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基于线性模型估计方程的自助法AI 解读

This paper presents a method of bootstrap estimation for the linear model. Rather than resampling from the original sample, as is conventional, the proposed method resamples summands in an estimating function used to produce the original estimate. The method is computationally simpler then existing competitors. However, its main advantage lies in the robustness to heteroscedasticity of the estimators it produces. These estimators are shown to have desirable asymptotic…

两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…

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.

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…

投影偏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…

利用小波检测跳跃与尖锐突点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.

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…

回归中缺失及辅助协变量数据的平均得分法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…

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一般不完全数据模型中的可忽略性AI 解读

Rubin (1976) defined ignorability conditions for frequentist and Bayes/likelihood analyses of data subject to missing observations. More recently, Heitjan & Rubin (1991) and Heitjan (1993) generalised the Rubin model to encompass other forms of incompleteness, establishing ignorability conditions for Bayes/likelihood inferences only. This paper extends the Heitjan-Rubin model by explicitly defining the observed degree of coarseness as a data element. This permits the…

删失数据中治疗无反应者问题的线性秩检验AI 解读

In a two-sample setting, a two-parameter mixture model is postulated for the treated patients where a proportion of the patients improve and the remaining proportion of nonresponders behave like the control patients. The response is subject to random censoring. Censored data versions of linear rank statistics are developed in order to detect improvement due to treatment. The tests are compared to standard tests such as the log rank test in terms of asymptotic relative…

通过条件化近似消除干扰参数AI 解读

The general problem of inference about a scalar parameter of interest θ in the presence of a nuisance parameter λ using conditional inference is considered.xml . A condition is given under which inference based on the conditional distribution of θ^, the maximum likelihood estimate of θ, given λ^o, the maximum likelihood estimate of λ for fixed θ = θ0, is optimal, in a certain sense. When this condition is not satisfied, it is shown that inference should be based on the…

含解释变量计数过程中的非参数核估计AI 解读

Cox's proportional hazards model assumes that the duration hazard rate factors into a product of a baseline hazard rate and a nonegative function of explanatory variables. An estimate of the baseline hazard rate, hence also of overall hazard rate, is proposed, based on a smoothing procedure using a kernel function. It is shown that the proposed estimator is uniformly consistent and converges weakly to a Gaussian process. Bandwidth selection issues are also discussed.

线性模型残差自相关检验的一项建议AI 解读

This note proposes a test of goodness of fit for time series models based on the sum of the squared residual partial autocorrelations. The test statistic is asymptotically X2. Its small-sample performance is studied through a Monte Carlo experiment. It appears sensitive to erroneous specifications especially when the fitted model understates the order of the moving average component.

通过响应变量变换实现回归线性化AI 解读

We consider the problem of choosing a transformation t(y) of a univariate response variable y so that the regression function E{t(y)| x}is linear in the predictor vector x. Let y^ be the fitted values from a linear regression of y on x. Given a few simple assumptions, we show that the plot with y on the horizontal axis and y^ on the vertical axis can be used to visualise the needed transformation t(y). A smoother can then be used as an aid to assessing t(y) visually.

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…

子集选择概率的高效计算及其在Cox回归中的应用AI 解读

An efficient method is presented to compute the probability of selection of a specified subset from the set of all subsets of a fixed size where the subsets are taken from a population whose units have varying individual probabilities of selection. The problem is motivated by the computation of the exact marginal likelihood for the Cox proportional hazards model.

异方差回归模型中非正则似然函数的一则注记AI 解读

The existence of maximum likelihood estimates for a class of heteroscedastic regression models is considered. For a given dispersion function we show that, under a weak condition, the likelihood is singular at points corresponding to nonreplicated observations, causing unrestricted maximum likelihood estimation to break down, whilst for an alternative class of dispersion functions we obtain a much stronger linear independence condition for the likelihood to be unbounded.

局部散度与关联性AI 解读

In applications of differential geometry to problems of parametric statistical inference, the notion of divergence is often used to measure the separation between two parametric densities. In this paper we move away from the parametric framework of much of statistical differential geometry and instead employ divergence in a covariate setting. Many data-analyses involve investigation of how the conditional distribution f(y|X = x) of a random variable Y changes with covariate…

基于准生命表的估计AI 解读

A large number of identical components are simultaneously set into operation at each of a regular sequence of times and, on failure, a component is instantaneously replaced. The functional form of the distribution of the component lifelength is assumed to be known and it is desired to estimate the parameters of this distribution. However, no observations of the lifelengths of individual components have been recorded: the only information available is the numbers of…

将疾病进展信息纳入生存分析的核方法AI 解读

This paper considers incorporating information on disease progression in the analysis of survival. A three-state model is assumed, with the distribution of each transition estimated separately. The distribution of survival following progression can depend on the time of progression. Kernel methods are used to give consistent estimators under general forms of dependence. The estimators for the individual transitions are then combined into an overall estimator of the survival…