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重新考察误差自相关的简单线性回归AI 解读

This paper studies properties of ordinary and generalised least squares estimators in a simple linear regression with stationary autocorrelated errors. Explicit expressions for the variances of the regression parameter estimators are derived for some common time series autocorrelation structures, including a first‐order autoregression and general moving averages. Applications of the results include confidence intervals and an example where the variance of the trend slope…

边际密度之间的相容性AI 解读

In the Lancaster representation a joint density is decomposed into a sum of additive interactions. Using these interactions, we derive conditions for checking compatibility among a collection of marginal densities. The representation also shows how to construct an all‐positive joint density additively from a given set of compatible marginals. An algorithm is proposed for reducing the dimension of the marginal densities so that compatibility can be checked in sequential…

提升核密度估计：一种偏差缩减技术？AI 解读

This paper proposes an algorithm for boosting kernel density estimates. We show that boosting is closely linked to a previously proposed method of bias reduction and indicate how it should enjoy similar properties. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research.

利用家庭数据估计遗传关联参数AI 解读

We consider the problem of estimating a parameter θ reflecting association between a disease and genotypes of a genetic polymorphism, using nuclear family data. In many applications, some parental genotypes are missing, and the distribution of these genotypes is unknown. Since misspecification of this distribution can bias estimators for θ, we consider estimating functions that are unbiased, regardless of how the distribution is specified. We call the resulting estimators…

谱密度的广义似然比检验AI 解读

There are few techniques available for testing whether or not a family of parametric times series models fits a set of data reasonably well without serious restrictions on the forms of alternative models. In this paper, we consider generalised likelihood ratio tests of whether or not the spectral density function of a stationary time series admits certain parametric forms. We propose a bias correction method for the generalised likelihood ratio test of Fan et al. (2001). In…

聚类与纵向数据非参数回归中平滑样条的等价核AI 解读

For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within‐cluster correlation. We show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly…

区分嵌套回归模型的序贯与非序贯设计比较AI 解读

SUMMARY Classical regression analysis is usually performed in two steps. In a first step an appro priate model is identified to describe the data-generating process and in a second step statistical inference is performed in the identified model. In this paper we investigate a sequential and a non-sequential design strategy, which take into account these different goals of the analysis for a class of nested models. It is demonstrated that non-sequential designs usually…

病例对照研究贝叶斯分析中前瞻与回顾模型的等价性AI 解读

The natural likelihood to use for a case‐control study is a ‘retrospective’ likelihood, i.e. a likelihood based on the probability of exposure given disease status. Prentice & Pyke (1979) showed that, when a logistic regression form is assumed for the probability of disease given exposure, the maximum likelihood estimators and asymptotic covariance matrix of the log odds ratios obtained from the retrospective likelihood are the same as those obtained from the ‘prospective’…

相关残差多因子模型的识别AI 解读

We specify some conditions for the identification of a multi‐factor model with correlated residuals, uncorrelated factors and zero restrictions in the factor loadings. These conditions are derived from the results of Stanghellini (1997) and Vicard (2000) which deal with single‐factor models with zero restrictions in the concentration matrix. Like these authors, we make use of the complementary graph of residuals and the conditions build on the role of odd cycles in this…

径向基函数网络的贝叶斯信息准则与平滑参数选择AI 解读

By extending Schwarz's (1978) basic idea we derive a Bayesian information criterion which enables us to evaluate models estimated by the maximum penalised likelihood method or the method of regularisation. The proposed criterion is applied to the choice of smoothing parameters and the number of basis functions in radial basis function network models. Monte Carlo experiments were conducted to examine the performance of the nonlinear modelling strategy of estimating the weight…

非高斯时间序列模型的多步采样器：对 Shephard 与 Pitt（1997）的评论AI 解读

This note points out a problem in the multi‐move sampler as proposed by Shephard & Pitt (1997) and provides an alternative correct formulation.

高斯时间序列中 Whittle 测度的相互毗连性AI 解读

For a stationary time series, Whittle constructed a likelihood for the spectral density based on the approximate independence of the discrete Fourier transforms of the data at certain frequencies. Whittle's likelihood has been widely used in the literature for constructing estimators. In this paper, we show that, for a Gaussian time series, the Whittle measure is mutually contiguous with the actual distribution of the data. As a consequence, most asymptotic properties of…

依赖数据的多峰性检验AI 解读

We propose a test for multimodality with dependent data by resampling from a suitably constructed transition probability kernel, which includes Silverman's test with independent data as a special case. We extend some theoretical properties of Silverman's test with independent and identically distributed data to weakly dependent data, and also discuss the robustness of Silverman's test against departure from independence.

