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共同典型变量AI 解读

Canonical correlation analysis measures the linear relationship between two random vectors X1 and X2 as the maximum correlation between linear combinations of X1 and linear combinations of X2. Several generalisations of canonical correlation analysis to k2 random vectors X1 …, Xk have been proposed in the literature (Kettenring, 1971, 1985), based on the principle of maximising some generalised measure of correlation. In this paper we propose an alternative generalisation,…

信息性一般删失下分类数据的贝叶斯方法AI 解读

This paper develops a Bayesian approach to the problem of incomplete categorical data informatively censored where the reported sets are not restricted to follow any specific pattern. It generalises that introduced by Paulino & Pereira (1992) in not requiring a censoring pattern by partitions of the set of sampling categories. Some extensions are also discussed.

关于位置—尺度族平滑拟合优度检验的说明AI 解读

In this note, we show that the test statistic given by Rayner & Best (1986) for Neyman's (1937) smooth test of goodness of fit for location-scale families does not, in general, have the alleged chi-squared distribution. As a result, gross error may result from using their test strategy. The size of this error is obtained for the logistic distribution.

似然比检验的 Bartlett 校正AI 解读

This note resolves two conflicting published corrections to Hayakawa's (1977) expansion of the likelihood ratio statistic, one of which suggests that a coefficient in the expansion is always zero and therefore irrelevant, the other suggesting that the formula for the coefficient is in error and that the coefficient should not be present. We present an example in which Hayakawa's formula for the coefficient yields nonzero values, explain why the argument that the reported…

线性回归中有效模型选择准则的相对收敛速度AI 解读

Two approaches to estimating a smooth regression function not specified by a finite number of parameters are (i) to fit a parametric model to the data, with the number of parameters selected by the Akaike information criterion, AIC, and (ii) to use nonparametric smoothing techniques, with the smoothing parameter selected by cross-validation or some other automatic method. We consider the relative rate of convergence of the mean integrated squared error of the selected…

多响应回归模型的曲率度量AI 解读

The Bates & Watts (1981) curvature measures developed for single response nonlinear least squares problems are extended to multiresponse parameter estimation problems based on the Box-Draper estimation criterion. Exact determination contours are approximated by contours of the generalised least squares model conditioned on the maximum likelihood estimate of the covariance matrix for the responses. By this approximation, curvature measures calculated for the generalised least…

重复测量广义线性模型中工作相关矩阵的使用问题AI 解读

In a seminal paper Liang & Zeger (1986) extended the use of generalised linear models to repeated measures data. They based the analysis on specifications for the means and variances of the observations, as usual for generalised linear models, but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a ‘working’ correlation matrix. In some cases the parameters involved in this matrix are subject to an uncertainty…

利用小波检测跳跃与尖锐尖点AI 解读

A method is proposed to detect jumps and sharp cusps in a function which is observed with noise, by checking if the wavelet transformation of the data has significantly large absolute values across fine scale levels. Asymptotic theory is established and practical implementation is discussed. The method is tested on simulated examples, and applied to stock market return data.

非线性自回归的可加性检验AI 解读

Additivity is commonly used in the statistical literature to simplify data analysis, especially in analysis of variance and in multivariate smoothing. In this paper, we propose three procedures for testing additivity in nonlinear time series analysis. The first procedure combines some smoothing techniques with analysis of variance, the second is a Lagrange multiplier test using nonparametric estimation, and the third is a permutation test which uses smoothing techniques to…

时间序列模型的模拟平滑器AI 解读

Recently suggested procedures for simulating from the posterior density of states given a Gaussian state space time series are refined and extended. We introduce and study the simulation smoother, which draws from the multivariate posterior distribution of the disturbances of the model, so avoiding the degeneracies inherent in state samplers. The technique is important in Gibbs sampling with non-Gaussian time series models, and for performing Bayesian analysis of Gaussian…

