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平均剩余寿命回归模型中的估计AI 解读

SUMMARY The proportional mean residual life model was originally proposed by Oakes and Dasu. This model can be extended to a regression model with explanatory variables. We consider the problem of estimation of the regression parameter in this general model. We investigate two types of estimator, of which one is based on the maximum likelihood equation of the exponential regression model, and the other is based on the underlying proportional hazards structure of the model…

用时间序列交叉验证自动平滑依赖数据AI 解读

SUMMARY The problem of selecting the bandwidth of a kernel regression estimator when the observed data are serially correlated is considered. The bandwidth is selected by using a version of cross-validation that seeks a good one-step-ahead predictor of the data. This method, referred to as time series cross-validation (TSCV), simultaneously estimates an optimal bandwidth and, given a time series model for the errors, the autocorrelation function of the data. In addition,…

贝叶斯模型选择：渐近分析与精确计算AI 解读

SUMMARY Model determination is a fundamental data analytic task. Here we consider the problem of choosing among a finite (without loss of generality we assume two) set of models. After briefly reviewing classical and Bayesian model choice strategies we present a general predictive density which includes all proposed Bayesian approaches that we are aware of. Using Laplace approximations we can conveniently assess and compare the asymptotic behaviour of these approaches.…

多元样本离群值检测方法的一项修正AI 解读

SUMMARY We modify a method for identifying outliers in multivariate samples proposed by Hadi. A simulation study shows that this modification controls the size of the test, leads to substantially improved power and is more effective in dealing with the masking and swamping problems.

鸟类环志回收模型中的边界估计AI 解读

SUMMARY A simple model for avian survival often leads to boundary estimates when the model is fitted to data by maximum likelihood. Data may result from ring recovery experiments alone, or in combination with a radio tracking investigation. A study of profile likelihoods enables the conditions under which boundary estimates occur to be completely specified. Fitting an incorrect model is shown to result in inconsistent estimators of all parameters, and an asymptotic certainty…

Gibbs 采样器的几何收敛AI 解读

SUMMARY The rate of convergence of the Gibbs sampler is discussed. The Gibbs sampler is a Monte Carlo simulation method with extensive application to computational issues in the Bayesian paradigm. Conditions for the geometric rate of convergence of the algorithm for discrete and continuous parameter spaces are derived, and an illustrative exponential family example is given.

位置参数的非参数条件推断AI 解读

SUMMARY Let Y 1, ..., Yn denote independent observations of the form Yj = θ + σεj where ε 1, ..., εn are independent random variables each distributed according to a density p, and θ and σ are unknown parameters. This paper presents a method for conditional inference about the location parameter θ that does not require the specification of a parametric family of densities for p. This method uses the configuration statistic to select the density p and is based on the work of…

通过 EM 算法获得的最大惩罚似然估计的方差AI 解读

SUMMARY We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The solution proposed represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed by Meng and Rubin that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping…

圆周数据的时间序列分析AI 解读

SUMMARY The paper considers the problem of modelling and analysing a time series of measurements which take the form of unit two-dimensional vectors. Several general classes of existing and new models are studied in terms of feasibility and flexibility. An approach is recommended which uses two of these classes, and which takes advantage of several standard time series algorithms that are available in modern software packages. An application is given to the analysis of a…

多元 M 估计量的经验鞍点近似AI 解读

SUMMARY In this paper, we investigate the use of the empirical distribution function in place of the underlying distribution function F to construct an empirical saddlepoint approximation to the density fn of a general multivariate M-estimator. We obtain an explicit form for the error term in the approximation, investigate the effect of renormalizing the estimator, carry out some numerical comparisons and discuss the regression problem.

复 Bingham 分布与形状分析AI 解读

SUMMARY A complex version of the Bingham distribution is defined on the unit complex sphere in Ck. Various statistical properties, including asymptotic normality under high concentration, are derived. Symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions. Strengths and weaknesses of this approach are investigated. Links and contrasts with Bookstein co-ordinates are discussed. A hybrid approach to principal…

通过贝叶斯抽样估计有限混合分布AI 解读

SUMMARY A formal Bayesian analysis of a mixture model usually leads to intractable calculations, since the posterior distribution takes into account all the partitions of the sample. We present approximation methods which evaluate the posterior distribution and Bayes estimators by Gibbs sampling, relying on the missing data structure of the mixture model. The data augmentation method is shown to converge geometrically, since a duality principle transfers properties from the…

