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由稳定分布构造的异质人群生存模型AI 解读

A new three-parameter family of distributions on the positive numbers is proposed. It includes the stable distributions on the positive numbers, the gamma, the degenerate and the inverse Gaussian distributions. The family is characterized by the Laplace transform, from which moments, convolutions, infinite divisibility, unimodality and other properties are derived. The density is complicated, but a simple saddlepoint approximation is provided. Weibull and Gompertz…

动物致癌实验中肿瘤发生时间分布的估计AI 解读

In most survival-sacrifice experiments for the detection and quantification of risks from chronic exposure to chemical agents, the onset of the condition of interest is not clinically observable. Cancer is typically such an event. In this paper, an approximate maximum likelihood method is proposed for parametric estimation of the distribution of unobservable tumour onset times in the presence of competing risks, when cause-of-death information is unavailable.

非嵌套假设检验的内在结构AI 解读

A comparison between fitted and observed log likelihoods is used to study likelihood ratio statistics for both nested and nonnested hypothesis tests. A study of the geometry involved in the nonnested case clarifies the relationship between Cox's likelihood ratio test and the complete parametric Wald encompassing test of Mizon and Richard. Further it is shown why the asymptotic distribution of these test statistics is sometimes degenerate. Also, a new test statistic is…

季节性移动平均模型的快速滤波AI 解读

Pearlman (1980) gives a fast filtering algorithm for an ARMA, i.e. autoregressive-moving average, model. When the algorithm is applied to a seasonal moving average model significant computational savings can be obtained by taking advantage of the structural zeros noted by Kohn & Ansley (1984) and Melard (1984). In this paper we identify a second set of structural zeros which leads to further significant computational savings. Our results can be applied to produce a fast…

非高斯平稳时间序列的独立同分布创新移动平均表示的唯一性AI 解读

Full-spectrum, non-Gaussian stationary series can have at most one representation as a moving average of independent and identically distributed random variables having finite moments of all orders.

寿命回归模型札记AI 解读

Lifetime regression models that are additive in some transform of either the survivor function or quantile function are considered. Graphical assessment and connections between the two families are discussed.

时间序列的非线性检验AI 解读

This paper considers two nonlinearity tests for stationary time series. The idea of Tukey's one degree of freedom for nonadditivity test is generalized to the time series setting. The case of concurrent nonlinearity is discussed in detail. Simulation results show that the proposed tests are more powerful than that of Keenan (1985).

异方差一阶自回归模型的得分检验AI 解读

A score test is proposed for simultaneous testing of independence and homoscedasticity in the first-order autoregressive model with nonconstant variance. The relationships between the score test statistic and the local influence of minor perturbations on a statistical model are examined.

若干序列结构方差矩阵的分解AI 解读

Serially-structured variance matrices which can be decomposed into lower-triangular band matrices are defined. These may be thought of as the variance matrices of finite realizations of generalized autoregressive-moving average processes. A large number of serially-generated stochastic processes are shown to be of this type.

离散判别分析中核密度估计的另一种平滑参数选择AI 解读

The kernel method of estimating the cell probabilities of a multivariate categorical distribution, due to Aitchison & Aitken (1976), depends crucially on an unknown smoothing parameter λ. A method of estimating A is introduced which is explicitly connected to multivariate discrimination. The method, based on maximization of the leaving-one-out estimator of the nonerror rate, is shown to be Bayes risk strongly consistent. An example is given to illustrate the application.

部分删失数据的半马尔可夫模型札记AI 解读

A recharacterization of the semi-Markov model described by Lagakos, Sommer & Zelen (1978) permits the nonparametric maximum likelihood estimators to be expressed in terms of familiar and easily computable quantities, such as event-specific hazard estimators and Kaplan & Meier (1958) survival estimators. In addition to simplifying the calculation and clarifying the interpretation of the previously derived estimators, this reformulation also facilitates the estimation of…

误设的比例风险模型AI 解读

The properties of an estimator based on a proportional hazards model are investigated when the model is incorrect. The estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly. The results are used to investigate the effects on estimation if the true model is accelerated failure time, or if covariates are omitted from the proportional hazards model.

