estimators using the expectation–maximisation algorithm based on the normality assumption of component error density. However, it is well known that the normality-based maximum likelihood estimation is very sensitive to outliers or heavy-tailed error distributions. This paper aims to give a selective overview of the recently proposed robust mixture regression methods and compare their performance using simulation studies.     

Model‐Assisted Regression Estimators for Longitudinal Data with Nonignorable Dropout

Estimation with longitudinal Y having nonignorable dropout is considered when the joint distribution of Y and covariate X is nonparametric and the dropout propensity conditional on (Y,X) is parametric. We apply the generalised method of moments to estimate the parameters in the nonignorable dropout propensity based on estimating equations constructed using an instrument Z, which is part of X related to Y but unrelated to the dropout propensity conditioned on Y and other covariates. Population means and other parameters in the nonparametric distribution of Y can be estimated based on inverse propensity weighting with estimated propensity. To improve efficiency, we derive a model‐assisted regression estimator making use of information provided by the covariates and previously observed Y‐values in the longitudinal setting. The model‐assisted regression estimator is protected from model misspecification and is asymptotically normal and more efficient when the working models are correct and some other conditions are satisfied. The finite‐sample performance of the estimators is studied through simulation, and an application to the HIV‐CD4 data set is also presented as illustration.     

Moment-based estimation of smooth transition regression models with endogenous variables

Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, smooth transition regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate processes, and have made a variety of assumptions, including stationary or cointegrated processes, uncorrelated, homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment-based methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure and a misspecification test for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature.     

Optimally combining censored and uncensored datasets

We develop a simple semiparametric framework for combining censored and uncensored samples so that the resulting estimators are consistent, asymptotically normal, and use all information optimally. No nonparametric smoothing is required to implement our estimators. To illustrate our results in an empirical setting, we show how to estimate the effect of changes in compulsory schooling laws on age at first marriage, a variable that is censored for younger individuals. Results from a small simulation experiment suggest that the estimator proposed in this paper can work very well in finite samples.     

On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data

This paper summarizes some results on random fuzzy variables with existing expectation and variance, called random fuzzy variables of second order. Using the Frechét-principle and – via support functions – the embedding of convex fuzzy sets into a Banach space of functions it especially presents a unified view on expectation and variance of random fuzzy variables. These notions are applied in developing linear statistical inference with fuzzy data. Detailed investigations are presented concerning best linear unbiased estimation in linear regression models with fuzzy observations. Received: November 1999     

坐标法在测量巷道断面及标定巷道腰线中的应用

采用全站仪坐标法,通过测定巷道断面上的假定坐标,标定巷道腰线和测定巷道断面尺寸,解决了以往巷道断面尺寸难以准确测定难题,简化了测量程序及计算步骤,提高了测量效率和精度。     

Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients

Heteroskedasticity-robust semi-parametric GMM estimation of a spatial model with space-varying coefficients. Spatial Economic Analysis. The spatial model with space-varying coefficients proposed by Sun et al. in 2014 has proved to be useful in detecting the location effects of the impacts of covariates as well as spatial interaction in empirical analysis. However, Sun et al.’s estimator is inconsistent when heteroskedasticity is present – a circumstance that is more realistic in certain applications. In this study, we propose a kind of semi-parametric generalized method of moments (GMM) estimator that is not only heteroskedasticity robust but also takes a closed form written explicitly in terms of observed data. We derive the asymptotic distributions of our estimators. Moreover, the results of Monte Carlo experiments show that the proposed estimators perform well in finite samples.     

A note on consistency and unbiasedness of point estimation with fuzzy data

Based on the SLLN for fuzzy random variables in uniform metric d, some asymptotical properties of point estimation with fuzzy random samples are investigated. The results of this paper establish a corresponding version on the consistency and unbiasedness of point estimation with n-dimensional fuzzy samples under considering a kind of fuzzy statistic.     

Local identifiability of the factor analysis and measurement error model parameter

Measurement error regression models are factor analysis models, the latent ‘correct’ regressors are the factors. There is however no common statistical method between the factor analysis and the regression model, because the covariance elements that are known identifying constituents of the former model are unknown in the latter. Instead, the idea that the data come from the same regression model, as with panel data, but can be grouped in two or more groups, each group having its own different regrressor generating process, is shown to supply credible restrictions. We generalize and compare relevant identifiability criteria and corresponding asymptotically efficient estimators that are recursive in the number of overidentifying restrictions.     

Estimation and testing for a partially linear single-index spatial regression model

ABSTRACT

Observations recorded on ‘locations’ usually exhibit spatial dependence. In an effort to take into account both the spatial dependence and the possible underlying non-linear relationship, a partially linear single-index spatial regression model is proposed. This paper establishes the estimators of the unknowns. Moreover, it builds a generalized F-test to determine whether or not the data provide evidence on using linear settings in empirical studies. Their asymptotic properties are derived. Monte Carlo simulations indicate that the estimators and test statistic perform well. The analysis of Chinese house price data shows the existence of both spatial dependence and a non-linear relationship.     

