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使用加权似然 Bootstrap 的近似贝叶斯推断AI 解读

SUMMARY We introduce the weighted likelihood bootstrap (WLB) as a way to simulate approximately from a posterior distribution. This method is often easy to implement, requiring only an algorithm for calculating the maximum likelihood estimator, such as iteratively reweighted least squares. In the generic weighting scheme, the WLB is first order correct under quite general conditions. Inaccuracies can be removed by using the WLB as a source of samples in the…

剖面似然与定向似然的调整形式及扩展似然AI 解读

SUMMARY Several adjusted and invariant versions of profile likelihood and of directed likelihood (short for signed log-likelihood ratio) are discussed. These adjusted versions, which fall into two groups, are closely related to modified profile likelihood and modified directed likelihood. The first group has the advantage of not requiring an explicit specification of an ancillary, but partly at a cost of a loss of asymptotic accuracy in comparison with the modified versions.…

非线性估计方程的求解AI 解读

SUMMARY In this paper we consider the numerical computation of a vector parameter estimate θ^ which is a root of a system of unbiased non-linear estimation equations. A sequence {θ (r)} is constructed which converges with a probability approaching 1 to θ^ from any starting value θ (0). Unlike Newton-type algorithms, the θ (r) do not involve matrices of partial derivatives. Furthermore it can be shown that θ(r)−θ^ is of the order Op(n – r/2) so that great accuracy is achieved…

交叉设计中的方差估计AI 解读

SUMMARY There is concern that the usual analysis of crossover designs with more than two treatments is subject to bias due to correlations between the measurements on the same experimental units. It has been shown by Kunert in the special case of balanced Latin squares that this bias can be present but that it is limited. Extending the work of Kunert we show in the present paper that there is a constant X* which guarantees that the estimate for the variance of any treatment…

近似非高斯贝叶斯估计与众数一致性AI 解读

SUMMARY A new recursive estimation procedure is proposed for the location of a dynamic linear model with non-normal errors. The procedure is a modification of a modal approximation algorithm, which is shown to be prone to instabilities. The modification is motivated by a notion of posterior modal consistency.

负值概率更低的改进方差分量估计量AI 解读

SUMMARY A linear model with two variance components is considered, one variance component (say, σ 1 2 ≥ 0) corresponding to a random effect, and a second variance component (say, σ 2 > 0) corresponding to the experimental errors. A class of invariant quadratic estimators (IQEs) is characterized, having uniformly smaller mean-squared error (MSE), and uniformly smaller probability of negativity, compared with the analysis-of-variance (ANOVA) estimator of σ 1 2. It turns out…

时间序列分析的高崩溃点方法AI 解读

SUMMARY A robust form of the discrete Fourier transform is developed that can handle large amounts of contamination and patchy outliers. We use robust regression to fit a sine and cosine coefficient at each Fourier frequency, and these coefficients are then inverse Fourier transformed to give a filtered version of the data. The filtered series can then be analysed with conventional methods. The limiting breakdown bound of the filter is 50%. Other properties of the filter are…

异方差 G 最优设计AI 解读

SUMMARY This paper addresses the issue of constructing large sample G-optimal designs when the variability of the response varies across a compact design space. A useful characterization theorem is presented along with a computer algorithm for generating (heteroscedastic) G-optimal designs. to facilitate comparisons between D- and G-optimal designs, Atwood's inequality for comparing D- and G-efficiencies in homoscedastic models is generalized to heteroscedastic models. Some…

时间序列的稳健似然计算AI 解读

SUMMARY We propose a computationally efficient method for calculating the likelihoods of a time series under many submodels, each of which assumes a patch of outliers or level shifts. We assume a state space representation of the time series model with a Bayesian-type treatment of anomalies. The calculations form the basis for an efficient and robust estimation procedure. The method is also applicable to linear regression with correlated errors and is illustrated with two…

通过最大稳定过程进行极端暴风雨的区域建模AI 解读

SUMMARY Asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena. Most such phenomena have a spatial dimension, and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events. A principal objective in the analysis—as with other current research on extremes—is to base inference on as much of the available data as possible. The…

非参数曲线估计中的Edgeworth展开与Bootstrap置信带AI 解读

SUMMARY The notion of pivoting and techniques of Edgeworth expansion have become basic tools for using and understanding bootstrap methods in finite parameter problems. This paper shows that these ideas have important contributions to make to infinite parameter problems, e.g. in the construction of simultaneous confidence bands for nonparametric density estimators. We propose a bootstrap method for confidence band construction based on a pivotal function estimator and…

