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层级与图式对数线性模型的 MCMC 模型选择AI 解读

We use reversible jump Markov chain Monte Carlo methods (Green, 1995) to develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linear models for high-dimensional contingency tables. Even for tables of moderate size, these sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the first example, a three-way table, the…

多变量概率分布对称性的检验AI 解读

A Monte Carlo test for multivariate symmetries is proposed. The Monte Carlo simulations are performed conditionally on a minimal sufficient statistic for the class of distributions with symmetric density. Additionally, a general purpose test statistic based on a distance measure between the probability density function and its symmetrised version is introduced. The Monte Carlo tests for spherical symmetry and multivariate reflection symmetry are studied numerically for this…

存在测量误差时的非参数回归AI 解读

In many regression applications the independent variable is measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different approaches to nonparametric regression. The first uses the SIMEX, simulation-extrapolation, method and makes no assumption about the distribution of the unobserved error-prone predictor. For this approach we derive an asymptotic theory for kernel regression which has…

病例对照数据下逻辑回归模型的卡方拟合优度检验AI 解读

We propose a chi-squared-type statistic to test the validity of the logistic regression model based on case-control data by adapting the goodness-of-fit test of Nikulin-Rao-Robson-Moore. The proposed test statistic requires a high-dimensional matrix inversion, but is otherwise easy to compute and has an asymptotic chi-squared distribution. This test statistic is an alternative to the Kolmogorov-Smirnov-type statistic of Qin & Zhang (1997) and does not need to employ a…

使用重复置信带的中期分析AI 解读

Clinical trials often include interim analyses that compare treatment groups with respect to the mean function of a response process. Sometimes it is unclear how the mean functions of the groups might differ, and thus one cannot confidently prespecify a simple metric upon which a stopping rule or repeated confidence interval can be based. This motivated us to extend the repeated confidence intervals approach for a finite-dimensional parameter (Jennison & Turnbull, 1989) to…

向量时间序列非线性检验札记AI 解读

A multivariate extension of the univariate nonlinearity test of Tsay (1986) is presented. Simulation results show that the multivariate test is more powerful than its univariate counterpart, especially for series having nonlinear structure involving several components of the vector process and weakly or moderately cross-correlated process error terms. For illustration, the test is applied to a set of seasonally adjusted quarterly capital expenditures and appropriations in…

图像模型推断的成对似然方法AI 解读

We consider parameter estimation for certain random set models for image data. For the spatial models considered here, a full likelihood-based approach to this problem is often difficult, since the likelihood generally cannot be computed for images of typical size. This has motivated the consideration of various less computationally demanding parameter estimation techniques. We discuss one method based on likelihoods for small subsets of the data. Consideration of the basic…

多元回归变量选择的非共轭贝叶斯决策论方法AI 解读

We consider the choice of explanatory variables in multivariate linear regression. Our approach balances prediction accuracy against costs attached to variables in a multivariate version of a decision theory approach pioneered by Lindley (1968). We also employ a non-conjugate proper prior distribution for the parameters of the regression model, extending the standard normal-inverse Wishart by adding a component of error which is unexplainable by any number of predictor…

时间序列分析中的子抽样与模型选择AI 解读

In this paper the subsampling method of Carlstein (1986) is used to estimate the risk of prediction for time series data. We extend Carlstein's result by proving strong consistency of the subsampling estimator and we propose a procedure for selecting a time series model empirically from a set of possibly nonnested and misspecified models by using estimated risk of prediction as a selection criterion. When this procedure is applied to the selection of the order of an…

相互相关的自回归时间序列面板建模AI 解读

We propose a method of modelling panel time series data with both inter- and intra-individual correlation, and of fitting an autoregressive model to such data. Estimators are obtained by a conditional likelihood argument. If there are few observations in each series, the estimators can be dramatically improved by Burg-type estimators taking edge effects into account. The consequences of ignoring the intercorrelation term are analysed. Partial lack of consistency is…

非线性时间序列的动态自适应分割AI 解读

We propose a dynamic adaptive partitioning scheme for nonparametric analysis of stationary nonlinear time series. It yields estimates of the whole probability distribution of the underlying process. We use information from past values to construct adaptive partitioning in a dynamic fashion which is then different from the more common static schemes in the regression set-up. The idea of dynamic partitioning is new. We make it constructive by an approach based on quantisation…

筛查项目的参数估计：多方式病例发现的稳定与非稳定疾病模型AI 解读

This paper develops methods for estimating the parameters associated with early detection programmes. Disease is considered to have three states: a disease-free state or a state in which the disease cannot be detected, a preclinical state and a clinical state. The natural history of the disease is assumed to be progressive. The parameters to be estimated are the sensitivity of one or two disease detection modalities and the characteristics of the preclinical sojourn time…

