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On Small Sample Properties of R 2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables

多元 t 误差与代理变量下线性回归 R² 的小样本性质

In this paper we consider the small sample properties of the coefficient of determination in a linear regression model with multivariate t errors when proxy variables are used instead of unobservable regressors. The results show that if the unobservable variable is an important variable, the adjusted coefficient of determination can be more unreliable in small samples than the unadjusted coefficient of determination from both viewpoints of the bias and the MSE.

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Median Unbiasedness of Estimators of Panel Data Censored Regression Models

面板删失回归估计量的中位数无偏性

This note proves that the estimator of panel data censored regression models proposed in Honoré [2] is median unbiased when only one parameter is estimated. This result is obtained without parametric assumptions about the distribution of the error terms.

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A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models

非参数回归函数估计中的一致模型设定检验

This paper proposes a general framework for specification testing of the regression function in a nonparametric smoothing estimation context. The same analysis can be applied to cases as varied as testing for omission of variables, testing certain nonlinear restrictions in the regressors, and testing the correct specification of some parametric or semiparametric model of interest, for example, testing a certain type of nonlinearity of the regression function. Furthermore,…

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The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case

混合过程近历相依函数的全局非平稳中心极限定理:渐近退化情形

The central limit theorem in Davidson [2] is extended to allow cases where the variances of sequence coordinates can be tending to zero. A trade-off is demonstrated between the degree of dependence and the rate of degeneration. For the martingale difference case, it is sufficient for the sum of the variances to diverge at the rate of log n .

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Asymptotic Expansions for Random Walks with Normal Errors

正态误差随机游走的渐近展开

The asymptotic distribution of the least-squares estimators in the random walk model was first found by White [17] and is described in terms of functional of Brownian motion with no closed form expression known. Evans and Savin [5,6] and others have examined numerically both the asymptotic and finite sample distribution. The purpose of this paper is to derive an asymptotic expansion for the distribution. Our approach is in contrast to Phillips [12,13] who has already derived…

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A Curious Result on Exact FIML and Instrumental Variables

精确全信息最大似然与工具变量之间的一个特殊结果

The iterative application of an instrumental variable method to a system of simultaneous equations may exactly produce FIML, upon convergence. Instruments achieving this target do not need to be either uncorrelated with the error terms or correlated as much as possible with the replaced explanatory variables. This curious mathematical result, which contradicts some common wisdom and intuition, is proved in our paper. Our proof also provides a unified scheme that covers the…

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Noncausality and Marginalization of Markov Processes

Markov 过程的非因果性与边际化

In this paper it is shown that a subprocess of a Markov process is markovian if a suitable condition of noncausality is satisfied. Furthermore, a markovian condition is shown to be a natural condition when analyzing the role of the horizon (finite or infinite) in the property of noncausality. We also give further conditions implying that a process is both jointly and marginally markovian only if there is both finite and infinite noncausality and that a process verifies both…

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Testing Identifiability and Specification in Instrumental Variable Models

工具变量模型中的可识别性与设定检验

The paper develops and explores tests, based on standard moment specifications, for the identifiability of parameters apparently estimable by instrumental variables. An asymptotic expansion under standard restrictive assumptions on the error distribution suggests a correction to the asymptotic distribution. A small sampling experiment indicates that the tests are of use.

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On the Asymptotic Power of Unit Root Tests

单位根检验的渐近功效

Closed forms for the distribution of some conventional statistics are given as a prelude to deriving their asymptotic power functions as unit root tests. In the process, an important distinction is drawn between two classes of statistics: one which relies on deterministic normalizations and the other which uses stochastic normalizations. When the data follow a driftless autoregression, a t test (which belongs to the second class) for a unit root is found to perform better…

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Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model

单整过程的连续弱收敛与随机等度连续性:回归估计应用

The concepts of continuous and uniform weak convergence and versions of stochastic equicontinuity are discussed in the context of integrated processes of order one. The considered processes depend on a parameter vector in a specific fashion which is relevant for integrated and cointegrated systems with non-linearities in parameters. The results of the paper can be applied to obtain asymptotic distributions of estimators and test statistics in such systems. In a correctly…

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Identification and Estimation of Continuous Time Dynamic Systems With Exogenous Variables Using Panel Data

利用面板数据识别和估计含外生变量的连续时间动态系统

This paper deals with the identification and maximum likelihood estimation of the parameters of a stochastic differential equation from discrete time sampling. Score function and maximum likelihood equations are derived explicitly. The stochastic differential equation system is extended to allow for random effects and the analysis of panel data. In addition, we investigate the identifiability of the continuous time parameters, in particular the impact of the inclusion of…

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