Non Asymptotic Minimax Estimation of Functionals with Noisy Observations

The minimax estimation of functionals by a finite number of noisy observations is considered. A new way to formalize the problem that enables one to calculate non asymptotic optimal estimates is proposed. The calculations can be turned into and executed as a computer algorithm or carried out analytically under week assumptions on random variables. Some examples are considered.     

存在自相关时检验和估计方法的改进——基于自回归分布滞后模型的自相关检验和参数估计

存在自相关时的自相关检验和参数估计是基础计量经济学的一个重要内容,并且存在自相关时的原模型已转化为自回归分布滞后模型。讨论存在自相关时的自相关检验和参数估计问题,提出了一种基于自回归分布滞后模型的自相关检验法,并同时给出了相应的参数估计。     

Sample Attrition and Labor Supply Response in Experimental Panel Data

Sample attrition is a potentially serious problem for analysis of panel data, particularly experimental panel data. In this article, a variety of estimation procedures are used to assess the importance of attrition bias in labor supply response to the Seattle and Denver Income Maintenance Experiments (SIME/DIME). Data from Social Security Administration earnings records and the SIME/DIME public use file are used to test various hypotheses concerning attrition bias. The study differs from previous research in that data on both attriters and nonattriters are used to estimate the experimental labor supply response. Although not conclusive, the analysis suggests that attrition bias is probably not a serious enough problem in the SIME/DIME data to warrant extensive correction procedures. The methodology used in this study could be applied to other panel data sets.     

洛伦兹曲线的半参数估计

洛伦兹曲线与基尼系数是研究社会收入分配差异的重要工具.社会收入分配是一个复杂的过程,用尽可能精确的曲线给出洛伦兹曲线的估计进而给出基尼系数的估计,历来是统计学者和经济学者的工作目标.基于将参数方法与非参数方法相结合的思想给出洛伦兹曲线的半参数估计,进而导出基尼系数的估计,并据此进行了实证分析.     

Estimation,Testing, and Finite Sample Properties of Quasi-Maximum Likelihood Estimators in GARCH-M Models

We provide three new results concerning quasi-maximum likelihood (QML) estimators in generalized autoregressive conditional heteroskedastic in mean (GARCH-M) models. We first show that, depending on the functional form that we impose in the mean equation, the properties of the model may change and the conditional variance parameter space may be restricted, in contrast to the theory of traditional GARCH processes. Second, we also present a new test for GARCH effects in the GARCH-M context which is simpler to implement than alternative procedures such as in Beg et al. (2001 Beg , R. , Silvapulle , M. , Silvapulle , P. ( 2001 ). Tests against inequality constraints when some nuisance parameters are present only under the alternative: test of ARCH in ARCH-M models . Journal of Business and Economic Statistics 19 : 245 – 485 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We propose a new way of dealing with parameters that are not identified by creating composites of parameters that are identified. Third, the finite sample properties of QML estimators are explored in a restricted ARCH-M model and bias and variance approximations are found which show that the larger the volatility of the process the better the variance parameters are estimated. The invariance properties that Lumsdaine (1995 Lumsdaine , R. L. ( 1995 ). Finite sample properties of the maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models: a Monte Carlo investigation . Journal of Business and Economic Statistics 13 ( 1 ): 1 – 10 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proved for the traditional GARCH are shown not to hold in the GARCH-M. For those researchers who choose not to rely on the first order asymptotic approximation of our proposed test statistic, we also show how our bias expressions can be used to bias correct the QML estimates with a view to improving the finite sample performance of the test. Finally, we show how our new proposed test works in practice in an empirical economic application.     

Nonparametric Estimation and Hypothesis Testing on the Partial Area Under Receiver Operating Characteristic Curves

ABSTRACT

The area under a receiver operating characteristic curve is a useful index of the accuracy of a diagnostic test. When the diagnostic ability of a new biomarker is of interest only in a certain range of specificity, the partial area under the curve becomes desirable. In this article, we extend Bamber's (1975 Bamber , D. ( 1975 ). The area above the ordinal dominance graph and the area below the receiver operating characteristics graph. J. Math. Psychol. 12 : 387 – 415 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) results and show that the partial area under a receiver operating characteristic curve is the probability of a constrained stochastic ordering. We then construct a ‘weighted’ Mann-Whitney statistic as an estimator of the partial area and investigate its statistical properties. A testing procedure is also developed to compare partial area under two receiver operating characteristic curves. The methods are exemplified with data from biomarkers associated with coronary heart disease.     

