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利用基因与环境独立性的病例对照半参数最大似然估计AI 解读

We consider the problem of maximum-likelihood estimation in case-control studies of gene-environment associations with disease when genetic and environmental exposures can be assumed to be independent in the underlying population. Traditional logistic regression analysis may not be efficient in this setting. We study the semiparametric maximum likelihood estimates of logistic regression parameters that exploit the gene-environment independence assumption and leave the…

混合效应模型的条件Akaike信息准则AI 解读

This paper focuses on the Akaike information criterion, AIC, for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and questions regarding the particular clusters in the data. We show that the AIC in current use is not appropriate for the focus on clusters, and we propose instead the conditional Akaike information and its corresponding criterion, the conditional AIC, cAIC. The penalty term in…

边际似然、条件似然与经验似然的联系及应用AI 解读

Marginal likelihood and conditional likelihood are often used for eliminating nuisance parameters. For a parametric model, it is well known that the full likelihood can be decomposed into the product of a conditional likelihood and a marginal likelihood. This property is less transparent in a nonparametric or semiparametric likelihood setting. In this paper we show that this nice parametric likelihood property can be carried over to the empirical likelihood world. We discuss…

惩罚样条的精确似然比检验AI 解读

Penalised-spline-based additive models allow a simple mixed model representation where the variance components control departures from linear models. The smoothing parameter is the ratio of the random-coefficient and error variances and tests for linear regression reduce to tests for zero random-coefficient variances. We propose exactlikelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines.…

协变量调整回归AI 解读

We introduce covariate-adjusted regression for situations where both predictors and response in a regression model are not directly observable, but are contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate. We demonstrate how the regression coefficients can be estimated by establishing a connection to varying-coefficient regression. The proposed covariate-adjustment method is illustrated with an analysis…

捕获—再捕获数据中异质性对总体规模估计的影响AI 解读

Part of the folklore of capture-recapture experiments is that ignoring heterogeneity of capture probabilities results in a downward bias. This has been based on experience and simulation studies but is often interpreted as being due to individuals with lower capture probabilities. Here estimating equation arguments are used to show that the effect on Horvitz–Thompson-type estimators of ignoring heterogeneity in capture-recapture experiments is to introduce a downward bias.…

利用发生时点对逐分量最大值进行似然推断AI 解读

Multivariate extreme value distributions arise as the limiting distributions of normalised componentwise maxima. They are often used to model multivariate data that can be regarded as the componentwise maxima of some unobserved underlying multivariate process. In many applications we have extra information. We often know the locations of the maxima within the underlying process. If the process is temporal this knowledge is frequently available through the dates on which the…

临床试验中寻找最佳治疗的自适应两阶段检验AI 解读

A main objective in clinical trials is to find the best treatment in a given finite class of competing treatments and then to show superiority of this treatment against a control treatment. The traditional procedure estimates the best treatment in a first trial. Then in an independent second trial superiority of this treatment, estimated as best in the first trial, is to be shown against the control treatment by a size α test. In this paper we investigate these two trials of…

基本区域层级模型下小区域估计量的变异性度量AI 解读

In this paper based on a basic area level model we obtain second-order accurate approximations to the mean squared error of model-based small area estimators, using the Fay & Herriot (1979) iterative method of estimating the model variance based on weighted residual sum of squares. We also obtain mean squared error estimators unbiased to second order. Based on simulations, we compare the finite-sample performance of our mean squared error estimators with those based on…

两样本问题中支持与反对似然比序的非参数检验AI 解读

We derive nonparametric procedures for testing for and against likelihood ratio ordering in the two-population setting with continuous distributions. We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions F and G. In particular, we focus on testing equality of F and G versus likelihood ratio ordering and testing for a violation of…

平滑秩估计量的标准误与协方差矩阵AI 解读

A ‘pseudo-Bayesian’ interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes…