利用误分类二元响应的非参数回归估计AI 解读

For random design nonparametric regression, in the case that the responses are binary and subject to misclassification, the performance of the kernel estimator is investigated. The kernel estimator is generally biased for the local proportion. To adjust for the bias, the double sampling scheme of Tenenbein (1970, 1971) is considered. A plugged-in kernel estimator and an imputed kernel estimator, which adjust for the effect of misclassification on the kernel estimator, are…

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两个总体比例风险假设的检验AI 解读

The assumption of proportional hazards in different populations leads to elegant analysis of survival data as initiated by Cox (1972). However, this model is not appropriate in all situations. In recent literature there have been several instances of crossing hazards, which may be modelled by an increasing hazard ratio. We present a U-statistic test for checking constancy of the hazard ratio against this alternative. The test is suitable for censored data and is found to…

两阶段抽样的方差估计及其在缺失数据插补中的应用AI 解读

Ratio estimation under two-phase simple random sampling is studied. A new linearisation variance estimator that makes more complete use of the sample data than a standard one is proposed. A jackknife variance estimator and its linearised version are also obtained. Unconditional and conditional repeated sampling properties of these variance estimators are studied through simulation. Applications to ‘mass’ imputation under two-phase sampling and deterministic imputation for…

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投影部分似然及其在纵向数据中的应用AI 解读

An estimating equation, which we call the projected partial score, is introduced for longitudinal data analysis. The estimating equation is obtained by projecting the partial likelihood score function onto the vector space spanned by a class of ‘conditionally linear’ estimating equations. We demonstrate that removing certain terms from the projection of the full likelihood score does not alter important inferential properties of the estimating equation, and doing so is…

时间序列线性的非参数检验AI 解读

We introduce tests of linearity for time series based on nonparametric estimates of the conditional mean and the conditional variance. The tests are compared to a number of parametric tests and to nonparametric tests based on the bispectrum. Asymptotic expressions give bad approximations, and the null distribution under linearity is constructed using resampling of the best linear approximation. The new tests perform well on the examples tested.

回归模型中缺失及辅助协变量数据的平均得分方法AI 解读

We consider regression analysis when incomplete or auxiliary covariate data are available for all study subjects and, in addition, for a subset called the validation sample, true covariate data of interest have been ascertained. The term auxiliary data refers to data not in the regression model, but thought to be informative about the true missing covariate data of interest. We discuss a method which is nonparametric with respect to the association between available and…

将两时期交叉设计的贝叶斯分析扩展至缺失数据AI 解读

A procedure is developed for performing a Bayesian analysis of a simple two-period crossover design when some observations are missing in one, or both, treatment periods. The approach requires the numerical evaluation of a single integral to be performed for each posterior marginal distribution of interest. The relative efficiency of this approach to one in which patients with missing data are excluded is investigated.

基于边际积分的结构化非参数回归核估计AI 解读

We define a simple kernel procedure based on marginal integration that estimates the relevant univariate quantity in both additive and multiplicative nonparametric regression.

使贝叶斯推断具有频率学有效性的先验AI 解读

We derive the differential equation that a prior must satisfy if the posterior probability of a one-sided credibility interval for a parametric function and its frequentist probability agree up to 0(n−1). This equation turns out to be identical with Stein's equation for a slightly different problem, for which also our method provides a rigorous justification. Our method is different in details from Stein's but similar in spirit to Dawid (1991) and Bickel & Ghosh (1990). Some…

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一阶移动平均模型似然函数的闭式表达AI 解读

The covariance matrix of a first order moving average process is expressed as the product of the covariance matrix of the dual autoregressive process of order one and a near identity matrix. Its inverse is then obtained. The closed form of the likelihood function is derived. A comparison is made with some approximate likelihood functions.

贝叶斯分析中有界影响的一个注记AI 解读

Let χ be a single observation from a distribution having unknown location parameter θ. Dawid (1973) provided sufficient conditions for the posterior distribution of θ to approach the prior distribution as χ tends to infinity, so that an outlier has bounded and vanishing influence on the posterior distribution. We present a result closely related to Dawid's theorem. This enables us to consider priors and likelihoods for the location problem which have bounded but nonvanishing…