Heteroskedasticity-consistent covariance matrix estimators for spatial autoregressive models

In the presence of heteroskedasticity, conventional test statistics based on the ordinary least squares (OLS) estimator lead to incorrect inference results for the linear regression model. Given that heteroskedasticity is common in cross-sectional data, the test statistics based on various forms of heteroskedasticity-consistent covariance matrices (HCCMs) have been developed in the literature. In contrast to the standard linear regression model, heteroskedasticity is a more serious problem for spatial econometric models, generally causing inconsistent extremum estimators of model coefficients. This paper investigates the finite sample properties of the heteroskedasticity-robust generalized method of moments estimator (RGMME) for a spatial econometric model with an unknown form of heteroskedasticity. In particular, it develops various HCCM-type corrections to improve the finite sample properties of the RGMME and the conventional Wald test. The Monte Carlo results indicate that the HCCM-type corrections can produce more accurate results for inference on model parameters and the impact effects estimates in small samples.     

ML– and semiparametric estimation in logistic models with incomplete covariate data

ML–estimation of regression parameters with incomplete covariate information usually requires a distributional assumption regarding the concerned covariates that implies a source of misspecification. Semiparametric procedures avoid such assumptions at the expense of efficiency. In this paper a simulation study with small sample size is carried out to get an idea of the performance of the ML–estimator under misspecification and to compare it with the semiparametric procedures when the former is based on a correct assumption. The results show that there is only a little gain by correct parametric assumptions, which does not justify the possibly large bias when the assumptions are not met. Additionally, a simple modification of the complete case estimator appears to be nearly semiparametric efficient.     

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.     

水库防洪分类预报调度方式及风险浅析

本文主要是通过对水库防洪分类预报调度方式的设计出发,详细介绍了设计的规则、指标的选择等方面,并设计时可能会对水库和上下游的防洪带来的风险进行了分析。     

Solving DSGE models with perturbation methods and a change of variables

This paper explores the application of the changes of variables technique to solve the stochastic neoclassical growth model. We use the method of Judd [2003. Perturbation methods with nonlinear changes of variables. Mimeo, Hoover Institution] to change variables in the computed policy functions that characterize the behavior of the economy. We report how the optimal change of variables reduces the average absolute Euler equation errors of the solution of the model by a factor of three. We also demonstrate how changes of variables correct for variations in the volatility of the economy even if we work with first-order policy functions and how we can keep a linear representation of the laws of motion of the model if we use a nearly optimal transformation. We discuss how to apply our results to estimate dynamic equilibrium economies.     

预期城乡收入差距及其对我国农村劳动力转移的影响

本文是在当前“用工荒”的社会背景下,以托达罗模型为理论基础,在比较优势的框架下,采用CHNS（中国健康营养调查）的微观数据,分析了我国农村劳动力转移的影响因素。具有内生选择的转换模型表明：①预期城乡收入差距是影响我国劳动力转移的最重要的因素; ②劳动力转移增加了农村劳动力的预期收入,从而在一定程度上缓解了城乡收入差距;③调查的我国农村劳动力数据存在自选择问题,因此在分析转移劳动力收入时应该考虑自选择的影响;④教育是影响我国农村劳动力收入的重要因素。     

工程竣工结算精确审核的关键点及实例分析

本文针对工程竣工结算工作中存在的问题,阐述了结算审核工作的关键事项,分析了签证、索赔、反索赔的关系,并列举实例进行说明,认为只有全面系统地进行工程项目管理,才能够精确做好竣工结算并有效控制工程造价.     

Karl Pearson and the Establishment of Mathematical Statistics

At the end of the nineteenth century, the content and practice of statistics underwent a series of transitions that led to its emergence as a highly specialised mathematical discipline. These intellectual and later institutional changes were, in part, brought about by a mathematical-statistical translation of Charles Darwin's redefinition of the biological species as something that could be viewed in terms of populations. Karl Pearson and W.F.R. Weldon's mathematical reconceptualisation of Darwinian biological variation and "statistical" population of species in the 1890s provided the framework within which a major paradigmatic shift occurred in statistical techniques and theory. Weldon's work on the shore crab in Naples and Plymouth from 1892 to 1895 not only brought them into the forefront of ideas of speciation and provided the impetus to Pearson's earliest statistical innovations, but it also led to Pearson shifting his professional interests from having had an established career as a mathematical physicist to developing one as a biometrician. The innovative statistical work Pearson undertook with Weldon in 1892 and later with Francis Galton in 1894 enabled him to lay the foundations of modern mathematical statistics. While Pearson's diverse publications, his establishment of four laboratories and the creation of new academic departments underscore the plurality of his work, the main focus of his life-long career was in the establishment and promulgation of his statistical methodology.     

隧道岩溶病害处理方法与实例分析

岩溶是隧道施工中经常遇到的一种地质现象,因受其特殊的地质构造影响,它容易导致开挖面涌水、突泥,围岩及支护结构变形、开裂、坍塌,影响施工进度,危及施工安全,破坏周围环境。因此,为提高岩溶隧道的修建水平,保护岩溶地区的人文环境,岩溶隧道的病害机理及其防治已引起人们的普遍关注。文章在概述岩溶对隧道的危害性和隧道岩溶病害处理原则的基础上,分析了施工超前地质预报对岩溶病害处理的重要性,探讨了隧道中不同类型的岩溶的处理方法和施工工艺,最后介绍了一个工程实例,以期能为类似隧道的岩溶病害处置提供借鉴。     

正确处理好PHOTOSHOP中的颜色显示和输出问题

图像处理软件PHOTOSHOP是教学中最为常见的软件。而大多数同学在软件学习初期,对电脑颜色的显示和打印输出后出现一些问题而烦恼,如何处理好这些常见的问题,结合平时的教学实践进行全面的总结,让学生处理软件色彩方面的问题有个很好理解。