平稳的平滑转移自回归过程之间的虚假回归问题研究

文章研究平稳的平滑转移自回归过程之间的虚假回归问题.通过推导最小二乘回归估计量及其对应的t统计量的极限分布,发现:标准的t检验流程中的t统计量并不趋于标准正态分布,其极限分布依赖于模型参数,从而导致了虚假回归的可能.采用蒙特卡洛模拟研究了有限样本下数据生成过程的各项参数对虚假回归的影响,研究表明:虚假回归现象也可能普遍存在于平稳变量之间,为此,在做统计推断时,考虑平稳变量的具体特征是必要的.     

季节趋势平稳过程间的虚假回归

文章推导了当数据生成过程是独立的季节趋势平稳过程情形下,OLS参数估计及检验统计量的极限分布.由于序列中的趋势会导致虚假回归现象的发生.文章借助Monte Cado试验,对上述虚假回归中OLS统计量(t类统计量、R2、DW)的大样本渐近分布进行模拟,发现确实存在虚假回归现象并且受样本容量的影响不大.文章还针对我国数据样本期比较短的特点,就虚假回归下统计量的小样本(T=10,15,30,50)特征进行了模拟.     

含非线性的平稳变量之间的虚假回归研究

研究含非线性的平稳变量之间的虚假回归问题。通过推导OLS估计的收敛性、t统计量和R2的极限分布,证明含非线性的平稳变量之间会出现虚假回归现象,除非回归模型能精确地捕捉变量中的非线性。蒙特卡洛模拟的证据与推导出的理论相符。研究表明:在经济分析中,甄别和正确地处理变量中的非线性部分是十分重要的。     

二次趋势模型的误设检验与仿真分析

在介绍两种生成二次趋势模型的基础上,指明两者具有某种内在的关系,并以隐性趋势模型为数据生成过程,使用显性趋势模型作为估计对象,进行参数估计和相应的假设检验。理论分析结果表明:显性趋势模型的参数、t检验统计量和联合F检验统计量的极限具有非标准的分布,且高度显著;以显性趋势模型为数据生成过程,使用隐性趋势模型作为估计对象,结果表明隐性趋势模型是带趋势项的单位根过程;采用LLR检验统计量对两类模型进行区分检验,使用仿真技术进行模拟,仿真结果支持上述理论分析结论和LLR统计量能够区分两种模型。     

非线性趋势KPSS检验、模型误设与检验流程构建

利用理论推导和蒙特卡洛模拟方法,研究非线性趋势数据生成模型中KPSS检验统计量、趋势项检验统计量分布规律,并总结出KPSS检验流程。理论研究表明,在原假设和备择假设成立时,相关检验统计量在大样本下都收敛到维纳过程的泛函,且KPSS检验不能有效区分趋势类型,模拟研究也得出类似结论。实证研究显示,通过使用KPSS检验流程,可以精确确定数据生成过程。     

LSTAR框架下一类针对单位根原假设的F检验

在LSTAR框架下构建了检验单位根原假设的F类型统计量,并推导了其极限分布。相较于之前学者的研究,对LSTAR模型线性系数和位置参数的约束得以放松,因此更具有普适性;有限样本下的仿真模拟表明,相比较ADF统计量以及刘雪燕等(2008)提出的t统计量,F统计量在LSTAR框架下具有更大的检验势。对人民币实际汇率的PPP检验进一步印证了F检验在相关应用研究中的适用性和优越性。     

ADF单位根检验中联合检验LM统计量研究

 本文研究了ADF单位根检验中参数联合约束的拉格朗日乘数检验。首先,本文构建了4个LM统计量并推导了它们的极限分布;然后,运用蒙特卡罗试验,模拟了有限样本容量常用检验水平下的临界值,拟合了临界值关于样本容量的响应面函数,并总结了LM统计量有限样本容量下的统计特性;比较分析了这4个LM统计量的检验功效及实际检验水平;最后,一个实例分析简要说明了这几个统计量在单位根检验中的应用。     

含方程误差的重复测量误差模型参数的假设检验

含方程误差的重复测量误差模型解决了协变量真值与响应变量真值之间存在的不完全匹配问题.为使中小型样本量下的假设检验结果更为准确,文章基于多元正态分布推导改进形式的Skovgaard似然比检验统计量,提高其在原假设下收敛到卡方分布的渐近速度,并应用该检验统计量对重复测量误差模型中回归参数的显著性进行假设检验.模拟研究的结果表明改进的似然比检验统计量在有限样本检验下的优越性;实例分析中通过检验气温与气压之间回归参数的显著性来说明该方法的实用性.     

单发线性结构突变对DF单位根检验的影响分析—“Perron现象”的进一步研究

 “Perron现象”是指当真实的数据生成过程为带有结构突变的（趋势）平稳过程时，传统的DF单位根检验易将其误判为单位根过程。本文考虑了水平突变、截距突变、斜率突变以及截距与斜率双突变等四种突变情形下DF统计量的检验功效，推导了前两种突变情形下DF统计量的渐近分布，并对四种突变情形下DF统计量的有限样本性质进行了探讨。本研究是对“Perron现象”的进一步深入分析，也是对DF单位根检验的进一步补充和完善。     

数据初始值对DF类IPS检验势的影响研究

 本文研究了DF类面板数据单位根IPS检验势受时序数据初始值的影响,推导了DF类面板单位根IPS检验统计量在局部备择假设下的极限分布和局部渐近势函数,发现了DF类面板数据单位根IPS检验统计量局部渐近势在异质性局部备择假设下是初始条件的单调递增函数;小样本Monte Carlo模拟分析结果表明,若假设初始条件为零,DF类IPS统计量的检验势将被低估。     

Testing Monotonicity of Regression Functions – An Empirical Process Approach

We propose several new tests for monotonicity of regression functions based on different empirical processes of residuals and pseudo‐residuals. The residuals are obtained from an unconstrained kernel regression estimator whereas the pseudo‐residuals are obtained from an increasing regression estimator. Here, in particular, we consider a recently developed simple kernel‐based estimator for increasing regression functions based on increasing rearrangements of unconstrained non‐parametric estimators. The test statistics are estimated distance measures between the regression function and its increasing rearrangement. We discuss the asymptotic distributions, consistency and small sample performances of the tests.     