贝叶斯相关系数估计AI 解读

We propose prior probability models for variance‐covariance matrices in order to address two important issues. First, the models allow a researcher to represent substantive prior information about the strength of correlations among a set of variables. Secondly, even in the absence of such information, the increased flexibility of the models mitigates dependence on strict parametric assumptions in standard prior models. For example, the model allows a posteriori different…

关于恢复自助法一致性的方法的一则札记AI 解读

We consider the property of consistency and its relevance for determining the performance of the bootstrap. We analyse various parametric bootstrap approximations to the distributions of the Hodges and Stein estimators, whose behaviour is typical of that of super‐efficient estimators employed in wavelet regression, kernel density estimation and nonparametric curve fitting. Our results reveal not only some of the difficulties in selecting good modifications to the intuitive…

二元随机变量的条件关联与边际关联AI 解读

The relationship between marginal and conditional distributions of binary random variables is analysed via a log‐linear model. Conditions for the Yule–Simpson effect are established and the implications for latent class analysis examined.

基于稳健离散度的主成分渐近分布AI 解读

Algebraically, principal components can be defined as the eigenvalues and eigenvectors of a covariance or correlation matrix, but they are statistically meaningful as successive projections of the multivariate data in the direction of maximal variability. An attractive alternative in robust principal component analysis is to replace the classical variability measure, i.e. variance, by a robust dispersion measure. This projection‐pursuit approach was first proposed in Li &…

随机删失下比例优势模型的检验AI 解读

In practical applications, it is not uncommon for the hazard functions of two groups to converge with time. One approach that allows for converging hazard functions is the proportional odds model. We develop a procedure for testing the proportional odds assumption when the available data consist of two independent random samples of randomly right‐censored lifetimes. Asymptotic normality of the test statistic is proved and the procedure is applied to two well‐known datasets.…

非线性及广义线性混合效应模型的混合估计方法AI 解读

A hybrid method that combines Laplace's approximation and Monte Carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects. Simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family. An asymptotic…

调整后的剖面估计函数AI 解读

In settings where the full probability model is not specified, consider a general estimating function g(θ, λ; y) that involves not only the parameters of interest, θ, but also some nuisance parameters, λ. We consider methods for reducing the effects on g of fitting nuisance parameters. We propose Cox–Reid‐type adjustment to the profile estimating function, g(θ, λ̂θ; y), that reduces its bias by two orders. Typically, only the first two moments of the response variable are…

关于“检验正态混合分布的成分数量”的札记AI 解读

In a recent paper, Lo et al. (2001) propose a test for the likelihood ratio statistic based on the Kullback–Leibler information criterion when testing the null hypothesis that a random sample is drawn from a mixture of k0 normal components against the alternative hypothesis of a mixture with k1 normal components with k0 less than k1. However, this result requires conditions that are generally not met when the null hypothesis holds. Consequently, the result is not proven and…

复杂入样机制下基于数据增广的条件似然推断AI 解读

In many applications, particularly in genetics, samples are drawn under complex ascertainment rules. For example, families may only be selected for study if two or more siblings have trait values exceeding some threshold. The correct likelihood for inference in such situations involves the probabilities of ascertainment, and these are frequently intractable. A consistent, but not fully efficient, method of analysis of such studies is proposed. The main idea is to augment the…

ARCH 与 GARCH 模型的最小绝对偏差估计AI 解读

Hall & Yao (2003) showed that, for ARCH/GARCH, i.e. autoregressive conditional heteroscedastic/generalised autoregressive conditional heteroscedastic, models with heavy‐tailed errors, the conventional maximum quasilikelihood estimator suffers from complex limit distributions and slow convergence rates. In this paper three types of absolute deviations estimator have been examined, and the one based on logarithmic transformation turns out to be particularly appealing. We have…

调查抽样中的最优校准估计量AI 解读

We show that the model‐calibration estimator for the finite population mean, which was proposed by Wu & Sitter (2001) through an intuitive argument, is optimal among a class of calibration estimators. We also present optimal calibration estimators for the finite population distribution function, the population variance, the variance of a linear estimator and other quadratic finite population functions under a unified framework. The proposed calibration estimators are optimal…