非等间隔动态面板数据模型：估计方法与应用实例

非等间隔动态面板数据模型由于相邻两期观测之间的时间长度不尽相同使得传统动态面板数据模型的估计方法失效,本文提出使用非线性最小二乘、最短距离以及它们的一步估计量对该模型进行估计,证明了这四个估计量的一致性和渐进正态性,同时借助蒙特卡洛模拟的方法验证了它们在有限样本中的估计精度,并且进一步使用所提出的估计量讨论了以往文献由于缺乏相应的估计方法而没有被研究或者充分讨论的问题,得到了一些新的结论。     

考虑结构突变时确定性趋势的估计与单位根检验式的选择——基于可行广义最小二乘估计的分析

单位根的检验功效依赖于回归检验式中的确定性趋势,而趋势估计量的分布又取决于序列的平稳性,两者相互制约。鉴于此,本文借鉴了Perron和Yabu(2009)提出的可行广义最小二乘估计,推导了相关统计量的分布,在考虑结构突变的情况下,构造了一套确定性趋势的估计和推断程序,并通过蒙特卡罗模拟对该程序的有限样本性质进行了分析。结论显示,大多数情形下根据该程序进行的单位根检验具有较高功效。     

Estimation and optimal designs for linear Haar-wavelet models

This paper gives an analytical expression for the best linear unbiased estimator (BLUE) of the unknown parameters in the linear Haar-wavelet model. From the analytical expression, we solve for the eigenvalues of the covariance matrix of the BLUE in analytical form. Further, we use these eigenvalues to construct some conventional discrete optimal designs for the model. The equivalences among these optimal designs are demonstrated and some examples are also given.      

Quantile models and estimators for data analysis

Quantile regression is used to estimate the cross sectional relationship between high school characteristics and student achievement as measured by ACT scores. The importance of school characteristics on student achievement has been traditionally framed in terms of the effect on the expected value. With quantile regression the impact of school characteristics is allowed to be different at the mean and quantiles of the conditional distribution. Like robust estimation, the quantile approach detects relationships missed by traditional data analysis. Robust estimates detect the influence of the bulk of the data, whereas quantile estimates detect the influence of co-variates on alternate parts of the conditional distribution. Since our design consists of multiple responses (individual student ACT scores) at fixed explanatory variables (school characteristics) the quantile model can be estimated by the usual regression quantiles, but additionally by a regression on the empirical quantile at each school. This is similar to least squares where the estimate based on the entire data is identical to weighted least squares on the school averages. Unlike least squares however, the regression through the quantiles produces a different estimate than the regression quantiles.     

Necessary and sufficient conditions for consistency of generalizedM-estimates

GeneralizedM-estimates (minimum contrast estimates) and their asymptotically equivalent approximate versions are considered. A relatively simple condition is found which is equivalent with consistency of all approximateM-estimates under wide assumptions about the model. This condition is applied in several directions. (i) A more easily verifiable condition equivalent with consistency of all approximateM-estimates is derived and illustrated on models with stationary and ergodic observations. (ii) A condition sufficient for inconsistency of all approximateM-estimates is obtained and illustrated on models with i.i.d. observations. (iii) A simple necessary and sufficient condition for consistency of all approximateM-estimates in linear regression with i.i.d. errors is found. This condition is weaker than sufficient conditions for consistency ofM-estimators known from the literature. A linear regression example is presented where theM-estimate is consistent and an approximateM-estimate is incosistent.Supported by CSAS grant N. 17503.     

Algorithms to compute CM- and S-estimates for regression

Constrained M-estimators for regression were introduced by Mendes and Tyler in 1995 as an alternative class of robust regression estimators with high breakdown point and high asymptotic efficiency. To compute the CM-estimate, the global minimum of an objective function with an inequality constraint has to be localized. To find the S-estimate for the same problem, we instead restrict ourselves to the boundary of the feasible region. The algorithm presented for computing CM-estimates can easily be modified to compute S-estimates as well. Testing is carried out with a comparison to the algorithm SURREAL by Ruppert.     

Asymptotic results and tests for the choice of approximative models in nonlinear two-phases regression models, heteroscedatic case

This paper is devoted to the study of the least squares estimator of f for the classical, fixed design, nonlinear model X (t _i)=f(t _i)+ε(t _i), i=1,2,…,n, where the (ε(t _i))_i=1,…,n are independent second order r.v.. The estimation of f is based upon a given parametric form. In Brodeau (1993) this subject has been studied in the homoscedastic case. This time we assume that the ε(t _i) have non constant and unknown variances σ²(t _i). Our main goal is to develop two statistical tests, one for testing that f belongs to a given class of functions possibly discontinuous in their first derivative, and another for comparing two such classes. The fundamental tool is an approximation of the elements of these classes by more regular functions, which leads to asymptotic properties of estimators based on the least squares estimator of the unknown parameters. We point out that Neubauer and Zwanzig (1995) have obtained interesting results for connected subjects by using the same technique of approximation. Received: February 1996