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广义双线性回归AI 解读

This paper discusses the application of generalised linear methods to bilinear models by criss-cross regression. It proposes an extension to segmented bilinear models in which the expectation matrix is linked to a sum in which each segment has specified row and column covariance matrices as well as a coefficient parameter matrix that is specified only by its rank. This extension includes a variety of biadditive models including the generalised Tukey degree of freedom for…

随机回归中条件方差函数的有效估计AI 解读

Conditional heteroscedasticity has often been used in modelling and understanding the variability of statistical data. Under a general set-up which includes nonlinear time series models as a special case, we propose an efficient and adaptive method for estimating the conditional variance. The basic idea is to apply a local linear regression to the squared residuals. We demonstrate that, without knowing the regression function, we can estimate the conditional variance…

随机删失观测下两样本加性风险模型的拟合优度检验AI 解读

The additive risk model assumes that the hazard function associated with a set of covariates is the sum of the baseline hazard function and the regression function of covariates. We propose two different test procedures for checking the adequacy of two-sample additive risk models for randomly censored observations. One is based on the martingale residuals and the other on the difference between weighted estimators of the excess risk. The test statistics are shown to be…

事件历史分析的非参数乘法风险率模型AI 解读

A major issue in exploring and analyzing life history data with multiple states and events is the development and availability of flexible methods that allow simultaneous incorporation and estimation of baseline hazards, detection and modelling of nonlinear functional forms of covariates and time-varying effects, and the possibility to include time-dependent covariates. In this paper we consider a nonparametric multiplicative hazard model that takes into account these…

通过最小化密度幂散度实现稳健高效估计AI 解读

A minimum divergence estimation method is developed for robust parameter estimation. The proposed approach uses new density-based divergences which, unlike existing methods of this type such as minimum Hellinger distance estimation, avoid the use of nonparametric density estimation and associated complications such as bandwidth selection. The proposed class of ‘density power divergences’ is indexed by a single parameter α which controls the trade-off between robustness and…

作为拟合优度度量的经验似然AI 解读

The method of empirical likelihood can be viewed as one of allocating probabilities to an n-cell contingency table so as to minimise a goodness-of-fit criterion. It is shown that, when the Cressie-Read power-divergence statistic is used as the criterion, confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the Cressie-Read parameter λ, including − 1, maximum entropy, 0, empirical…

经验似然的功效与条件性性质评估AI 解读

Empirical and dual likelihood are two of a growing array of artificial or approximate likelihoods currently in use in statistics. A question of major interest focuses on the performance of these new constructs relative to ordinary parametric likelihoods. We consider here two criteria, local power and conditional properties. Looking at tests of a scalar parameter, we show that there is no loss of efficiency in using a dual or empirical likelihood model, to second order. To…

杂论：非线性问题中的序贯设计AI 解读

In this paper we study the consistency of parameter estimators in sequential nonlinear design. Our main tool is a recursion which holds for the sequence of posterior variances. Under mild conditions, we establish the strong consistency of Bayes estimators in stochastic regression models which cover a broad range of nonlinear problems. Four examples from nonlinear sequential design are discussed.

自相关有限总体的最优抽样设计AI 解读

In this paper, under Cochran's (1946) model we give a class of optimum sampling designs, in the exact and asymptotic cases, for estimating the finite population mean when the autocorrelation function in that model is convex. This class is a generalisation of Blight's (1973) sampling designs.

杂论：Matusita 距离的渐近分布及其在位置模型中的应用AI 解读

The extension of Mahalanobis's distance to the case of a mixture of discrete and continuousvariables is useful in many applications of discriminant analysis. In this note, the asymptotic chisquared distribution of the estimator of Matusita's distance under the null hypothesis is obtained and the rate of convergence is evaluated through simulations in the case of the location model.

杂记：非参数曲线估计中的设计变换与等数量分箱AI 解读

Methods based on design transformation and equal-number binning are shown to overcome problems of design sparseness, while retaining excellent theoretical properties. In company with local linear smoothing they produce optimal estimators, although with optirnality defined a little differently from in the nontransformed case. When used in conjunction with wavelet techniques they overcome problems of stochastic design, but, unlike related techniques based on convolution and…

杂记：参数冗余模型中的估计AI 解读

The likelihood surface resulting from a parameter-redundant stochastic model is maximised along a completely flat ridge. This ridge may be orthogonal to some parameter axes, so that these parameters have unique maximum likelihood estimates. For exponential-family models, we show how to determine which parameter combinations are estimable. The approach requires the calculation of a derivative matrix and the determination of its null space, both of which are readily achieved…