圆周拟合优度检验的分组修正AI 解读

SUMMARY Simple corrections are outlined for the application to grouped seasonal data of Watson's and Maag's tests. These tests are circular or seasonal analogues of one-sample and k- (≥2) sample tests, of Cramér–von Mises type, and have several natural advantages over their competitors. The provision of simple grouping corrections may enhance the use of these tests, which otherwise have very good features. The corresponding grouping corrections are also presented for…

蒙特卡洛最大似然计算的收敛性AI 解读

SUMMARY Monte Carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models. Given any family {hθ: θ ∈ θ} of non-negative integrable functions, maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by Monte Carlo simulation, the only regularity conditions being a compactification of the parameter space such that the evaluation maps θ → hθ(x) remain…

基于失效源遮蔽的系统寿命试验数据估计部件寿命AI 解读

SUMMARY In this paper we study the model of masked data sets, i.e. data sets consisting of failure times of a system and sets of failed components. Failing components can yield further failures. The initially failed component is unknown. Initial failures and later failures are indistinguishable. A nonparametric estimator of the component lifetime distribution is derived. We prove weak convergence of the estimator to a Gaussian process.

仿射不变的多元多样本符号检验AI 解读

SUMMARY Invariant sign-type tests for the multivariate, multisample location models are developed. The definition of sign is based on the Oja criterion function. Emphasis is on the two-sample location model and the associated equivariant estimate of shift. Asymptotic theory is developed to provide large sample approximations for the null distribution of the test and to provide a framework for a discussion of efficiency. Tests are then developed for the one-way and two-way…

仿射不变的多元单样本符号检验AI 解读

SUMMARY Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies…

SUMMARY When εi = yi – x′i β, it is known that minimizing ΣΣ|εi – εj| yields an estimate of regression that attains a bounded influence of the residual with 95% efficiency for the normal distribution. We show that introducing weights ΣΣbij|εi – εj| achieves bounded total influence with positive breakdown. Mallows weights in particular are optimally efficient under a predefined bound on the gross error sensitivity. A generalization of Mallows weights allows additional local…

ARMA 模型递归估计的稳健方法AI 解读

SUMMARY In this paper we consider the problem of fitting, recursively in time, an autoregressive moving average (ARMA) model to time series data where outliers may be present. Although many recursive estimation procedures are available for fitting ARMA models, they are based on the recursive least squares algorithm which is known to be badly affected by additive outliers. to minimize the impact of these sort of outliers we investigate some robustified versions of the…

调整似然与条件似然：功效性质及Bartlett型调整AI 解读

SUMMARY Under contiguous alternatives the adjusted likelihood ratio (ALR) test is seen to have the same power properties as the conditional likelihood ratio test up to the third order of comparison. In particular, an optimum property of the ALR test in terms of second-order local maximinity follows. It is also seen that the ALR statistic admits a Bartlett-type adjustment.

不规则采样时间序列的连续时间自回归模型参数化AI 解读

SUMMARY An increasingly valuable tool for modelling irregularly sampled time series data is the continuous time autoregressive model. The natural parameters in this model are the coefficients of the linear stochastic differential equation describing the process which gives rise to the data. A transformation of these parameters is introduced, based on the Cayley–Hamilton transformation. The new parameter space is identical with that of discrete time autoregressive models. The…

通过有效分形维数估计刻画表面平滑度AI 解读

SUMMARY The fractal dimension D of stationary Gaussian surfaces may be expressed very simply in terms of behaviour of the covariance function near the origin. Indeed, only the covariance of line transect samples is required, and that fact makes practical estimation of D relatively straightforward. The case of non-Gaussian surfaces is more poorly understood, but we might define ‘effective fractal dimension’ in terms of the covariance function, as though the surface were…

区间删失与截断观测下分布函数非参数估计的说明AI 解读

SUMMARY This paper is concerned with the nonparametric estimation of the distribution function F from interval-censored and truncated data as discussed by Turnbull. It is observed that Turnbull's characterization of F̂, the maximum likelihood estimator of F, is not applicable in general when the data are interval censored and truncated. It is shown, however, that Turnbull's characterization can be easily modified to obtain the appropriate characterization of F̂.

广义混合模型中的估计AI 解读

SUMMARY Regression models containing fixed and random effects may have a response variable which is not normally distributed. The generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model. Best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures. Applications in modelling discrete…