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平移原点三参数模型中区间删失数据的最大似然估计存在性AI 解读

SUMMARY Given data in the form of interval-censored observations from a three-parameter distribution, practical criteria are established for the existence of maximum likelihood estimates for three kinds of parameter space. These criteria can be derived by analysing the behaviour of the log-likelihood near a type of boundary of the parameter space, called the probability contents inner boundary. The effectiveness of the criteria is discussed. In the case where the underlying…

无需固定模型集上界的自回归阶数递归估计AI 解读

SUMMARY In a recent paper, we proved that Rissanen's 'predictive least squares' (PLS) criterion for model selection provides strongly consistent order estimates for autoregressive (AR) processes, i.e. the PLS order estimate p̂(n) based on the first n data points converges almost surely to p 0 as n → ∞ when the data are generated by an AR process of order p 0, and p 0 is known to belong to the finite model set M = {1, 2, ..., K}, K < ∞. In the present paper we strengthen this…

构造准确参数经验贝叶斯置信区间的样本再利用方法AI 解读

SUMMARY Parametric empirical Bayes (EB) methods of point estimation for a vector of unknown parameters date to the landmark paper of James and Stein (1961). The usual approach is to use the mean of the estimated posterior distribution of each parameter, where the estimation of the prior parameters (‘hyperparameters’) is accomplished through the marginal distribution of the data. While point estimates computed this way usually perform well, interval estimates based on the…

一致鞍点近似与对数凹密度AI 解读

SUMMARY For a one-dimensional variable with a log-concave density it is shown that the saddlepoint approximations to the density and the distribution function of the mean are uniformly valid. A double-saddlepoint approximation to a conditional distribution function is introduced, which is uniformly valid for a two-dimensional log-concave density. The results are illustrated with the log-normal distribution and the gamma distribution.

污染分布部分已知时的 ε 污染稳健贝叶斯分析AI 解读

SUMMARY Prior distributions of the form π=(1−ϵ)π0+ϵq,π0 being the base elicited prior, q being contamination and ϵ reflecting the amount of error in π0 that is deemed possible, are considered. It is assumed that π0 is completely specified and that only some quantiles of q are known. As π varies over this class, the ranges of the posterior mean and of the posterior probabilities of an arbitrary set are determined. Some examples including hypotheses testing related to a…

后验贝叶斯因子AI 解读

SUMMARY A general procedure for computing Bayes factors for the comparison of arbitrary models is described, based on the use of the posterior mean of the likelihood under each model rather than the usual prior mean. The use of the posterior mean has several advantages, including reduced sensitivity to variations in the prior and the avoidance of the Lindley paradox in testing point null hypotheses. The frequency properties of the new procedure are evaluated in standard…

曲线数据均值与协方差结构的非参数估计AI 解读

SUMMARY We develop methods for the analysis of a collection of curves which are stochastically modelled as independent realizations of a random function with an unknown mean and covariance structure. We propose a method of estimating the mean function non-parametrically under the assumption that it is smooth. We suggest a variant on the usual form of cross-validation for choosing the degree of smoothing to be employed. This method of cross-validation, which consists of…

具有时间序列误差的核回归估计AI 解读

SUMMARY Suppose that data y 1, ..., yn are observed according to the model yi=f((i−12)/n)+ϵi,i=1,…,n, where f is a smooth function and {ϵ1,…,ϵn} is a sample from a zero-mean, covariance stationary time series. The problem of objectively choosing the bandwidth of a kernel estimate for f is addressed. It is shown both theoretically and by simulation that cross-validation produces extremely rough kernel estimates when the data are sufficiently positively correlated. This makes…

似然与预序参照框架下的费舍尔推断AI 解读

SUMMARY In celebration of the centenary of the birth of Sir Ronald Fisher, this paper explores Fisher's conception of statistical inference, with special attention to the importance he placed on choosing an appropriate frame of reference to define the inferential model. In particular, we investigate inferential models which respect the likelihood principle or the prequential principle, and argue that these will typically have an asymptotic sampling theory justification.

门限自回归似然比检验的临界值AI 解读

SUMMARY Likelihood ratio tests for threshold autoregression have been considered by Chan, and Chan and Tong. However, except for the simplest case, percentage points of the (asymptotic) null distribution of the test statistic have not been tabulated. The purpose of this paper is to tabulate the approximate upper percentage points for the general case. This is done via the Poisson clumping heuristic developed by Aldous. Monte Carlo experiments show that the approximation is…

家族数据中多元类间与类内相关指标的推断AI 解读

SUMMARY Multivariate measures of interclass and intraclass correlations are introduced to assess the degree of resemblance between family members with respect to more than one characteristic. Unified estimators for the multivariate measures are proposed as the eigenvalues of certain random matrices constructed by the matrices of the weighted sums of squares and products of observations. Asymptotic distributions of the proposed estimators are derived under the assumption of…

具有两个重复的行列设计构造札记AI 解读

SUMMARY This paper shows that useful designs for variety trials with two replicates, each arranged in a compact array of plots, can be derived from existing row-and-column designs for two non-interacting sets of treatments. Combinatorial and statistical properties are preserved; in particular, if the original design is efficient, then so is the new design.

