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稳定且具不变性的调整定向似然AI 解读

SUMMARY For the purpose of making inferences for a one-dimensional interest parameter, or constructing approximate complementary ancillaries or residuals, the directed likelihood or signed square root of the likelihood ratio statistic can be adjusted so that the resulting modified directed likelihood is under ordinary repeated sampling approximately standard normal with error of O(n-312), conditional on a suitable ancillary statistic and hence unconditionally. In general,…

最大化熵的有限总体加权抽样AI 解读

Attention is drawn to a method of sampling a finite population of N units with unequal probabilities and without replacement. The method was originally proposed by Stern & Cover (1989) as a model for lotteries. The method can be characterized as maximizing entropy given coverage probabilities πi, or equivalently as having the probability of a selected sample proportional to the product of a set of ‘weights’ wi. We show the essential uniqueness of the wi given the πi. We…

区间删失数据的最大似然：一致性与计算AI 解读

Standard convex optimization techniques are applied to the analysis of interval censored data. These methods provide easily verifiable conditions for the self-consistent estimator proposed by Turnbull (1976) to be a maximum likelihood estimator and for checking whether the maximum likelihood estimate is unique. A sufficient condition is given for the almost sure convergence of the maximum likelihood estimator to the true underlying distribution function.

扫描统计量检测伯努利序列变化区段的功效AI 解读

Fu & Curnow (1990) derive recursive equations to find the level of significance and power of a likelihood ratio test for a changed segment of specified length, based on the scan statistic, the maximum number of successes within the specified length. Their method is computationally feasible for segment lengths of 20 or less. We present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for…

重新审视连续多元位置—尺度模型的稳健性AI 解读

We consider the location-scale family of all multivariate continuous sampling distributions. Any model from the subclass induced by fixing a particular distribution on the unit sphere, combined with a standard improper prior on the scale parameter, will lead to the same inference on location and observables. This finding sheds light on many robustness results in less general models and its implications are illustrated in a number of examples.

平稳与部分非平稳 VARMA 过程精确似然的快速算法AI 解读

An expression for the likelihood function of a stationary vector autoregressive-moving average process is developed. The expression is very efficient numerically and applies to any stationary but not necessarily invertible model. In particular, when the multivariate process is autoregressive, the exact likelihood can be evaluated with a small number of operations depending on the order of the autoregressive operator and the process dimension, but not on the size of the…

状态空间模型的吉布斯抽样AI 解读

We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our…

将疾病进展信息纳入生存分析的核方法AI 解读

This paper considers incorporating information on disease progression in the analysis of survival. A three-state model is assumed, with the distribution of each transition estimated separately. The distribution of survival following progression can depend on the time of progression. Kernel methods are used to give consistent estimators under general forms of dependence. The estimators for the individual transitions are then combined into an overall estimator of the survival…

基于加权残差的比例风险检验与诊断AI 解读

SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp { fl(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function /3(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher…

正态不完整数据的一类模式混合模型AI 解读

Likelihood-based methods are developed for analyzing a random sample on two continuous variables when values of one of the variables are missing. Normal maximum likelihood estimates when values are missing completely at random were derived by Anderson (1957). They are also maximum likelihood providing the missing-data mechanism is ignorable, in Rubin's (1976) sense that the mechanism depends only on observed data. A new class of pattern-mixture models (Little, 1993) is…

大分层Logistic回归中的加权平方最小中位数估计AI 解读

One aim of robust regression is to find estimators with high finite sample breakdown points. Although various robust estimators have been proposed in logistic regression models, their breakdown points are not yet known. Here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point, provided the estimator has to fulfill a weak condition. In logistic regression models with large strata however, a…

交叉相关建模：双曲正割回归AI 解读

The problem of determining if a bivariate normal correlation changes with respect to time or some other covariate is considered. It is assumed that the means and standard deviations of the normal random variables can be consistently estimated from the entire data run, and do not need to be re-estimated for each covariate value. A new estimator of a bivariate normal correlation is given that has useful performance down to samples of size one. This allows regression type…

离散时间生存数据的动态建模与惩罚似然估计AI 解读

This paper describes a dynamic or state-space approach for analyzing discrete time or grouped survival data. Simultaneous estimation of baseline hazard functions and of time-varying covariate effects is based on maximization of posterior densities or, equivalently, a penalized likelihood, leading to Kalman-type smoothing algorithms. Data-driven choice of unknown smoothing parameters is possible via an EM-type procedure. The methods are illustrated by applications to real…

