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依赖且异质过程的强大数定律AI 解读

This paper presents maximal inequalities and strong law of large numbers for weakly dependent heterogeneous random variables. Specifically considered are L r mixingales for r > 1, strong mixing sequences, and near epoch dependent (NED) sequences. We provide the first strong law for L r -bounded L r mixingales and NED sequences for 1 > r > 2. The strong laws presented for α-mixing sequences are less restrictive than the laws of McLeish [8].

无限方差创新的积分过程中的 M 估计极限理论AI 解读

We consider the limiting distributions of M -estimates of an “autoregressive” parameter when the observations come from an integrated linear process with infinite variance innovations. It is shown that M -estimates are, asymptotically, infinitely more efficient than the least-squares estimator (in the sense that they have a faster rate of convergence) and are conditionally asymptotically normal.

模型选择对推断的影响AI 解读

The asymptotic properties of parameter estimators which are based on a model that has been selected by a model selection procedure are investigated. In particular, the asymptotic distribution is derived and the effects of the model selection process on subsequent inference are illustrated.

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利用最小绝对误差估计非线性动态模型AI 解读

We consider least absolute error estimation in a dynamic nonlinear model with neither independent nor identically distributed errors. The estimator is shown to be consistent and asymptotically normal, with asymptotic covariance matrix depending on the errors through the heights of their density functions at their medians (zero). A consistent estimator of the asymptotic covariance matrix of the estimator is given, and the Wald, Lagrange multiplier, and likelihood ratio tests…

协整回归的渐近有效估计AI 解读

An asymptotic optimality theory for the estimation of cointegration regressions is developed in this paper. The theory applies to a reasonably wide class of estimators without making any specific assumptions about the probability distribution or short-run dynamics of the data-generating process. Due to the nonstandard nature of the estimation problem, the conventional minimum variance criterion does not provide a convenient measure of asymptotic efficiency. An alternative…

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稳健 M 检验AI 解读

This paper investigates the local robustness properties of a general class of multidimensional tests based on M -estimators. These tests are shown to inherit the efficiency and robustness properties of the estimators on which they are based. In particular, it is shown that small perturbations of the distribution of the observations can have arbitrarily large effects on the asymptotic level and power of tests based on estimators that do not possess a bounded influence…

未知扰动协方差结构下最小二乘回归系数协方差矩阵的估计AI 解读

This paper deals with the problem of estimating the covariance matrix of the least-squares regression coefficients under heteroskedasticity and/or autocorrelation of unknown form. We consider an estimator proposed by White [17] and give a relatively simple proof of its consistency. Our proof is based on more easily verifiable conditions than those of White. An alternative estimator with improved small sample properties is also presented.

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加性交互回归模型：绕开维数灾难AI 解读

This paper considers series estimators of additive interactive regression (AIR) models. AIR models are nonparametric regression models that generalize additive regression models by allowing interactions between different regressor variables. They place more restrictions on the regression function, however, than do fully nonparametric regression models. By doing so, they attempt to circumvent the curse of dimensionality that afflicts the estimation of fully non-parametric…

非线性回归中的强一致性AI 解读

Sufficient conditions are given to ensure the existence of a sequence of strongly consistent estimators of an unknown parameter for a nonlinear regression model. The parameter space includes all separable metric spaces but is not assumed to be compact.

特征函数的函数形式与多元分布刻画AI 解读

During the Oxford Conference of the Econometric Society in 1936, Ragnar Frisch proposed a problem of characterization of distributions based on the property of linear regression of one linear function of random variables on the other. This problem has been solved, partially by Allen [1], and then completely by Rao [24,25], Fix [7], and Laha [13] relaxing the conditions imposed on the component random variables. The purpose of this paper is to solve the above mentioned…