Effects of correlated disturbances of some regression problems

In a linear regression model the disturbances are assumed to be independently distributed. If the correlation among the disturbances exists, then the usual F statistics have not the F distribution and the distributions depend on the regressor variables. This paper gives bounds on the F statistics, whose distributions do not depends on the regressor variables. The bounds are applied to a test on a general linear hypothesis of the regression coefficients and to evaluate the confidence level of a prediction set.     

GNR, MGR, and exact misspeclfication testing

The Gauss-Newton regression (GNR) is widely used to compute Lagrange multiplier statistics. A regression described by Milliken and Graybill yields an exact F test in a certain class of nonlinear models which are linear under the null. This paper shows that the Milliken-Graybill regression is a GNR. Hence one interpretation of Milliken-Graybill is that they identified a class of nonlinear models for which the GNR yields an exact test.     

GNR,MGR, and exact misspeclfication testing

The Gauss-Newton regression (GNR) is widely used to compute Lagrange multiplier statistics. A regression described by Milliken and Graybill yields an exact F test in a certain class of nonlinear models which are linear under the null. This paper shows that the Milliken-Graybill regression is a GNR. Hence one interpretation of Milliken-Graybill is that they identified a class of nonlinear models for which the GNR yields an exact test.     

Test for Trend With a Multinomial Outcome

ABSTRACT

There is no established procedure for testing for trend with nominal outcomes that would provide both a global hypothesis test and outcome-specific inference. We derive a simple formula for such a test using a weighted sum of Cochran–Armitage test statistics evaluating the trend in each outcome separately. The test is shown to be equivalent to the score test for multinomial logistic regression, however, the new formulation enables the derivation of a sample size formula and multiplicity-adjusted inference for individual outcomes. The proposed methods are implemented in the R package multiCA.     

Regression analysis with partially labelled regressors: carbon dating of the Shroud of Turin

The twelve results from the 1988 radio carbon dating of the Shroud of Turin show surprising heterogeneity. We try to explain this lack of homogeneity by regression on spatial coordinates. However, although the locations of the samples sent to the three laboratories involved are known, the locations of the 12 subsamples within these samples are not. We consider all 387,072 plausible spatial allocations and analyse the resulting distributions of statistics. Plots of robust regression residuals from the forward search indicate that some sets of allocations are implausible. We establish the existence of a trend in the results and suggest how better experimental design would have enabled stronger conclusions to have been drawn from this multi-centre experiment.     

ADF单位根检验中联合检验F统计量研究

摘　　要:ADF检验是实际中最常用的单位根检验之一。ADF检验式有三种：（1）不含漂移项和趋势项;（2）只含漂移项不含趋势项;（3）既含漂移项也含趋势项。选用的检验式是否合适将直接影响到ADF检验的功效。为解决ADF检验过程中检验式的选择问题,本文首先从理论上推导了检验式（3）中时间趋势项系数δ与yz-1系数γ的联合检验统计量F的渐近分布;然后,应用蒙特卡罗模拟的方法研究了上述统计量与检验式（2）中关于漂移项α与系数γ的联合检验统计量的分布特征,进而给出了两统计量分布百分位数关于样本容量的响应面函数,从而进一步完善了单位根检验理论与方法。     

Confidence intervals for finite difference solutions

Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it is only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential equations. In line with this very recent trend, we show how certain commonly used finite difference schemes for numerical solutions of ordinary and partial differential equations can be considered in a regression setting. Focusing on this regression framework, we apply a simple Bayesian strategy to obtain confidence intervals for the finite difference solutions. We apply this framework on several examples to show how the confidence intervals are related to truncation error and illustrate the utility of the confidence intervals for the examples considered.     

Dickey-fuller tests with trend

The Dickey-Fuller [rcirc]_τ and [pcirc]_τ tests are based on a regression of a variable on its lagged value, an intercept, and a trend term. The distributions of both statistics depend on the coefficient of the trend, and the usual Dickey-Fuller tabulations assume that this coefficient equals zero. This paper provides tabulations for the case that the coefficient of the trend is non-zero.     

An Empirical Process View of Inverse Regression

A common approach taken in high‐dimensional regression analysis is sliced inverse regression, which separates the range of the response variable into non‐overlapping regions, called ‘slices’. Asymptotic results are usually shown assuming that the slices are fixed, while in practice, estimators are computed with random slices containing the same number of observations. Based on empirical process theory, we present a unified theoretical framework to study these techniques, and revisit popular inverse regression estimators. Furthermore, we introduce a bootstrap methodology that reproduces the laws of Cramér–von Mises test statistics of interest to model dimension, effects of specified covariates and whether or not a sliced inverse regression estimator is appropriate. Finally, we investigate the accuracy of different bootstrap procedures by means of simulations.