反卷积问题的离散变换方法AI 解读

If Fourier series are used as the basis for inference in deconvolution problems, the effects of the errors factorise out in a way that is easily exploited empirically. This property is the consequence of elementary addition formulae for sine and cosine functions, and is not readily available when one is using methods based on other orthogonal series or on continuous Fourier transforms. It allows relatively simple estimators to be constructed, founded on the addition of…

惩罚样条回归的理论AI 解读

Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to…

聚类数据的局部多项式回归分析AI 解读

This paper proposes a classical weighted least squares type of local polynomial smoothing for the analysis of clustered data, with the key idea of using generalised inverses of correlation matrices. The estimator has a simple closed-form expression. Simplicity is achieved also for nonparametric generalised linear models with arbitrary link function via a transformation. Our approach can be characterised by ‘local observations with local variances’, which yields intuitively…

贝叶斯指数倾斜经验似然AI 解读

While empirical likelihood has been shown to exhibit many of the properties of conventional parametric likelihoods, a formal probabilistic interpretation has so far been lacking. We show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric Bayesian procedure which places a type of noninformative prior on the space of distributions. This prior gives preference to distributions having a small support and, among those…

摘要暂缺

收缩切片逆回归札记AI 解读

We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new estimator performs well when its tuning parameter is selected by either the…

总体分位数的校准插值置信区间AI 解读

Beran & Hall's (1993) simple linear interpolation provides a very convenient approach for constructing nonparametric confidence intervals for population quantiles based on a random sample of size n. We show that the coverage error of the interpolated interval, which is of order O(n−1), can be improved upon by calibrating the nominal coverage level. Three distinct methods of calibration are considered. The analytical and Monte Carlo methods succeed in reducing the order of…

删失生存数据平均剩余寿命的半参数回归分析AI 解读

As function of time t, a mean residual life is the remaining life expectancy of a subject given survival up to t. The proportional mean residual life model, proposed by Oakes & Dasu (1990), provides an alternative to the Cox proportional hazards model for studying the association between survival times and covariates. In the presence of censoring, we use counting process theory to develop semiparametric inference procedures for the regression coefficients of the Oakes–Dasu…

高斯图模型中删边检验的功效AI 解读

Asymptotic multivariate normal approximations to the joint distributions of edge exclusion test statistics for saturated graphical Gaussian models are derived. Non-signed and signed square-root versions of the likelihood ratio, Wald and score test statistics are considered. Noncentral chi-squared approximations are also considered for the non-signed versions. These approximations are used to estimate the power of edge exclusion tests and an example is presented.

用于非参数函数估计的多尺度广义线性模型AI 解读

We present a method for extracting information about both the scale and trend of local components of an inhomogeneous function in a nonparametric generalised linear model. Our multiscale framework combines recursive partitions, which allow for the incorporation of scale in a natural manner, with systems of piecewise polynomials supported on the partition intervals, which serve to summarise the smooth trend within each interval. Our estimators are formulated as solutions of…

两样本生存数据中短期与长期风险比的半参数分析AI 解读

Standard approaches to semiparametric modelling of two-sample survival data are not appropriate when the two survival curves cross. We introduce a two-sample model that accommodates crossing survival curves. The two scalar parameters of the model have the interpretations of being the short-term and long-term hazard ratios respectively. The time-varying hazard ratio is expressed semiparametrically by the two scalar parameters and an unspecified baseline distribution. The new…

两个t变量之差的分布AI 解读

In this paper, the difference between two correlated t variables is divided by a function of their sample correlation and the distribution of the resulting quantity is examined. Functions of the sample correlation are found for which this quantity is approximately pivotal and has a t distribution, asymptotically. Simulations show that the asymptotic results hold well for small sample sizes. The results yield a useful test for comparing the difference in standardised scores…

支撑集位于对角线上方的多元分布AI 解读

A general family of distributions for the empirical modelling of ordered multivariate data is proposed. The family is based on, but greatly extends, the joint distribution of order statistics from an independent and identically distributed univariate sample. General properties, including marginal and conditional distributions, bivariate dependence, limiting distributions and links to the Dirichlet distribution are described. Univariate and bivariate special cases of the…