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状态空间时间序列分析的简便高效模拟平滑器AI 解读

A simulation smoother in state space time series analysis is a procedure for drawing samples from the conditional distribution of state or disturbance vectors given the observations. We present a new technique for this which is both simple and computationally efficient. The treatment includes models with diffuse initial conditions and regression effects. Computational comparisons are made with the previous standard method. Two applications are provided to illustrate the use…

非高斯观测的状态空间时间序列分析：经典与贝叶斯视角AI 解读

Summary The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state…

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傅里叶级数回归残差偏序列相关系数的近似分布AI 解读

Approximations are found to the joint distributions of noncircular and circular partial serial correlation coefficients calculated from residuals from regression on Fourier series. Results for coefficients calculated from deviations from the true mean and from the sample mean are obtained as special cases. It is shown that when the observations are independent the partial coefficients are approximately independently distributed in beta distributions that are the same for all…

充分估计量密度的近似方法AI 解读

A simple method of obtaining asymptotic expansions for the densities of sufficient estimators is described. It is an extension of the one developed by Barndorff-Nielsen & Cox (1979) for exponential families. A series expansion in powers of n−1 is derived of which the first term has an error of order n−1 which can effectively be reduced to n− / by renormalization.The results obtained are similar to those given by Daniels's (1954) saddlepoint method but the derivations are…

傅里叶级数回归残差偏序列相关系数的近似分布AI 解读

Approximations are found to the joint distributions of noncircular and circular partial serial correlation coefficients calculated from residuals from regression on Fourier series. Results for coefficients calculated from deviations from the true mean and from the sample mean are obtained as special cases. It is shown that when the observations are independent the partial coefficients are approximately independently distributed in beta distributions that are the same for all…

充分估计量的密度近似AI 解读

A simple method of obtaining asymptotic expansions for the densities of sufficient estimators is described. It is an extension of the one developed by Barndorff-Nielsen & Cox (1979) for exponential families. A series expansion in powers of n−1 is derived of which the first term has an error of order n−1 which can effectively be reduced to n− / by renormalization.The results obtained are similar to those given by Daniels's (1954) saddlepoint method but the derivations are…

Cramér–von Mises 统计量的分量（二）AI 解读

Summary Let θ^ be an asymptotically efficient estimator of parameter vector θ based on an ordered sample of n independent observations y 1, ..., y n from a distribution with distribution function F(y, θ) and let x^j=F(yj,θ^), j = 1, ..., n. Let Ŵn 2 be the Cramér–von Mises statistic calculated from ◯ 1, ..., ◯ n. This paper shows how to construct components ẑ n1, ẑ n2, ... such that Ŵ n 2 = ∑j=1 ∞ μj ẑ nj 2 where ẑ n1, ẑ n2, ... are asymptotically independent N(0, 1)…

检验回归关系随时间保持稳定的方法AI 解读

Summary Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are…

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参数由样本估计时经验分布函数的弱收敛AI 解读

The weak convergence of the sample df is studied under a given sequence of alternative hypotheses when parameters are estimated from the data. For a general class of estimators it is shown that the sample df, when normalised, converges weakly to a specified normal process. The results are specialised to the case of efficient estimation.

Cramér–von Mises 统计量的分量：第一部分AI 解读

Summary Let Fn(x) be the sample distribution function derived from a sample of independent uniform (0, 1) variables. The paper is mainly concerned with the orthogonal representation of the Cramér-von Mises statistic Wn2 in the form ∑j=1∞(jπ)−2znj2 where the znj are the principal components of n{Fn(x)−x}. It is shown that the znj are identically distributed for each n and their significance points are tabulated. Their use for testing goodness of fit is discussed and their…

最小二乘回归中的序列相关检验（三）AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

最小二乘回归中的序列相关检验：第三篇AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

This article shows how to transform residuals from regression on an arbitrary set of k regressors to a set of values having the same joint distribution as the residuals from regression on a different set L of k regressors. Let d′ denote the value of the statistic $\\Sigma (z_{t}-z_{t-1})^{2}/\\Sigma z_{t}^{2}$ calculated from these values. It is shown that for a suitable choice of L the distribution of d′ is the same as that of $d_{U}$ , the significance values of which are…

The construction of tests of model specification is considered from a general point of view. The results are applied to testing the serial independence of the disturbances in a regression model where some of the regressors are lagged dependent variables. It is shown that the asymptotic distribution of the lag-1 serial correlation coefficient calculated from the least-squares residuals differs from that of the coefficient calculated from the true disturbances. A consequence…

论 Birnbaum 关于充分性、条件性与似然关系的定理AI 解读

If the conditioning variable is required to depend only on the value of the minimal sufficient statistic, Birnbaum's proof fails.

论 Birnbaum 定理中充分性、条件性与似然的关系AI 解读

If the conditioning variable is required to depend only on the value of the minimal sufficient statistic, Birnbaum's proof fails.

基于最小二乘残差周期图的回归序列相关检验AI 解读

A well-known procedure for testing for serial correlation is to plot out the sample path of the cumulated periodogram and to compare the resulting graph with the Kolmogorov-Smirnov limits. The paper considers small-sample aspects of this procedure when the periodogram is calculated from the residuals from least-squares regression. It is shown that for a test against an excess of low-frequency relative to high-frequency variation in the errors of the regression model, a pair…

基于最小二乘残差周期图的回归序列相关检验AI 解读

A well-known procedure for testing for serial correlation is to plot out the sample path of the cumulated periodogram and to compare the resulting graph with the Kolmogorov-Smirnov limits. The paper considers small-sample aspects of this procedure when the periodogram is calculated from the residuals from least-squares regression. It is shown that for a test against an excess of low-frequency relative to high-frequency variation in the errors of the regression model, a pair…

时间序列回归模型的参数估计AI 解读

Summary We consider the estimation of the coefficients in a general linear regression model in which some of the explanatory variables are lagged values of the dependent variable. For discussing optimum properties the concept of best unbiased linear estimating equations is developed. It is shown that when the errors are normally distributed the method of least squares leads to optimum estimates. The properties of the least-squares estimates are shown to be the same…

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