再捕获研究中鞅方法的效率AI 解读

The asymptotic variances of various estimators of the population size from a recapture study are calculated. The estimation methods compared are maximum likelihood and a class of natural martingale estimators with both time variation and behavioural response. It is found that (i) the martingale methods appropriate for time variation or behavioural response are fully efficient, (ii) there is no loss of efficiency at all in allowing for time variation, (iii) there is large…

HIV 感染者中感染诊断率的估计AI 解读

Estimation of the rate of diagnosis of HIV infection in a population of HIV infected persons is considered based on AIDS case reports and associated times of first diagnosis of HIV infection. The incorporation of a model for HIV infection diagnosis into the usual backcalculation framework is described. The methods are illustrated for AIDS reports on homosexual men in England and Wales.

指数模型的多参数检验：基于似然的三阶近似AI 解读

For composite testing of several canonical components in an exponential model, a conical or directional test provides a one-dimensional measure of departure. We approximate the distribution of this test statistic to third order by numerical inversion of a profile likelihood. The method extends the Lugannani & Rice type formula to kernels other than the normal.

图像数据离散薄板平滑样条的快速计算AI 解读

This paper describes a fast method of computation for a discretized version of the thin-plate spline for image data. This method uses the Discrete Cosine Transform and is contrasted with a similar approach based on the Discrete Fourier Transform. The two methods are similar from the point of view of speed, but the errors introduced near the edge of the image by use of the Discrete Fourier Transform are significantly reduced when the Discrete Cosine Transform is used. This is…

椭圆轮廓误差下的贝叶斯卡尔曼滤波AI 解读

SUMMARY The basic recursive equations of the Kalman filter, for independent normally distributed error sources in both the observation and the system equations, are shown to hold for a larger class of distributions. It is shown that, for error sources following jointly a general elliptical distribution, the conditional posterior distribution of the parameters and the one-step ahead predictive distribution at every stage t are also elliptical. This generalizes some recent…

偏态分布下温莎化均值的统计性质AI 解读

Sampling properties of estimators of the mean of a positive random variable that Winsorize the largest or the two largest observations in the sample are investigated. Exact and approximate expressions for the mean squared errors of these estimators are derived. Optimal Winsorization schemes are obtained for various skewed distributions. Efficiency comparisons between the sample mean and Winsorized means are presented for several families of skewed distributions. A nearly…

配对数据尺度差异的简单稳健检验AI 解读

The classical statistical test for assessing the difference between the two scale parameters in paired data due to Pitman (1939) and Morgan (1939) is not robust. This paper explores robust alternatives to Pitman's test, using the framework of the one-sample t-test. The asymptotic behaviour of the tests under the null hypothesis is examined. In general, it is easy to construct tests that are asymptotically distribution-free, provided the data come from a symmetric bivariate…

适用于相依数据的交叉验证方法AI 解读

In this paper we extend the technique of cross-validation to the case where observations form a general stationary sequence. We call it h-block cross-validation, because the idea is to reduce the training set by removing the h observations preceding and following the observation in the test set. We propose taking h to be a fixed fraction of the sample size, and we add a term to our h-block cross-validated estimate to compensate for the underuse of the sample. The advantages…

基于枢轴估计函数的重抽样方法AI 解读

SUMMARY Suppose that, under a semiparametric model setting, one is interested in drawing inferences about a finite-dimensi onal parameter vector /? based on an estimating function. Generally a consistent point estimator /J for /?0, the true value for /J, can be easily obtained by finding a root of the corresponding estimating equation. To estimate the variance of ft, however, may involve complicated and subjective nonparametric functional estimates. In this paper, a general…

Monte Carlo 近似与迭代自助法AI 解读

We discuss optimal choice of the numbers of resamples in the two stages of the iterated bootstrap, when that technique is used to calibrate bootstrap confidence intervals. If the numbers of resamples in the first and second stages are denoted by B and C respectively, we show that it is optimal to take C to be approximately a constant multiple of B½. The value of the constant is derived, and shown to depend only on the nominal coverage level of a confidence interval. However,…

基于中位生存时间的期中分析AI 解读

For a typical two-arm survival study, analyses are usually performed periodically to evaluate, for example, the treatment difference. In this paper, we propose to use differences or ratios of estimated median survival times repeatedly during a study to evaluate the relative merit of two treatment groups. This new procedure provides quantitative assessments of the treatment difference and is completely model-free. Our method is illustrated with a recent aids clinical study…