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非正则问题中的修正最大似然法AI 解读

SUMMARY Maximum likelihood (ML) estimation can break down for distributions like the three-parameter Weibull or gamma where one of the parameters is a limit of the range of the distribution. It is suggested that use of the product of densities for the likelihood function is a misapplication of the ML method in such non-regular cases, and that this is the reason for its failure. It is shown that ML works quite satisfactorily if the likelihood is corrected in an appropriate…

Bootstrap 与连续性校正AI 解读

SUMMARY A continuity correction to the bootstrap is suggested, useful when the bootstrap is employed to approximate distributions of lattice-valued sample means. Versions of the correction are available quite generally, even in multivariate cases. Asymptotic theory reveals that the correction can reduce maximum rounding error by up to 50%. An example, where continuity correction is used in the construction of confidence intervals, illustrates the performance of the procedure…

单阶段抽样中平衡半样本方差估计量的若干预测性质AI 解读

SUMMARY The balanced half-sample (BHS) method of variance estimation is a widely used technique in complex sample surveys. Large-sample prediction properties of the BHS method are given here for the separate ratio and regression estimators. Results are obtained when a large number of units are sampled and divided into two groups within each stratum. An empirical study examines the conditional and unconditional performance of the BHS method when estimating mean squared errors…

利用秩估计回归参数AI 解读

SUMMARY In this paper we consider the estimation of a regression parameter in a partially specified model where, after an unknown monotone increasing transformation, the response is normally distributed and related to an explanatory variable by a linear model. We consider a Monte Carlo resampling technique due to Doksum and various modifications of it. In addition a simple estimate based on a modification of Fisher and Yates' normal scores method and an estimate using the…

具有二维可交换观测的两样本问题AI 解读

SUMMARY In comparing two groups of subjects, suppose that each subject has two observations which are probabilistically exchangeable. Univariate rank tests which utilize this symmetry property are proposed for testing the equality of the two groups. Efficiencies of these tests are discussed. Point and interval estimators of the location shift parameter are obtained through the proposed rank tests. Examples are also provided to illustrate the proposed procedures.

参数正交性与近似条件推断AI 解读

SUMMARY We consider inference for a scalar parameter Ψ in the presence of one or more nuisance parameters. The nuisance parameters are required to be orthogonal to the parameter of interest, and the construction and interpretation of orthogonalized parameters is discussed in some detail. For purposes of inference we propose a likelihood ratio statistic constructed from the conditional distribution of the observations, given maximum likelihood estimates for the nuisance…

椭圆分布误差下因子分析的峰度调整AI 解读

SUMMARY Simple corrections to normal theory tests of fit of the factor analysis model are provided for the situation where common factors have arbitrary distributions and errors have a distribution from the elliptical class. It is shown that normal theory estimators are asymptotically efficient in this situation and appropriate modifications for the asymptotic covariance matrix of estimators are provided. Factor analysis models with structured error covariance matrices are…

单调随机场的紧性AI 解读

SUMMARY For monotone random fields (e.g. gradients of convex functions) pointwise convergence implies uniform convergence on bounded subsets. This result was used in Brown (1985) but an incorrect proof was given. We give a new proof.

基于偏差函数的 M 估计量的一致性AI 解读

SUMMARY In a general estimation problem, the deviance function generates statistics that are similar to squared standardized residuals. A deviance-based M estimator (DBME) is defined as an adaptively weighted maximum-likelihood estimator, where the weights depend upon the deviances. In both a single-parameter and a regression setting, we give some general conditions under which a DMBE is consistent. For a suitable weighting scheme, these conditions are satisfied in many…

平稳过程谱密度的最小对比估计AI 解读

SUMMARY Let {z(n)} be a stationary process with mean zero and true spectral density g(λ). In this paper we approximate g(λ) by a parametric family f θ(λ) and propose a minimum contrast estimator θ^ which minimizes D(fθ,g^N)=∫−ππK{fθ(λ)/g^N(λ)}dλ with respect to θ, where K(.) is an appropriate function and ĝ N(λ) is a nonparametric spectral estimator of g(λ). We give the asymptotic distribution of θ^ and sufficient conditions such that θ^ is asymptotically efficient. Also, we…

关于混合模型假设检验中 Aitkin–Rubin 方法的札记AI 解读

SUMMARY In testing for the number of components in a mixture, it is well known that regularity conditions do not hold for minus twice the log likelihood ratio to have its usual asymptotic null distribution of chi-squared. In an attempt to overcome some of the problems, it has been proposed in the literature that a prior distribution be placed on the mixing proportions. We show here that the usual regularity conditions still do not hold.

