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多重保序回归问题的检验AI 解读

A new procedure for testing the homogeneity of normal mean vectors versus order restricted alternatives is proposed and its performance discussed.

调查抽样中渐近设计无偏的预测量AI 解读

A probability sampling plan is suggested in this paper for drawing the sample so that the linear least-squares predictor of the total of a finite population is made asymptotically design-unbiased. Conditions are given for the sampling plan to reduce to the more familiar sample designs discussed in the literature.

状态空间模型的似然AI 解读

This paper derives an expression for the likelihood for a state space model. The expression can be evaluated with the Kalman filter initialized at a starting state estimate of zero and associated estimation error covariance matrix of zero. Adjustment for initial conditions can be made after filtering. Accordingly, initial conditions can be modelled without filtering implications. In particular initial conditions can be modelled as ‘diffuse’. The connection between the…

二项参数估计量的损失估计AI 解读

A loss function is introduced, which combines the estimation error of a statistical procedure with a measure of its accuracy. The properties of this loss function are illustrated by the estimator of a binomial parameter. The choice of a conjugate prior distribution is discussed from this point of view. It is shown that there exists a unique beta prior with a conservatively biased accuracy estimate.

比较异方差回归的保守检验与置信域AI 解读

The problem of comparing two regression planes without the assumption of equal variances is considered. A natural analogue of the Behrens-Fisher statistic is proposed and its distribution bounded in terms of the studentized maximum and minimum chi-squared distributions. The results are used to construct conservative tests and confidence regions for comparing the regression parameters. Numerical comparisons with more specialized bounds due to Hsu (1938), Hájek (1962) and…

大量小样本中的序列相关检验AI 解读

Methods are outlined for testing for serial correlation in large numbers of small samples, emphasis being placed on samples of size three. Some data on pulse rates are analysed in illustration.

多参数函数的似然置信区间AI 解读

Methods described first by Madansky (1965) and revived more recently by Cox & Oakes (1984, pp. 51–2) are extended to incorporate the calculation of likelihood-based confidence intervals for functions of many parameters. Examples involving failure time data are used to illustrate the techniques.

封闭序贯检验后估计的改进近似AI 解读

Siegmund (1978) has developed a procedure for estimation following a closed sequential test, known as the repeated significance tests. Here a more elaborate approximation is proposed for a wider class of closed sequential tests. The major goal is to account for the excess over boundary in addition to the stopping time when the sequential test is terminated. Some hypothetical examples are used for comparing the two approximations. To investigate the properties of these…

利用再捕获抽样估计总体规模AI 解读

A design called recapture debugging is proposed to get extra information to estimate the original number of faults, N, in a reliability system. The system is observed for a fixed amount of time τ and the failures are assumed to follow an exponential law with an unknown common parameter λ. The maximum likelihood and moment estimators of N and λ are derived and compared with the existing estimators. The recapture sampling provides substantially more information and improved…

两阶段病例对照数据的 Logistic 回归AI 解读

Samples of diseased cases and nondiseased controls are drawn at random from the population at risk. After classification according to the exposure of interest, subsamples of cases and controls are selected for purposes of covariable ascertainment. A modification of the usual logistic regression analysis yields consistent estimates of covariable adjusted relative risks and their standard errors. By balancing the numbers of exposed and nonexposed for whom covariable…

误分类下子群均值估计的新方法AI 解读

This paper considers the estimation of the subgroup means of a response variable when the individuals in a random sample are allocated to the subgroups or classes by a fallible device. A double sampling scheme under which we determine also the true classes of the individuals in a subsample is utilized. A simple distributional-free estimator is proposed and the associated large-sample properties are also derived. The proposed estimator is also demonstrated by simulation…

不等概率抽样下分布函数与中位数的估计AI 解读

We consider sampling with probability proportional to size or aggregate size and derive a number of estimators of the finite population distribution function. The estimators are compared theoretically and empirically. By inverting the distribution function estimators, we obtain estimators of the finite population median. The performance of these median estimators are investigated.

