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再生模拟在马尔可夫链蒙特卡洛中的适用性AI 解读

We consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in Markov chain Monte Carlo. Chan & Geyer (1994) established a central limit theorem for ergodic averages by assuming that the underlying Markov chain is geometrically ergodic and that a simple moment condition is satisfied. While it is relatively straightforward to check Chan & Geyer's conditions, their theorem does not lead to a consistent and easily…

前向搜索中的附加变量t检验与被掩盖异常值对模型选择的影响AI 解读

Monitoring the t‐tests for individual regression coefficients in ‘forward’ search fails to identify the importance of observations to the significance of the individual regressors. This failure is due to the ordering of the data by the search. We introduce an added‐variable test which has the desired properties since the projection leading to residuals destroys the effect of the ordering. An example illustrates the effect of several masked outliers on model selection.…

作为平滑器的鞍点近似AI 解读

This note investigates the sense in which saddlepoint approximations act as smoothers of discrete distributions. The discrete problem is embedded in a continuous model that closely matches it on the discrete sample space, with saddlepoint approximation yielding an inference that is almost exact for the continuous model. The same applies to conditional distributions. An example is given and implications for inference are discussed.

纵向数据估计方程方法中可忽略缺失的检验AI 解读

We address the matter of determining whether or not missing data in longitudinal studies are ignorable with regard to quasilikelihood or estimating equations approaches. This involves testing for whether or not the zero‐mean property of estimating equations holds true. Chen & Little (1999) proposed testing for significant differences among parameter estimators calculated from sample subsets with different patterns of missing data, whereas we propose a more unified…

计算机模型输出不确定性分布的贝叶斯推断AI 解读

We consider a problem of inference for the output of a computationally expensive computer model. We suppose that the model is to be used in a context where the values of one or more inputs are uncertain, so that the input configuration is a random variable. We require to make inference about the induced distribution of the output. This distribution is called the uncertainty distribution, and the general problem is known to users of computer models as uncertainty analysis. To…

通过条件矩方程渐近逼近后验分布AI 解读

We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow…

基于 M 估计的经验最优预测统一刀切理论AI 解读

The paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases. The paper develops jackknife theory for the important, but so far neglected, prediction problem for the general mixed model. For estimation of fixed parameters, a jackknife method is considered for a general class of M-estimators which includes the maximum likelihood, residual…

多元位置的投影估计AI 解读

In this paper we study the maximum asymptotic bias of the projection estimate for multivariate location based on univariate estimates of location and dispersion. In particular we study the projection estimate that uses the median and median absolute deviation about the median (MAD) as univariate location and dispersion estimates respectively. This estimator may be considered a natural affine equivariant multivariate median. For spherical distributions the maximum bias of…

约翰·W. 图基对稳健统计的贡献AI 解读

We summarize John W. Tukey's contributions to robust statistics, separating them into four categories: conceptual; tools; techniques; procedures.

John W. Tukey 对多重比较的贡献AI 解读

This article provides a historical overview of the philosophical, theoretical and practical contributions made by John Tukey to the field of simultaneous inference. His early work, culminating in the monograph "The Problem of Multiple Comparisons," established him as one of the pioneers in the field, investing it with both academic respectability and a focus on practical problems. For many years afterward, Tukey only published sporadically in the area but remained convinced…

Tukey中位数的影响函数与最大偏差AI 解读

Tukey's median is among one of the earliest known high breakdown point multivariate location statistics. Aside from its breakdown point, though, little else appears to be known about its robustness properties. In this paper we investigate other aspects of Tukey's median, and in particular we derive and study its influence function and its maximum contamination bias function. When judged by these other robustness criteria, Tukey's median again proves to be highly robust.

非正交不可观测成分模型中针对随机游走成分的最优检验AI 解读

In this paper we consider the problem of testing the null hypothesis that a series has a constant level (possibly as part of a more general deterministic mean) against the alternative that the level follows a random walk. This problem has previously been studied by, inter alia, Nyblom and Makelainen (1983) in the context of the orthogonal Gaussian random walk plus noise model. This model postulates that the noise component and the innovations to the random walk are…

条件异方差模型的残差诊断AI 解读

We examine the residual-based diagnostics for univariate and multivariate conditional heteroscedasticity models. The tests are based on the parameter estimates of an autoregression with the squared standardized residuals or the cross products of the standardized residuals as dependent variables. As the regression involves estimated regressors the standard distribution theories of the ordinary least squares estimates do not apply. We provide the asymptotic variance of the…

时变参数随机波动率均值模型的矩与动态结构AI 解读

This paper introduces and discusses some of the statistical properties of a time-varying parameter stochastic volatility (SV) in mean model. We derive the autocovariance function of an observed series, under the assumption that the conditional variance follows a flexible parameterization, which nests the autoregressive SV and the exponential GARCH specifications. Furthermore, the mean parameter can be time varying. We also present the autocovariance functions of higher…

仅在备择假设下存在干扰参数时的推断界AI 解读

In hypothesis testing with nuisance parameters present only under the alternative two issues typically arise: (i) critical values are data dependent and so cannot be tabulated; (ii) we need to choose a functional over the nuisance parameter space. We address the first issue by providing easily computable bounds for the case of dependent and heterogeneous observations. We tackle the second issue by suggesting a weighted average statistic with weights given by the (quasi)…

随机场方法的线性检验与似然推断准确性考察AI 解读

We analyze the random field regression model approach recently suggested by Hamilton (2001, Econometrica, 69, 537--73). We show through extensive simulation studies that although the random field approach is indeed very closely related to the non-parametric spline smoother it seems to offer several advantages over the latter. First, tests for neglected nonlinearity based on Hamilton's random field approach seem to be more powerful than existing test statistics developed…

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允许序约束与边际建模的扩展 RC 关联模型AI 解读

In the context of two-way contingency tables, the RC model may be seen as a way of modeling the set of log-odds ratios for adjacent 2 × 2 subtables through row and column scores. This article presents an extended class of RC models that allows simultaneous modeling of the marginal distributions and the association between two categorical variables; these components are parameterized with logits and log-odds ratios that may be of different types (e.g., global or continuation)…

排序集样本中的秩回归AI 解读

The use of statistical methods based on ranked-set sampling can lead to a substantial improvement over analog methods associated with simple random sampling schemes. This article develops a rank-based estimator and testing procedures for linear models for ranked-set samples. The estimator is defined as the minimizer of the rank dispersion function with Wilcoxon scores. It is shown that the estimator of the regression parameter is asymptotically normal and has higher Pitman…