带宽限制下的一致估计AI 解读

SUMMARY Ion channels are molecular structures embedded in cell membranes which selectively allow ions to cross the membranes. The electrical activity of ion channels has been successfully described by a finite state space semi-Markov process. In this model, some of these states are closed and do not permit any ions to flow through the channel. The remaining states are open and permit ions to cross with a fixed conductance, producing a fixed measurable current across the cell…

Gibbs 采样、Metropolis 算法及其他单点更新动力学的收敛速率AI 解读

SUMMARY Sampling from a Markov random field II can be performed efficiently via Monta Carlo methods by simulating a Markov chain that converges weakly to II. We consider a class of local updating dynamics that are reversible with respect to II. It includes the Metropolis algorithm (MA) and the Gibbs sampler (GS). We investigate the speed of weak convergence of these Markov chains in terms of their second-largest eigenvalues in absolute value. We study the general algebraic…

复合假设拟合优度检验的样本间距统计量大样本理论AI 解读

SUMMARY Let X 1,…, Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Often we would like to test a null hypothesis concerning the goodness of fit of F to some distribution function which is fully specified or belongs to some parametric family, i.e. in some applications the null hypothesis is simple whereas in others it may be composite. In this paper we present the large…

利用条件分布刻画联合概率分布AI 解读

SUMMARY We derive conditions under which a set of conditional and marginal probability distributions will uniquely specify an all-positive joint distribution. Our theoretical result may yield insights into the construction and simulation of multivariate probability models.

块独立性、球形性及方差协方差相等检验的鞍点近似AI 解读

SUMMARY Approximations for the null distribution of various test statistics arising in multivariate analysis using Skovgaard's saddlepoint formula are discussed. In each case an approximation is found with such accuracy as to obviate the need for exact computation.

含不可忽略无应答的调查数据对数线性模型AI 解读

SUMMARY We demonstrate the feasibility of constructing, interpreting and fitting computable log-linear models to categorical survey data with arbitrary non-nested patterns of non-ignorable non-response. Under our approach, the non-response probability for each cell of the classification defined by the categories of interest is modelled separately from the classification probability itself, and we adopt a model formulation which allows the non-response model to depend on…

非参数回归中的异方差检测AI 解读

SUMMARY Diagnostic tests and plots are proposed for detecting heteroscedasticity in nonparametric regression. The large and small sample power properties are studied for a class of test statistics for the hypothesis of homogeneous variances. New diagnostic plots are also developed and illustrated.

非线性回归模型中的参数随机变动检验AI 解读

SUMMARY This paper addresses the problem of testing for purely random parameter variation in nonlinear regression models. Based on different approximations to the true density of the data, score-type tests are constructed and their asymptotic distributions are derived. The local power of the tests is investigated both theoretically and via Monte Carlo simulation. An empirical testing example, involving a well-known non-linear aggregate demand for money function, is also…

非线性回归中调整剖面似然的一则札记AI 解读

SUMMARY The problem of partial non-linear regression is used to provide an example of McCullagh and Tibshirani's profile likelihood adjustment for more than one parameter of interest, where for one linear nuisance parameter an expression for the adjusted profile likelihood can be derived.

复杂模型建模：Gibbs 抽样在医学中的应用AI 解读

SUMMARY We review applications of Gibbs sampling in medicine, involving longitudinal, spatial, covariate measurement and survival models. Applications in immunology, pharmacology, transplantation, cancer screening, industrial epidemiology and genetic epidemiology are discussed.

空间统计与贝叶斯计算AI 解读

SUMMARY Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recently, the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a Markov random field has opened the way to the use of…

SUMMARY The use of the Gibbs sampler for Bayesian computation is reviewed and illustrated in the context of some canonical examples. Other Markov chain Monte Carlo simulation methods are also briefly described, and comments are made on the advantages of sample-based approaches for Bayesian inference summaries.

似然比统计量带符号根的简易修正AI 解读

SUMMARY In the context of inference about a scalar parameter in the presence of nuisance parameters, some simple modifications for the signed root of the log-likelihood ratio statistic R are developed that reduce the order of error in the standard normal approximation to the distribution of R from O(n -1/2) to O(n -1). Barndorff-Nielsen has introduced a variable U such that the error in the standard normal approximation to the distribution of R + R -1 log(U/R) is of order…