液体化学动力学的统计模型AI 解读

SUMMARY Statistical methods are used increasingly in theoretical chemistry. Applications range from the use of stochastic relaxation techniques in determining minimum energy molecular configurations to dynamical Monte Carlo simulations of molecular motion in liquids. This paper focuses on diffusion-controlled reactions in radiation chemistry. Here the interest is in describing the evolution of isolated clusters, containing a few chemically active particles, resulting from…

通过紧凑编码进行估计与推断AI 解读

SUMMARY The systematic variation within a set of data, as represented by a usual statistical model, may be used to encode the data in a more compact form than would be possible if they were considered to be purely random. The encoded form has two parts. The first states the inferred estimates of the unknown parameters in the model, the second states the data using an optimal code based on the data probability distribution implied by those parameter estimates. Choosing the…

SUMMARY It is argued that all the useful information in observed data that can be extracted with a selected class of modeled distributions, will be obtained if we calculate the stochastic complexity, defined to be the shortest description length of the data. The same quantity also determines the greatest lower bound for prediction errors when the data are sequentially predicted. An abstract definition of stochastic complexity is given along with two fundamental theorems…

再论随机过程的后验渐近正态性AI 解读

SUMMARY The problem of demonstrating the limiting normality of a posterior distribution arising from some stochastic process is revisited. It is shown that certain processes of practical interest are not covered by conditions currently available in the literature. In this paper we present a fairly general set of conditions for asymptotic posterior normality which cover a wide class of problems. The theory is applied to a nonhomogeneous Poisson process and birth process.

Galton–Watson过程的后验渐近正态性与估计量渐近正态性AI 解读

SUMMARY For a Galton-Watson process with offspring distribution pθ, where θ is an unknown parameter, asymptotic posterior normality is established for θ and for the mean of the offspring distribution. A form of asymptotic normality for the mean of the offspring distribution is also obtained, without restriction on whether the process is supercritical or not, provided that the total number of offspring increases to infinity. A non-Bayesian procedure is suggested for testing…

精度、复杂度与贝叶斯模型确定AI 解读

SUMMARY In this paper a new criterion for model determination is proposed. An explicit decision theoretic approach to model selection is employed to derive a Bayes decision rule. The operational characteristics of the criterion are discussed and consistency is shown.

回归问题中平滑参数选择技术的共同结构AI 解读

SUMMARY Two general methods have been used for choosing the degree of smoothing in both linear ridge-regression and nonparametric regression. One is based on a criterion of minimum risk and the other is based on a measure of fit to the data as summarised by a statistic based on the residuals. The comparative effects of these two approaches are investigated and one popular version of the second method is shown to oversmooth quite drastically. The work also generates…

回归预测值的交叉验证收缩AI 解读

SUMMARY Copas (1983) suggests that shrinkage of predictors can be related to the least squares slope of actual on predicted values in a new set of data. Considering multiple regression in a crossvalidatory setting, this shrinkage slope is approximated by an estimable function of the fitted residuals. Patterns of heteroscedasticity of residual variance can lead to more, or less, shrinkage of least squares. A new predictor using a nonparametric shrinkage multiplier is proposed.

风险率与强度函数的惩罚似然估计AI 解读

SUMMARY A nonparametric estimate is proposed for the hazard function using penalized likelihood methods. The estimate turns out to be a hyperbolic spline function which is continuous with its first derivative discontinuous only at a finite number of points. It always assumes positive values, unlike Anderson and Senthilselvan’s (1980) quadratic spline estimate. This method is modified for the estimation of the intensity function of a nonstationary Poisson process. An example…

切比雪夫多项式逼近与特征函数估计AI 解读

SUMMARY A new procedure for estimating characteristic functions based on a Chebyshev polynomial expansion for the density of the Cosine is developed. Simulation results confirm the usefulness of the method. It is applied to the estimation of two stochastic process models for daily stock returns. The Press compound events model is also estimated by maximum likelihood methods. Results are suggestive of the adequacy of the compound events model and the vg model (a variant of…

指数离散模型AI 解读

SUMMARY We study general properties of the class of exponential dispersion models, which is the multivariate generalization of the error distribution of Nelder and Wedderburn’s (1972) generalized linear models. Since any given moment generating function generates an exponential dispersion model, there exists a multitude of exponential dispersion models, and some new examples are introduced. General results on convolution and asymptotic normality of exponential dispersion…

正交级数密度估计量的收敛速率AI 解读

SUMMARY We derive a lower bound to the rate of convergence of nonparametric density estimators on compact sets, and show that it is achieved by estimators based on orthogonal series. Unlike earlier work on this type of problem, the bound depends on the size of Fourier coefficients rather than explicitly on smoothness assumptions.

非高斯状态空间模型及其纪录预测应用AI 解读

SUMMARY We develop a class of state space models for censored data. The basic model assumes an exponential distribution for the observations, conditionally on unobserved state variables. The model may be generalised by allowing transformations. We develop an application to the prediction of records. This is illustrated with some athletics data, though we also discuss briefly the possibility of more general applications connected with extreme values.