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With the cointegration formulation of economic long–run relations the test for cointegrating rank has become a useful econometric tool. The limit distribution of the test is often a poor approximation to the finite sample distribution and it is therefore relevant to derive an approximation to the expectation of the likelihood ratio test for cointegration in the vector autoregressive model in order to improve the finite sample properties. The correction factor depends on…

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高斯向量自回归模型中协整向量的估计与假设检验AI 解读

This paper contains the likelihood analysis of vector autoregressive models allowing for cointegration. The author derives the likelihood ratio test for cointegrating rank and finds it asymptotic distribution. He shows that the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations. The author shows that the asymptotic distribution of the maximum…

面向生存分析应用的乘积积分综述AI 解读

The correspondence between a survival function and its hazard or failure-rate is a central idea in survival analysis and in the theory of counting processes. This correspondence is shown to be a special case of a more general correspondence between multiplicative and additive matrix-valued measures on the real line. Additive integration of the survival function produces the hazard, while the multiplicative integral, or so-called product-integral, of the hazard yields the…

Hotelling 管体积定理：同时推断与数据分析中的应用AI 解读

We illustrate with contemporary examples Hotelling's geometric approach to simultaneous probability calculations. Hotelling reduces the evaluation of certain normal theory significance probabilities to finding the volume of a tube about a curve in a hypersphere, and shows that this volume is often exactly given by length times cross-sectional area. We review Hotelling's result together with some recent complements, and then use the approach to set simultaneous prediction…

函数关系、随机系数与非线性回归：动力学数据应用AI 解读

List of Contents.- 1. An example from physiology.- 1.1 The experiment and the data.- 1.2 The model.- 2. The general linear model.- 2.1 Independent observations with the same variance.- 2.2 Correlated observations with known covariance matrix.- 2.3 Correlated observations with unknown covariance matrix.- 2.4 The general linear model with estimated weights.- 3. The linear functional relation.- 3.1 Introduction.- 3.2 The model and the estimates.- 3.3 Comments on the model.- 3.4…

修订与勘误：加权线性回归残差平方和分布的 Welch–James 近似AI 解读

Soren Johansen, Amendments and Corrections: The Welch--James Approximation to the Distribution of the Residual Sum of Squares in a Weighted Linear Regression, Biometrika, Vol. 69, No. 2 (Aug., 1982), p. 491