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普通最小二乘与最小绝对误差估计的比较AI 解读

In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.

Durbin–Watson 检验的局部最优性质AI 解读

Although originally designed to detect AR(1) disturbances in the linear-regression model, the Durbin-Watson test is known to have good power against other forms of disturbance behavior. In this paper, we identify disturbance processes involving any number of parameters against which the Durbin–Watson test is approximately locally best invariant uniformly in a range of directions from the null hypothesis. Examples include the sum of q independent ARMA(1,1) processes, certain…

回归结构稳定性的多重决策理论分析AI 解读

Using the theory of multiple decisions, this paper conducts an analysis of structural stability in location and variance for the linear-regression model. It shows that both cusum and cusum-of-squares techniques are in certain senses optimal. However, the same tests are optimal for changes in location and variance. It is also shown that there is an inherent contradiction between the use of recursive residuals and cusum techniques. The concept of a localized Bayes rule is…

含单整过程回归的统计推断：第一部分AI 解读

This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions, and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F tests is explored and new transformations are introduced to deal with these…

基于广义 t 分布的回归模型部分自适应估计AI 解读

This paper considers M-estimators of regression parameters that make use of a generalized functional form for the disturbance distribution. The family of distributions considered is the generalized t (GT), which includes the power exponential or Box-Tiao, normal, Laplace, and t distributions as special cases. The corresponding influence function is bounded and redescending for finite “degrees of freedom.” The regression estimators considered are those that maximize the GT…

带协方差限制的线性随机模型估计AI 解读

The purpose of this paper is to provide a systematic treatment of the problem of estimation in systems of linear stochastic equations where some of the disturbances are uncorrelated and where the identifying equations are equivalent to a linear system.

自回归移动平均过程的若干精确公式AI 解读

This paper demonstrates that for a finite stationary autoregressive moving average process the inverse of the covariance matrix differs from the matrix of the covariances of the inverse process by a matrix of low rank. The formula for the exact inverse of the covariance matrix of the scalar or multivariate process is provided. We obtain approximations based on this formula and evaluate some of the approximate results in the existing literature. Applications to computational…

通过鞅逼近证明样本协方差矩阵向随机积分的弱收敛AI 解读

Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral ∫ 0 1 BdB′ , where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is ∫ 0 1 BdB′ + Λ and involves a constant matrix Λ of bias terms whose magnitude depends on the serial correlation properties of the sequence. This…

相依非同分布随机变量的大数定律AI 解读

This paper provides L 1 and weak laws of large numbers for uniformly integrable L 1 -mixingales. The L 1 -mixingale condition is a condition of asymptotic weak temporal dependence that is weaker than most conditions considered in the literature. Processes covered by the laws of large numbers include martingale difference, ø(·), ρ(·), and α(·) mixing, autoregressive moving average, infinite-order moving average, near epoch dependent, L 1 -near epoch dependent, and mixingale…

连续时间计量经济模型的历史AI 解读

Although it is only during the last decade that continuous-time models have been extensively used in applied econometric work, the development of statistical methods applicable to such models commenced over 40 years ago. The first significant contribution to the problem of estimating the parameters of continuous-time stochastic models from discrete data was made by the British statistician Bartlett [1946] only three years after the pioneering contribution of Haavelmo [1943]…

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