分位数比较函数的半参数推断及其在受试者工作特征曲线中的应用AI 解读

In studies to compare two samples, more information may be available on one treatment than the other. When one population is modelled parametrically and the other nonparmetrically, we study large sample properties of a semiparametric sample quantile comparison function and show that it can have substantially smaller asymptotic variance than its nonparametric counterpart, especially near the boundaries. We describe applications to both two-sample tests and receiver operating…

杂论：含加性噪声的时间序列AI 解读

We put forward a state space model where the unobservable state variable can be any Gaussian stochastic process. We discuss both maximum likelihood estimation and Bayesian inference for this generalised model. The methodology developed in this paper is particularly important for the class of long memory plus noise models. Armed with the simulation smoother introduced in this paper, we can estimate a class of non-Gaussian measurement time series models with long memory in the…

纵向数据广义线性模型中回归估计量的效率AI 解读

Liang & Zeger (1986) introduced a generalised estimating equations approach based on a 'working' correlation matrix to obtain consistent and efficient estimators of regression parameters in the class of generalised linear models for repeated measures data. As demonstrated by Crowder (1995), because of the uncertainty of definition of the working correlation matrix, the Lian-Zeger approach may in some cases lead to a complete breakdown of the estimation of the regression…

非参数保序判别方法AI 解读

In many situations it is desirable that prediction/discriminant rules should satisfy ordering properties with respect to the explanatory variables. Here, optimal rules under both L1 and L2 type loss functions are characterised under the restriction that the rules be isotonic with respect to the partial ordering on the explanatory variables. An example is given where college grade-point average is predicted based upon high school rank and American College Testing scores.

多元生物等效性的统计检验AI 解读

Although the U.S. Food and Drug Administration (FDA, 1992) recommends testing bioequivalence of individual pharmacokinetic parameters one at a time, it seems reasonable and interesting to conduct a test simultaneously for all the parameters. In this paper, we discuss several ways to construct such tests. It is shown that the confidence set approach leads to a test which can be uniformly improved by the intersection of Schuirmann's two one-sided tests procedure. The latter…

全有或全无处理不依从与后续结果缺失下的意向治疗分析AI 解读

We study the combined impact that all-or-none compliance and subsequent missing outcomes can have on the estimation of the intention-to-treat effect of assignment in randomised studies. In this setting, a standard analysis, which drops subjects with missing outcomes and ignores compliance information, can be biased for the intention-to-treat effect. To address all-or-none compliance that is followed by missing outcomes, we construct a new estimation procedure for the…

对数线性模型精确条件检验的重要性抽样算法AI 解读

SUMMARY A simple but quite general simulation method for conducting exact conditional lackof-fit tests in log-linear models is proposed. Our Monte Carlo approximation utilises an importance sampling method motivated by the crude normal approximation to the Poisson distribution. Examples considered include tests of quasi-symmetry and related models for square tables and tests concerning higher-order interactions in multi-way tables. The method is competitive with direct…

双典型相关分析中的秩似然比检验AI 解读

The likelihood-ratio test for the hypothesis that the smallest of two canonical correlations is zero is Bartlett adjustable. This theoretical property says that the moments of the test criterion and of a scaled version of the asymptotic distribution have the same second-order expansion. Simulations show that scaling with the exact expectation improves the asymptotic distribution, but the expectation is approximated poorly by its second-order expansion. This can be explained…

频率学派与贝叶斯推断尾概率的简便通用近似公式AI 解读

We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of computer algebra packages. Examples are given and the relationship to Barndorff-Nielsen's approximation is discussed.

似然比统计量的经验调整AI 解读

Consider a model parameterised by a scalar parameter of interest ψ and a nuisance parameter λ. Inference about ψ may be based on the signed square root of the likelihood ratio statistic, R. The statistic R is asymptotically distributed according to a standard normal distribution, with error O(n-½). To reduce the error of this normal approximation, several modifications to R have been proposed such as Barndorff-Nielsen's modified directed likelihood statistic, R*. In this…

杂论：线性过程的时间可逆性AI 解读

A necessary and sufficient condition for time-reversibility of stationary linear processes is given which, contrary to previous results, does not require existence of moments of order higher than two.

两个伽马总体均值之比的概率误差AI 解读

The two-sample Student's t-interval can be derived by parametric bootstrap coverage calibration of the naive, plug-in interval that fails to account for the estimation of the common variance parameter. The same technique results in an essentially exact confidence interval for the ratio of two means based on independent samples from gamma distributions. The gamma problem is more difficult computationally because an exact pivot is not available. However, the computational…