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有效自由度与似然比检验AI 解读

Normal-theory problems involving several unknown variances may require use of estimates not having simple chi-squared distributions. Confidence intervals are then commonly based on the use of ‘effective degrees of freedom’, i.e. the fitting of a gamma distribution via the first two moments, replacing parameters by estimates. The confidence intervals given by this method are compared with those resulting from the likelihood ratio test, inserting a Bartlett adjustment factor…

关于删失与替代响应变量的一点讨论AI 解读

Summary Survival data are often subject to right censoring and to a consequent loss of information about the effect of explanatory variables. Sometimes it is possible to recover some of this lost information via a surrogate response variable measured on censored individuals and intended to predict the remaining life-time. This possibility is studied theoretically under idealized assumptions.

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Edgeworth 与鞍点近似及其统计应用AI 解读

Summary A simple exposition is given of Edgeworth and saddle-point approximations for some univariate, multivariate and conditional distributions. The application of these approximations to some problems of conditional statistical inference within the exponential family is illustrated. Examples connected with the time-dependent Poisson process, the von Mises distribution and with bioassay are among those studied in a little detail. Some general results are derived about…

稀少记录错误的抽样与估计AI 解读

For each individual in a finite population a recorded value is available. A small proportion of the values is in error, all the errors being of the same sign and the maximum fractional error being known. It is required to obtain an upper confidence limit for the total error in the population. Various solutions, including a Bayesian one, are discussed for sampling with probability proportional to the recorded values, and the appropriateness of this form of sampling is…

稀少记录误差的抽样与估计AI 解读

For each individual in a finite population a recorded value is available. A small proportion of the values is in error, all the errors being of the same sign and the maximum fractional error being known. It is required to obtain an upper confidence limit for the total error in the population. Various solutions, including a Bayesian one, are discussed for sampling with probability proportional to the recorded values, and the appropriateness of this form of sampling is…

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通过判别分析进行稳健回归AI 解读

For linear regression with grouped data, and with an equal number of observations per grouping point, linear discriminant analysis is applied to the ordered response variables to find that combination which shows strongest linear regression. After a modification to remove weights with an anomalous sign, there results a robust estimate of slope. Generalizations are outlined.

有限泊松过程经验贝叶斯推断札记AI 解读

A Poisson process of events is considered which terminates after a random time. Termination is not direotly observable but has to be inferred from the nonoccurrence of events. The analysis of data from such processes is considered with particular emphasis on empirical Bayes methods, it being supposed that data on many similar processes are available. An application to inventory control is outlined.

部分贝叶斯推断与线性模型的一则札记AI 解读

Some results are outlined for estimation in a replicated linear model in which the variance changes from cell to cell in accordance with an inverse gamma prior density. The primary parameters of the linear model are, however, treated as fixed unknown parameters. The analysis thus exemplifies the treatment of problems in which the nuisance parameters have a prior distribution but the parameters of primary interest do not.

偏似然AI 解读

A definition is given of partial likelihood generalizing the ideas of conditional and marginal likelihood. Applications include life tables and inference in stochastic processes. It is shown that the usual large-sample properties of maximum likelihood estimates and tests apply when partial likelihood is used.

随机终止泊松过程的经验贝叶斯推断札记AI 解读

A Poisson process of events is considered which terminates after a random time. Termination is not direotly observable but has to be inferred from the nonoccurrence of events. The analysis of data from such processes is considered with particular emphasis on empirical Bayes methods, it being supposed that data on many similar processes are available. An application to inventory control is outlined.

部分贝叶斯推断与线性模型札记AI 解读

Some results are outlined for estimation in a replicated linear model in which the variance changes from cell to cell in accordance with an inverse gamma prior density. The primary parameters of the linear model are, however, treated as fixed unknown parameters. The analysis thus exemplifies the treatment of problems in which the nuisance parameters have a prior distribution but the parameters of primary interest do not.

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回归模型与生命表AI 解读

Summary The analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations…

论由残差计算的检验统计量AI 解读

In an earlier paper the authors gave a general definition of residuals and derived some asymptotic properties. In the present paper the results are extended to study test statistics computed from residuals.

由残差计算的检验统计量AI 解读

In an earlier paper the authors gave a general definition of residuals and derived some asymptotic properties. In the present paper the results are extended to study test statistics computed from residuals.

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残差的一般定义AI 解读

Summary Residuals are usually defined in connection with linear models. Here a more general definition is given and some asymptotic properties found. Some illustrative examples are discussed, including a regression problem involving exponentially distributed errors and some problems concerning Poisson and binomially distributed observations.

关于最小二乘估计效率的一则札记AI 解读

Summary A linear model is considered in which errors are independent and identically distributed with zero mean. If the error distribution is specified, except possibly for unknown parameters, the asymptotic efficiency of least-squares estimates relative to maximum-likelihood estimates can be found. For regression parameters orthogonal to the general mean the asymptotic efficiency, which is independent of the design matrix, is calculated explicitly for an Edgeworth series,…

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