广义线性模型中的偏误校正AI 解读

SUMMARY In this paper we derive general formulae for first-order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias-corrected maximum likelihood estimates to order n −1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is…

一个似然悖论AI 解读

SUMMARY The Fraser–Monette–Ng example, strengthened by Joshi, is simplified and further strengthened. The claim by Joshi that it gives a counter-example to the likelihood principle, and that this counter-example also covers the case of a finite parameter space, is disputed.

贝叶斯与非贝叶斯区间估计之间的关系AI 解读

SUMMARY Let Y 1, ..., Y n denote independent observations each distributed according to a density depending on a scalar parameter θ. Suppose that we are interested in constructing an interval estimate for 0. One approach is to construct a confidence region with a specified coverage probability based on the likelihood ratio test statistic. Another approach is to construct a highest posterior density region with a specified posterior probability. The goal of this paper is to…

光滑迭代程序的一步Bootstrap方法AI 解读

SUMMARY Resampling techniques have the potential to provide useful information about the sampling distribution of estimators of many population characteristics. Ambitious schemes such as the bootstrap and iterated bootstrap imply a substantial increase in computational effort. For some iterative procedures, such as generalized least squares or the EM algorithm, it is possible to avoid fully iterating each bootstrap replication to convergence. By analysing expansions of the…

Logistic 测量误差模型的半参数估计AI 解读

SUMMARY We describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors. The particular measurement error model consists of a primary data set in which only the response Y and a fallible surrogate W of the true predictor X are observed, plus a smaller validation data set for which (Y, X, W) are observed. Except for the underlying assumption of a logistic model in the true predictor, no parametric distributional…

核密度估计的一种可靠数据驱动带宽选择方法AI 解读

SUMMARY We present a new method for data-based selection of the bandwidth in kernel density estimation which has excellent properties. It improves on a recent procedure of Park and Marron (which itself is a good method) in various ways. First, the new method has superior theoretical performance; second, it also has a computational advantage; third, the new method has reliably good performance for smooth densities in simulations, performance that is second to none in the…

作为路径积分的似然与成本AI 解读

SUMMARY We consider the optimal estimation, prediction and control etc. of time series. The essence of a path integral characterization is considered to be that optimal estimates and decisions etc. are obtained by the free extremization of some form. In Sections 2–5 it is shown for some stock situations that this property is ensured by the direct maximization of likelihood (rather than by appeal to the formally equivalent but operationally contrasting least square…

两样本位置问题的二元符号秩检验AI 解读

SUMMARY A signed rank affine invariant test for the difference in location between two elliptically symmetric populations is proposed. Asymptotic properties of the test are developed under the null hypothesis and under contiguous alternatives. The proposed statistic is compared with three of its competitors using Monte Carlo studies and Pitman asymptotic relative efficiencies. It is seen that the signed rank statistic introduced is especially powerful when the underlying…

平移幂变换模型的分组似然AI 解读

SUMMARY Estimation of parameters is considered in the shifted power transformation family of models. The ordinary likelihood function is shown to behave poorly, often having no local maximum. It is argued that a grouped likelihood approach avoids these difficulties, and the practical implementation of this approach is considered. Bayesian inference is also considered, though more briefly, and it is argued that there are again difficulties with an ungrouped likelihood…

简单线性回归中基于变换二次距离的最小距离方法AI 解读

SUMMARY Minimum distance estimators and test statistics based on quadratic distances for transforms are introduced in simple linear regression models. Asymptotic properties of quadratic distance estimators and tests for the error distributions are derived. The modified quadratic distance estimator is shown to be efficient provided that the error distribution is symmetric and the derivative of the logarithm of the error density is a linear combination of the transforms.

非参数回归中的最优局部带宽选择AI 解读

SUMMARY Kernel estimators of a regression function are investigated. The bandwidths are locally chosen by a data-driven method based on the minimization of a local cross-validation criterion. This method is shown to be asymptotically optimal with respect to local quadratic measures of errors. Monte Carlo experiments are presented, and finally the method is applied to some data of medical interest.

通过再杠杆调整构造异方差线性模型的可靠置信区间AI 解读

SUMMARY Under heteroscedasticity, ordinary least squares regression can fail to yield adequate inference on parameter coefficients with respect to hypothesis testing or confidence intervals. For example, confidence intervals can have coverage well below that claimed. This is especially the case in small or moderate-sized imbalanced samples and holds even if the ordinary least squares variance estimator is replaced by a robust-against-heteroscedasticity variance estimator. A…