生物测定效价曲线的线性贝叶斯估计AI 解读

The prior distribution on the class of potency curves in quantal bioassay is assumed to be Ferguson's Dirichlet distribution. Given integrated squared error loss and quantal response data, we derive the Bayes estimator in a linear space generated by the data. Some numerical examples and asymptotic results are also given.

方差分量估计的最优设计AI 解读

The design problem for the estimation of variance components by the method of unweighted squares of means, under a multifactor random effects model, is considered. First it is shown that with the numbers of levels of the factors fixed, a balanced design, if it exists, is optimal. Next the numbers of levels are also treated as decision variables and the derivation of minimax designs is indicated.

随机临床试验中无处理效应的检验AI 解读

We propose a test of the null hypothesis of no treatment effect in a randomized clinical trial that is based on the randomization distribution of residuals. These residuals result from regressing the response on covariates, but not treatment. In contrast to model-based score tests, this procedure maintains nominal size when the model is misspecified, and, in particular, when relevant covariates are omitted from the regression. The efficiency of the procedure is evaluated for…

非标准条件下非正则广义最大似然估计的渐近行为AI 解读

In this paper we generalize Huber's (1967) results to include the nonregular case. Resistant estimators which turn out to be asymptotically unbiased in a neighbourhood of the model are given for some univariate models. Their order of consistency achieves the rate of the maximum likelihood estimates. Moreover, some of the estimates are asymptotically efficient under the central model, in the sense that they have the same asymptotic distribution as the maximum likelihood…

用 Edgeworth 级数表示密度的条件AI 解读

The conditions for the correct approximation of a density by the truncated Edgeworth series for a random variable given in a finite interval are found. These conditions restrict the values of skewness and kurtosis to achieve a positive approximating function.

有限封闭总体规模的精确极大似然估计札记AI 解读

Using data obtained by the general capture-recapture sequential sampling process, an analytical expression for the maximum likelihood estimate of the population size is introduced. It is shown that the bounded likelihood functions have at most two maxima. For the simple one-to-one case the estimate is unique.

协变量随测量变化的重复测量设计分析AI 解读

A model proposed by Patel (1986) is re-examined. It is shown that the model can be written as seemingly unrelated regressions and estimation can be carried out simply. Estimation under constraints given by the general linear hypothesis is also discussed and a two-stage procedure proposed. Connexions with seemingly unrelated regressions with constraints between the regression parameters and the sum of profiles model of Verbyla & Venables (1988) are also given.

非高斯平稳时间序列的时间可逆性与移动平均表示唯一性AI 解读

A recent result by Findley (1986) on the uniqueness of moving average representations for non-Gaussian time series is shown to establish a conjecture by Weiss (1975) on the time-reversibility of general linear processes.

指数族响应下的试验设计札记AI 解读

Some simple design problems are considered when responses have an exponential family distribution with the difference between ‘treatment’ groups in the canonical parameter being the objective of study. It is shown that normal theory conclusions apply to a possibly surprising extent. The loss from randomizing followed by subsequent stratification is the equivalent of one observation per stratum. For binary data heterogeneity has to be quite large before failure to stratify…

比例风险回归中协变量形式误设造成的效率损失AI 解读

This note considers partial likelihood score tests for association between a covariate process and survival time based on a proportional hazards regression model. We derive the asymptotic efficiency of the test based on a misspecified form of the covariate process relative to the test based on the correct form. The results can be used to assess the consequences of various types of misspecification.

利用专家判断估计稀有误差AI 解读

Cox & Snell (1979) investigate inference about the total population error when most observations are zero. Their approach is parametric and assumes that errors are positive. Empirical evidence indicates, however, that negative errors are not uncommon and that the error distribution is unlikely to be modelled by any standard parametric distribution. We propose a more general nonparametric approach that uses Ferguson's Dirichlet process. Our model allows the investigator to…

估计总体与词汇规模的多项分布贝叶斯方法AI 解读

We approach estimation of the size of a population or a vocabulary through a Bayesian analysis of the multinomial distribution. We view the sample as being generated from such a distribution with an unknown number of cells and unknown cell probabilities, and develop a Bayesian procedure to estimate the number of cells and the coverage of the sample. The prior distribution of the number of cells is arbitrary. Given that number, the cell probabilities are assumed to follow a…