多元失效时间模型中异质性得分检验对遗漏协变量的不敏感性AI 解读

The multivariate Weibull distribution often provides a point of departure for modelling repeated, or a sequence of, failure times for a particular individual. It is then natural to want to test the implied assumption of homogeneity, and a number of authors have derived a score test for this purpose; see, for example, Kimber (1996). In the present paper it is shown that the proposed score test for neglected heterogeneity can be insensitive to specification error in the…

Neyman–Scott 模型与线样带调查中的聚集及丰度估计AI 解读

This paper considers the estimation of clustering parameters and mean species intensity based on likelihood theory for the simplified Neyman-Scott Poisson model, with observations taken from line transect surveys with a Gaussian detection function. The estimators and accompanying standard error expressions are tractable and easy to calculate, and, coming from likelihood methods, often will have high efficiency. Such properties compare favourably with those of existing…

小波中的多重收缩与子集选择AI 解读

This paper discusses Bayesian methods for multiple shrinkage estimation in wavelets. Wavelets are used in applications for data denoising, via shrinkage of the coefficients towards zero, and for data compression, by shrinkage and setting small coefficients to zero. We approach wavelet shrinkage by using Bayesian hierarchical models, assigning a positive prior probability to the wavelet coefficients king zero. The resulting estimator for the wavelet coefficients is a multiple…

渐近校准AI 解读

Can we forecast the probability of an arbitrary sequence of events happening so that the stated probability of an event happening is close to its empirical probability? We can view this prediction problem as a game played against Nature, where at the beginning of the game Nature picks a data sequence and the forecaster picks a forecasting algorithm. If the forecaster is not allowed to randomise, then Nature wins; there will always be data for which the forecaster does…

多变量 Probit 模型分析AI 解读

This paper provides a practical simulation-based Bayesian and non-Bayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods and maximum likelihood estimates are obtained by a Monte Carlo version of the EM algorithm. A practical approach for the computation of Bayes factors from the simulation output is also developed. The methods are applied to a dataset with a bivariate binary…

群组序贯试验置信区间的重抽样方法AI 解读

Resampling methods are introduced for the construction of confidence intervals for treatment effects associated with the primary and secondary endpoints of a clinical trial whose stopping rule is specified by a group sequential test. These methods are nonparametric and compare favourably with the exact methods that assume the responses to be normally distributed.

病例—对照家系研究数据的关联与家族聚集联合分析AI 解读

Genetic epidemiologists are increasingly interested in family studies using the casecontrol family study design, and this has motivated several recent developments in related statistical methodology. By summarising and extending some of these developments, this paper proposes an estimating-equation-based framework for analysing family data collected from case-control studies, motivated by the likelihood approach proposed by Whittemore (1995). The proposed estimating equation…

空间统计中的泊松／伽马随机场模型AI 解读

Doubly stochastic Bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models. Inhomogeneous gamma process random fields and, more generally, Markov random fields with infinitely divisible distributions are used to construct positively autocorrelated intensity measures for spatial Poisson point processes; these in turn are used to model the number and location of individual events.…

连续阈值自回归模型最小二乘估计量的极限性质AI 解读

The continuous threshold autoregressive model is a sub-class of the threshold autoregressive model subject to the requirement that the piece-wise linear autoregressive function be continuous everywhere. In contrast with the discontinuous case, it is shown that, under suitable regularity conditions, the conditional least squares estimator of the pararneters including the threshold parameter is root-n consistent and asymptotically normally distributed. The theory is…

修正剖面似然函数的一种近似AI 解读

An approximation to the modified profile likelihood function is proposed. This approximation is invariant under interest-respecting reparameterisations, it agrees with the modified profile likelihood function to order O(n−1) in the moderate-deviation sense and to order O(n−½) in the large-deviation sense, and it is stable in the sense of conditional inference. For the case of a curved exponential family model this approximation agrees with the one proposed by…

局部线性平滑的偏差降低AI 解读

The standard approach to local linear regression involves fitting a straight line segment to a curve in a symmetrical way, in that the segment is fitted directly above a small region whose midpoint is the abscissa, x, at which we wish to estimate the curve. In this paper we show that, if the segment is fitted in a skew manner, with its centre a little to the left or right of x, then bias can be reduced by an order of magnitude, without affecting the order of magnitude of…

Current status data arise when the only knowledge about the failure time of interest is whether the failure occurs before or after a random monitoring time. We propose to analyse such data by the semiparametric additive hazards model, which specifies that the hazard function for the failure time associated with a set of possibly time-dependent covariates is the sum of an arbitrary baseline hazard function and a regression function of covariates. Under certain conditions on…