Testing for residual correlation of any order in the autoregressive process

We are interested in the implications of a linearly autocorrelated driven noise on the asymptotic behavior of the usual least-squares estimator in a stable autoregressive process. We show that the least-squares estimator is not consistent and we suggest a sharp analysis of its almost sure limiting value as well as its asymptotic normality. We also establish the almost sure convergence and the asymptotic normality of the estimated serial correlation parameter of the driven noise. Then, we derive a statistical procedure enabling to test for correlation of any order in the residuals of an autoregressive modelling, giving clearly better results than the commonly used portmanteau tests of Ljung–Box and Box–Pierce, and appearing to outperform the Breusch–Godfrey procedure on small-sized samples.     

Estimation and testing procedures for the reliability functions of a general class of distributions

We consider here the general class of distributions proposed by Sankaran and Gupta (2005) by zeroing in on two measures of reliability, R(t) = P(X > t) and P = P(X > Y). Thereafter, we develop point estimation for R(t) and ‘P’ and develop uniformly minimum variance unbiased estimators (UMVUES). Then we derive testing procedures for the hypotheses related to different parametric functions. Finally, we compare the results using the Monte Carlo simulation method. Using real data set, we illustrate the procedure clearly.     

Testing for the Cointegrating Rank of a VAR Process With Structural Shifts

Tests for the cointegrating rank of a vector autoregressive process are considered that allow for possible exogenous shifts in the mean of the data-generation process. The break points are assumed to be known a priori. It is proposed to estimate and remove the deterministic terms such as mean, linear-trend term, and a shift in a first step. Then systems cointegration tests are applied to the adjusted series. The resulting tests are shown to have known limiting null distributions that are free of nuisance parameters and do not depend on the break point. The tests are applied for analyzing the number of cointegrating relations in two German money-demand systems.     

中国城乡居民信息消费的半参数估计分析#

以中国1993-2008年30个省份的面板数据为研究对象,通过构建中国城镇和农村居民信息消费的半参数模型,对信息消费的恩格尔曲线、总消费支出和价格指数对信息消费支出份额的边际影响进行了非参数估计,并在此基础上分析比较中国城乡居民信息消费的差异性。实证结果表明：地区经济发展水平仅对农村信息消费支出有显著影响,而居民受教育水平、居民总消费支出以及价格水平均对城乡居民信息消费支出有显著影响;居民总消费支出和价格水平变量对城乡居民信息消费支出的边际影响均存在一个极大值水平;价格水平对农村居民信息消费支出的负效应要大于总消费支出对信息消费支出的正效用,而城镇居民信息消费中没有表现出这一特征。通过控制价格水平、增加农村居民收入、增加农村基础设施投入等方式,可以缩小城乡居民信息消费的差异。     

Nonparametric Estimation of Average Growth Curve with General Nonstationary Error Process

The nonparametric estimation of the growth curve has been extensively studied in both stationary and some nonstationary particular situations. In this work, we consider the statistical problem of estimating the average growth curve for a fixed design model with nonstationary error process. The nonstationarity considered here is of a general form, and this article may be considered as an extension of previous results. The optimal bandwidth is shown to depend on the singularity of the autocovariance function of the error process along the diagonal. A Monte Carlo study is conducted in order to assess the influence of the number of subjects and the number of observations per subject on the estimation.     

Estimation of a probability density function using interval aggregated data

ABSTRACT

In economics and government statistics, aggregated data instead of individual level data are usually reported for data confidentiality and for simplicity. In this paper we develop a method of flexibly estimating the probability density function of the population using aggregated data obtained as group averages when individual level data are grouped according to quantile limits. The kernel density estimator has been commonly applied to such data without taking into account the data aggregation process and has been shown to perform poorly. Our method models the quantile function as an integral of the exponential of a spline function and deduces the density function from the quantile function. We match the aggregated data to their theoretical counterpart using least squares, and regularize the estimation by using the squared second derivatives of the density function as the penalty function. A computational algorithm is developed to implement the method. Application to simulated data and US household income survey data show that our penalized spline estimator can accurately recover the density function of the underlying population while the common use of kernel density estimation is severely biased. The method is applied to study the dynamic of China's urban income distribution using published interval aggregated data of 1985–2010.     

Lessons From Quantile Panel Estimation of the Environmental Kuznets Curve

We employ quantile regression fixed effects models to estimate the income-pollution relationship on NO _x (nitrogen oxide) and SO ₂ (sulfur dioxide) using U.S. data. Conditional median results suggest that conditional mean methods provide too optimistic estimates about emissions reduction for NO _x , while the opposite is found for SO ₂. Deleting outlier states reverses the absence of a turning point for SO ₂ in the conditional mean model, while the conditional median model is robust to them. We also document the relationship's sensitivity to including additional covariates for NO _x , and undertake simulations to shed light on some estimation issues of the methods employed.     

