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基于扩散过程离散观测的贝叶斯因子AI 解读

We present an approach to model selection for a time series of data on a fine time scale. The underlying process generating the data is modelled as a continuous time stochastic process. The underlying continuous processes are assumed to be diffusions with time varying drift and diffusion coefficient. Several approaches to modelling the diffusion coefficient are described. To perform model selection, we propose an approximation to the Bayes factor that uses only the discrete…

高阶渐近理论与似然原则：单参数模型AI 解读

Inferences based on higher-order asymptotics, in contrast to those based on standard first-order methods, approximate exact inferences closely enough to depend on the reference set. We use this feature to quantify the effect of the reference set on exact inferences. In particular, the difference in P-values for two reference sets can be at most O(n−½), and it is seen that one can often identify the coefficient of n−½. Although this is useful from a foundational viewpoint,…

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…

关于Jorgensen迭代定义统计量的札记AI 解读

The Newton-Raphson and Fisher scoring iteratively reweighted least squares methods are two fundamental tools for computing parameter estimators and deletion diagnostics. Jorgensen (1993) proposed a modified method to compute deletion diagnostics. In this paper, we study the relationship between Jorgensen's, Newton-Raphson and Fisher scoring one-step deletion estimators by using the observed and expected Fisher information matrices. In addition, we extend Jorgensen's true…

线性模型残差自相关检验的一种方案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.

摘要暂缺

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.

广义线性模型中三种经典检验的非零假设渐近分布AI 解读

This paper develops simple formulae for the asymptotic expansions up to order n−½ of the distributions of the likelihood ratio, Wald and score statistics in generalised linear models, under a sequence of Pitman alternatives. The powers of all three criteria, which are equivalent to first order, are compared under specific conditions based on second order approximations. The asymptotic distributions of all three statistics are obtained for testing a subset of linear…

一般不完整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…

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…

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…

一般相对风险回归中参数可识别性与偏似然有效性札记AI 解读

In this note we deal with the question of identifiability of the regression parameter in general relative risk regression. We show that, apart from the well understood kind of nonidentifiability, as usually occurs with regression, there is a second kind of nonidentiliability of the regression parameter which may still be present even if the information matrix is positive definite. However, when this happens, the partial likelihood approach is still valid, even though some…

含解释变量的计数过程非参数核估计AI 解读

SUMMARY Cox's proportional hazards model assumes that the duration hazard rate factors into a product of a baseline hazard rate and a nonnegative 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.

指数族的稳健预测分布AI 解读

The bootstrap predictive distribution considered by Harris (1989) is modified by replacing the maximum likelihood estimator of the unknown parameter by its minimum Hellinger distance estimator. The predictive distribution thus obtained is asymptotically superior to the corresponding estimative distribution in terms of the average Kullback-Leibler divergence, when the true distribution is in the natural exponential family. Simulation results are provided for the binomial and…

自相关数据的逻辑回归及其重复测量应用AI 解读

A stochastic model is proposed for the study of the influence of time-dependent covariates on the marginal distribution of the binary response in serially correlated binary data. Markov chains are expressed in terms of transitional rather than marginal probabilities. We show how to construct the model so that the covariates relate only to the mean value of the process, independently of the association parameter. After formulating the stochastic model for a simple sequence of…

删失数据中无响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…

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ECME 算法：具有更快单调收敛的 EM 与 ECM 扩展AI 解读

A generalisation of the ecm algorithm (Meng & Rubin, 1993), which is itself an extension of the em algorithm (Dempster, Laird & Rubin, 1977), can be obtained by replacing some CM-steps of ECM, which maximise the constrained expected complete-data loglikelihood function, with steps that maximise the correspondingly constrained actual likelihood function. This algorithm, which we call ecme algorithm, for Expectation/Conditional Maximisation Either, shares with both em and ecm…

循环协方差结构下组内相关系数的估计AI 解读

The maximum likelihood estimates of the parent-sib interclass correlation and other parameters are obtained, when the between sibs correlation matrix has a circular structure. The problem of testing hypotheses about interclass correlation is also considered.

子集选择概率的高效计算及其在Cox回归中的应用AI 解读

SUMMARY 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.

Kaplan–Meier积分的刀切法估计AI 解读

We derive an explicit formula for the jackknife estimate of a Kaplan-Meier integral. From this the asymptotic analysis of the jackknifed Kaplan-Meier process becomes straightforward. In a small simulation study it is demonstrated that jackknifing may lead to a considerable reduction of the bias.

异方差回归模型中非正则似然函数的札记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…

基于准寿命表的估计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…