二元生存数据关联模型中的半参数推断AI 解读

Clayton's (1978) model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem, that is a problem where inference about a parameter is required in the presence of nuisance functions. We derive the asymptotic variance of Clayton's estimator, obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random…

基于信息增益的正态模型与指数模型依赖度量AI 解读

The principle of obtaining a measure of dependence based on the notion of information gain is examined for normal models and for several bivariate exponential models. It is shown that, under normal models, the principle usually gives good measures. It is also shown that it gives interesting measures for some exponential models.

近似预测似然AI 解读

A predictive likelihood is given which approximates both Bayes and maximum likelihood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n–2), and from exact predictive likelihood by Op(n–2) but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot…

基于标准化有符号对数似然比的全部或部分参数推断AI 解读

For parametric models it is shown in general that by adjusting the mean and variance of the signed log likelihood ratio for a single parameter of interest ψ one obtains a statistic which is asymptotically standard normally distributed to order O(n–23) , under repeated sampling. This statistic may also be used as an ancillary in the associated problem of drawing inference on the complementary parameter χ for known value of ψ in which case it entails accuracy to the same order…

指数族独立随机变量序列的变点检验与置信区域AI 解读

SUMMARY Maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables, with particular emphasis on the exponential distribution. The exact null and alternative distributions of the test statistics are found, and the power is compared with a test based on a linear trend statistic. Exact and approximate confidence regions for the change-point are based on the values accepted by a level x likelihood ratio test and a…

利用先验信息的自助法AI 解读

Bayesian analysis is subject to the same kinds of misspeciflcation problems which motivate the robustness and nonparametric literature. We present a method of incorporating prior information which performs well without direct knowledge of the error distribution. This is accomplished by replacing the likelihood in Bayes's formula by a bootstrap estimate of the sampling density of a robust estimator. The flexibility of the method is illustrated by examples, and its performance…

密度估计的贝叶斯方法AI 解读

Assume a priori that the log density is a sample function from a Gaussian process subject to the condition that the density integrates to one. The posterior distribution given a number of observations is then still a Gaussian process with the same condition and the same covariance function. The mean value function is changed according to a simple formula. This prior may thus be regarded as a conjugate prior for an unknown density. The mode of the posterior distribution is…

非线性回归中参数子集的置信区域AI 解读

SUMMARY Confidence regions for some of the parameters in nonlinear regression models are often based on the large sample distribution of the least squares estimator, or equivalently a linear approximation to the model. These regions have a simple ellipsoidal shape but their nominal level is often misleading. Confidence regions based on the likelihood ratio and on the scores are examined and geometric interpretations are given. A simple method of approximating both types of…

利用迭代广义最小二乘分析多层混合线性模型AI 解读

Models for the analysis of hierarchically structured data are discussed. An iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case. There is a discussion of applications to complex surveys, longitudinal data, and estimation in multivariate models with missing responses. An example is given using educational data.

协方差分析中的随机化AI 解读

When examining any linear contrast of adjusted treatment means in the analysis of covariance it is shown that balancing on the covariates is desirable in that it minimizes the model variance of the treatment contrast averaged over the randomization distribution. Approximate balancing, through truncation of the randomization distri bution, is examined empirically. It is shown empirically that robustness of the test statistic can be achieved through truncated randomization.…

用于处理与对照比较的渐近最优平衡处理不完全区组设计子类AI 解读

Incomplete block designs for estimation of treatment-control differences are studied. A class of designs for this purpose, called balanced treatment incomplete block designs, has recently been proposed and studied by several authors. Here, a relatively small subclass of these designs is shown to contain the asymptotically optimal design under the criterion of minimizing the length of simultaneous confidence intervals for treatment-control differences. These results can be…

作为拟合优度检验工具的累积卡方统计量AI 解读

The cumulative chi-squared statistic in the one-way analysis of variance model is characterized as the weighted sum of independent one degree of freedom chi-squared random variables, which are linear, quadratic, and so on, components in the sense of Čebyšev's orthogonal polynomials for finite points. This suggests that the cumulative chi-squared should be an appropriate goodness-of-fit test statistic for a hypothesized model against a systematic departure that is mainly but…