E-Bayesian Estimation and Hierarchical Bayesian Estimation of Failure Probability

This article introduces a new parameter estimation method, named E-Bayesian estimation, to estimate failure probability. The method is suitable for the censored or truncated data with small sample sizes and high reliability. The definition, properties and related simulation study of the E-Bayesian estimation are given. A real data set is also discussed. Through the examples, the efficiency and easiness of operation of this method are commended.     

Nonparametric Simultaneous Tests for Location and Scale Testing: A Comparison of Several Methods

The two-sample location-scale problem arises in many situations like climate dynamics, bioinformatics, medicine, and finance. To address this problem, the nonparametric approach is considered because in practice, the normal assumption is often not fulfilled or the observations are too few to rely on the central limit theorem, and moreover outliers, heavy tails and skewness may be possible. In these situations, a nonparametric test is generally more robust and powerful than a parametric test. Various nonparametric tests have been proposed for the two-sample location-scale problem. In particular, we consider tests due to Lepage, Cucconi, Podgor-Gastwirth, Neuhäuser, Zhang, and Murakami. So far all these tests have not been compared. Moreover, for the Neuhäuser test and the Murakami test, the power has not been studied in detail. It is the aim of the article to review and compare these tests for the jointly detection of location and scale changes by means of a very detailed simulation study. It is shown that both the Podgor–Gastwirth test and the computationally simpler Cucconi test are preferable. Two actual examples within the medical context are discussed.     

An Applied Comparison of Area-Level Linear Mixed Models in Small Area Estimation

This article reviews four area-level linear mixed models that borrow strength by exploiting the possible correlation among the neighboring areas or/and past time periods. Its main goal is to study if there are efficiency gains when a spatial dependence or/and a temporal autocorrelation among random-area effects are included into the models. The Fay–Herriot estimator is used as benchmark. A design-based simulation study based on real data collected from a longitudinal survey conducted by a statistical office is presented. Our results show that models that explore both spatial and chronological association considerably improve the efficiency of small area estimates.     

Efficient Estimation of the Seemingly Unrelated Regression Cointegration Model and Testing for Purchasing Power Parity

This paper studies the efficient estimation of seemingly unrelated linear models with integrated regressors and stationary errors. We consider two cases. The first one has no common regressor among the equations. In this case, we show that by adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. In the second case we consider, there is a common regressor to all equations, and we discuss efficient minimum distance estimation in this context. Simulation results suggests that our new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of the proportionality and symmetry conditions implied by purchasing power parity (PPP) among the G-7 countries. The tests based on the efficient estimates easily reject the joint hypotheses of proportionality and symmetry for all countries with either the United States or Germany as numeraire. Based on individual tests, our results suggest that Canada and Germany are the most likely countries for which the proportionality condition holds, and that Italy and Japan for the symmetry condition relative to the United States.     

Efficient Estimation of the Seemingly Unrelated Regression Cointegration Model and Testing for Purchasing Power Parity

Abstract

This paper studies the efficient estimation of seemingly unrelated linear models with integrated regressors and stationary errors. We consider two cases. The first one has no common regressor among the equations. In this case, we show that by adding leads and lags of the first differences of the regressors and estimating this augmented dynamic regression model by generalized least squares using the long-run covariance matrix, we obtain an efficient estimator of the cointegrating vector that has a limiting mixed normal distribution. In the second case we consider, there is a common regressor to all equations, and we discuss efficient minimum distance estimation in this context. Simulation results suggests that our new estimator compares favorably with others already proposed in the literature. We apply these new estimators to the testing of the proportionality and symmetry conditions implied by purchasing power parity (PPP) among the G-7 countries. The tests based on the efficient estimates easily reject the joint hypotheses of proportionality and symmetry for all countries with either the United States or Germany as numeraire. Based on individual tests, our results suggest that Canada and Germany are the most likely countries for which the proportionality condition holds, and that Italy and Japan for the symmetry condition relative to the United States.     

Estimation of linear models with anonymised panel data

The paper analyses the biasing effect of anonymising micro data by multiplicative stochastic noise on the within estimation of a linear panel model. In short panels, additional bias results from serially correlated regressors. Results in this paper are related to the project “Firms’ Panel Data and Factual Anonymisation,” which is financed by Federal Ministry of Education and Research. We would like to thank the anonymous referees for helpful comments.     

Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength

In this paper, we estimate multicomponent stress-strength reliability by assuming Burr-XII distribution. The research methodology adopted here is to estimate the parameter using maximum likelihood estimation. Reliability is estimated using the maximum likelihood method of estimation and results are compared using the Monte Carlo simulation for small samples. Using real data sets we illustrate the procedure clearly.