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啮齿动物致瘤实验的效率稳健得分检验AI 解读

The standard statistical test for assessing adverse effects in rodent tumourigenicity experiments is based on a time-adjusted analysis of lethal and incidental tumours. This test is shown to arise as the sum of two score statistics for fatal and incidental lesions respectively, the former optimal against extreme value hazard alternatives and the latter optimal against logistic prevalence alternatives in terms of asymptotic relative efficiency in the Pitman sense. An…

小样本中的回归与时间序列模型选择AI 解读

A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better…

形状数据的统计分析AI 解读

The paper deals with the statistical shape analysis of landmark data. Bookstein (1986) introduced a plausible model and obtained a useful normal approximation for three landmarks. We use exact distribution theory and a normal approximation to consider maximum likelihood estimation. The Fisher information matrix for the normal approximation is given and we consider the hypothesis of shape change. Using these results, we analyse a practical example based on digitized shapes.…

偏差残差与正态分数图AI 解读

We discuss the use of normal order statistics plots, based on deviance residuals, to check distributional assumptions in regression models. Continuous and discrete error distributions are considered, as are censored data. Misspecified error distributions and discrimination between competing models are discussed, with an example.

指数族非线性模型的改进似然比统计量AI 解读

This paper gives a general formula for the expected likelihood ratio statistic for exponential family nonlinear models, corrected up to order n−1, where n is the sample size. This result generalizes previous work by Cordeiro (1983). Various general Bartlett adjustment formulae are given to some special models and improved likelihood ratio tests are discussed.

状态空间模型中信号提取、影响诊断与交叉验证的快速算法AI 解读

A fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model. The resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector. The ideas of studentized residuals and leverage from regression analysis are generalized to state space models, and the new algorithm is used to compute the various measures. The results are also…

偏群时延的估计AI 解读

The partial group delay between two channels of a multiple time series has an interpretation as the time lag between frequency components of the two channels after adjustments have been made for the influence of the remaining channels. A procedure for estimating partial group delay is proposed, and conditions for consistency and asymptotic normality of the estimating sequence are obtained.

Durbin–Watson 检验的三次样条扩展AI 解读

We propose a new test for model misspecification in linear regression, based on a measure of ‘smoothness’ of the regression residuals. This ‘curvature statistic’ is related to a property of cubic splines and leads to a convenient, powerful test for patterns. The distribution of the curvature statistic may be derived from assumptions of normality. For equally spaced data, the calculations are simplified and a table of significance points of the distribution is given.…

带随机干扰参数的信号估计AI 解读

We describe two models in which n records of a signal in white noise are taken. In the first model the signal parameters of interest do not change between records, but the amplitude varies in a random way. In the second model, the location is the random nuisance parameter. We describe an efficient estimator for the first model. For the second model an estimator is described which is n½ consistent, invariant to the distribution of the location and efficient for a particular…

平稳时间序列上叠加单调趋势的一致检测AI 解读

Consider a time series made up of a signal and a stationary autocorrelated error series. A statistic is proposed for examining the hypothesis that the signal term is constant versus the hypothesis that it is monotonic in time. The statistic is the ratio of a linear combination of the time series values, with coefficients introduced by Abelson & Tukey (1963), to an estimate of the standard error of the linear combination. The statistic has asymptotic power 1 for a broad class…

局部最强序贯 t 检验的一个候选方案AI 解读

A sequential t test is presented based on a simple function of the usual student t statistic. This function is shown to possess the martingale property that, conditional on previous observations, the expectation of a future increment is zero. This property facilitates calculation of error probabilities and expected sample sizes, so that the resulting test is relatively straightforward to use. It is argued that this test behaves in a manner similar to that of the locally most…

两个变量均有测量误差时简单线性回归的似然估计AI 解读

Likelihood based methods for obtaining approximate confidence intervals for the slope in a simple linear regression when both variables are measured with error are discussed and compared. We also derive a Bartlett correction factor for the likelihood ratio statistic. The improvement of the chi-squared approximation is appreciable in the unknown variance case. Further, the distribution of the maximum likelihood slope estimator is obtained from the joint distribution of sample…

捕获实验的统计分析AI 解读

A procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture-recapture data when it is possible to model the capture probabilities of individuals in the population using covariates. The results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size. Confidence intervals for…

利用多个小样本估计非对称密度AI 解读

A method for estimation of the measurement error probability density from three or more measurements on each of several dissimilar items is presented. Differences between measurements on the same item provide estimates of the densities of the first and second differences between error realizations. The relations between these densities and the error density, expressed in terms of characteristic functions and Hermite function expansions, are the basis for a nonlinear…

典型变量分析中的置信区域AI 解读

It is argued that confidence circles as traditionally drawn on canonical variate diagrams are incorrect, because no allowance is made in their construction for the sampling variability of the canonical variate axes. A series of approximations is employed to obtain tractable expressions for the correct regions. Despite the rather broad approximations involved, empirical assessment via bootstrapping shows the new regions to have much more accurate probability content than the…

指数回归模型分析中使用非正常先验的几点讨论AI 解读

We consider Bayesian inference on the exponential regression model. It is known that standard improper priors on the parameters of this model lead to marginal posterior distributions on one of the parameters involved which are also improper on the interval (0, 1). This has sometimes been interpreted as meaning that the observations are irrelevant. We re-analyse this problem using a finitely-additive approach and show that the above conclusion is not generally correct. This…

移动平均误差下的单位根检验AI 解读

In this paper we propose a new approach to testing for unit roots in a time series {yt} with moving average innovations based on an instrumental variable estimator. If {yt} is a random walk with moving average innovations, we derive the limiting distribution of the instrumental variable estimator when the estimated model is either (i) the true model, (ii) a random walk with shift in mean, or (iii) a random walk with shift in mean and a linear time trend. These distributions…

若干系数恒定性检验统计量的分布AI 解读

This paper investigates the distribution of the locally best invariant test for coefficient constancy, against the random walk alternative, in a regression model which may contain nonvarying coefficients. Unfortunately, the distribution of the locally best invariant test depends critically on the exogenous variables of the model, even asymptotically. A modification is suggested which has a known asymptotic distribution regardless of the regression effect.

变量含测量误差模型中的稳健估计AI 解读

Orthogonal regression analogues of M estimates of regression, called here orthogonal regression M estimates, are defined. These estimates are shown to be consistent at elliptical errors-in-variables models and robust, if the corresponding loss function is bounded. The orthogonal regression analogues of regression scale estimates, called here orthogonal regression S estimates, are considered as well. In particular, they provide a robust estimate for the scale of the…

病例队列设计的替代方差与效率计算AI 解读

We define a bootstrap sampling plan for the case-cohort design and present bootstrap variance estimates and confidence intervals for the log relative hazard. The coverages of these confidence intervals are found to be near nominal levels in simulations. A simple null variance calculation, based on a superpopulation model, is shown to provide good estimates of the power and efficiency of the case-cohort design.

非参数回归在模型检验中的应用AI 解读

The use of nonparametric regression is explored to check the fit of a parametric regression model. The principal aim is to check the validity of the regression curve rather than necessarily to detect outliers. A pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model. The types of data considered include discrete response variables, where standard diagnostic techniques…

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非高斯时间序列的相位滞后估计AI 解读

An important problem in the physical sciences is estimation of the innovations of a noninvertible linear process. Here the problem of deconvolving such a time series containing a phase-lead is investigated. A compensating phase-lag filter is sought, and is estimated by maximization of a chosen statistic or projection index. It is demonstrated by simulation that a statistic which is superior to another in the ideal case of a full-band time series can be substantially inferior…