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高阶连续时间自回归模型的估计AI 解读

A method is presented for computing maximum likelihood, or Gaussian, estimators of the structural parameters in a continuous time system of higherorder stochastic differential equations. It is argued that it is computationally efficient in the standard case of exact observations made at equally spaced intervals. Furthermore it can be applied in situations where the observations are at unequally spaced intervals, some observations are missing and/or the endogenous variables…

最小二乘估计量的零一律结果AI 解读

The least squares estimator for the linear regression model is shown to converge to the true parameter vector either with probability one or with probability zero. In the latter case, it either converges to a point not equal to the true parameter with probability one, or it diverges with probability one. These results are shown to hold under weak conditions on the dependent random variable and regressor variables. No additional conditions are placed on the errors. The…

局部备择下高斯 ARMA 过程似然比统计量分布的渐近展开AI 解读

In this paper, we shall derive the asymptotic expansion for the distribution of the likelihood ratio criterion for a Gaussian autoregressive moving average process under a sequence of local alternative hypotheses converging to the null hypothesis with rate of convergence where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).

一般结构方程中工具变量估计量的联合与边际密度AI 解读

Starting from the conditional density of the instrumental variable (IV) estimator given the right-hand-side endogenous variables, we provide an alternative derivation of Phillips' result on the joint density of the IV estimator for the endogenous coefficients, and derive an expression for the marginal density of a linear combination of these coefficients. In addition, we extend Phillips' approximation to the joint density to 0( T −2 ,) and show how this result can be used to…

联合及条件数据生成过程与向量自回归的非参数时间序列估计AI 解读

In this paper we develop nonparametric estimators of the joint time series data generating process (DGP) of ( x t , y t ) at different t -values, of conditional DGP, of the conditional mean of x t given the past values of x and y , and, more generally, the conditional mean of ( x t , y t ) given their past values (vector autoregression). We establish, among other results, the central limit theorems for these estimators under far weaker mixing conditions than those used in…

希尔伯特空间中的非参数函数估计AI 解读

This paper is concerned with the estimation of a nonlinear regression function which is not assumed to belong to a prespecified parametric family of functions. An orthogonal series estimator is proposed, and Hilbert space methods are used in the derivation of its properties and the proof of several convergence theorems. One of the main objectives of the paper is to provide the theoretical basis for a practical stopping rule which can be used for determining the number of…