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动态回归与滤波数据：小样本滤波效应的拉普拉斯近似AI 解读

It is common for an applied researcher to use filtered data, like seasonally adjusted series, for instance, to estimate the parameters of a dynamic regression model. In this paper, we study the effect of (linear) filters on the distribution of parameters of a dynamic regression model with a lagged dependent variable and a set of exogenous regressors. So far, only asymptotic results are available. Our main interest is to investigate the effect of filtering on the small sample…

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二次型之比各阶矩的拉普拉斯近似AI 解读

The Laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables. The technique utilises the existence of a dominating peak at the boundary point on the range of integration. As closed form and tractable formulae do not exist in general, this simple approximation, which only entails basic algebraic operations, has evident practical appeal. We exploit the approximation to provide an…

统计学中鞍点展开的近似AI 解读

The saddlepoint approximation as developed by Daniels [3] is an extremely accurate method for approximating probability distributions. Econometric and statistical applications of the technique to densities of statistics of interest are often hindered by the requirements of explicit knowledge of the c.g.f. and the need to obtain an analytical solution to the saddlepoint defining equation. In this paper, we show the conditions under which any approximation to the saddlepoint…

正态变量二次型之比分布的鞍点近似AI 解读

In this article, the saddlepoint approximations to the density and tail probability of a ratio of quadratic forms in normal variables are derived. A numerical exposition via the Durbin-Watson test statistic reveals several desirable features. The approximations, which involve only a limited number of computable functions, provide the practitioner with an accessible and a very powerful tool.

一阶自回归最小二乘估计量的鞍点近似AI 解读

Phillips (1978) extended Daniels' (1956) approximation to the density of a modified correlation coefficient to obtain a saddlepoint approximation to the density of the least squares estimator in the first order noncircular autoregression. The resulting approximation is undefined in a substantial part of the tails. In this note, we establish that asuitable deformation of the contour of integration leads to a different type of saddlepoint approximation defined everywhere on…

二次型之比各阶矩的Laplace近似AI 解读

The Laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables. The technique utilises the existence of a dominating peak at the boundary point on the range of integration. As closed form and tractable formulae do not exist in general, this simple approximation, which only entails basic algebraic operations, has evident practical appeal. We exploit the approximation to provide an…

误设回归模型中线性约束预检验的最优检验水平AI 解读

When the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model, it is well known that a minimax (risk) regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value, regardless of the degrees of freedom. We show that this result no longer holds in the (likely) event that relevant regressors are excluded…