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极稀疏网络的一般成对比较模型AI 解读

Statistical estimation using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this article, we propose a general framework to model the mutual interactions in a network, which enjoys ample flexibility in terms of model parameterization. Under this setup, we show that the maximum likelihood estimator for the latent score vector of the subjects is uniformly consistent under a near-minimal condition on network sparsity. This…

线性化最大秩相关估计AI 解读

Summary We propose a linearized maximum rank correlation estimator for the single-index model. Unlike the existing maximum rank correlation and other rank-based methods, the proposed estimator has a closed-form expression, making it appealing in theory and computation. The proposed estimator is robust to outliers in the response and its construction does not need knowledge of the unknown link function or the error distribution. Under mild conditions, it is shown to be…

广义半参数与非参数回归中参数及函数的有效估计与计算AI 解读

The efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature (Bickel et al., 1993). In this paper, we study efficient estimators for both parameters and nonparametric functions in a class of generalized semi/non-parametric regression models, which cover commonly used semiparametric models such as partially linear models, partially linear single index models, and two-sample semiparametric models. We propose a maximum…

非正态误差下变换线性回归的最大似然估计AI 解读

This paper discusses the transformed linear regression with non-normal error distributions, a problem that often occurs in many areas such as economics and social sciences as well as medical studies. The linear transformation model is an important tool in survival analysis partly due to its flexibility. In particular, it includes the Cox model and the proportional odds model as special cases when the error follows the extreme value distribution and the logistic distribution,…

完全依从或完全不依从生存研究中的因果推断：半参数变换模型AI 解读

Summary We consider causal inference in randomized survival studies with right-censored outcomes and all-or-nothing compliance, using semiparametric transformation models to estimate the distribution of survival times in treatment and control groups, conditionally on covariates and latent compliance type. Estimands depending on these distributions, e.g. the complier average causal effect, the complier effect on survival beyond time t and the complier quantile effect, are…

最小绝对相对误差估计AI 解读

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statistical estimation for linear regression model. However, in many practical…

非参数比例风险模型的全局偏似然AI 解读

As an alternative to the local partial likelihood method of Tibshirani and Hastie and Fan, Gijbels, and King, a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model, λ(t|x) = exp{ψ(x)}λ(0)(t). The estimator, ψ̂(x), reduces to the Cox partial likelihood estimator if the covariate is discrete. The estimator is shown to be consistent and semiparametrically efficient for linear functionals of ψ(x). Moreover,…

聚类数据的部分线性回归模型AI 解读

This article considers the analysis of clustered data via partial linear regression models. Adopting the idea of modeling the within-cluster correlation from the method of generalized estimating equations, a least squares type estimate of the slope parameter is obtained through piecewise local polynomial approximation of the nonparametric component. This slope estimate has several advantages: (a) It attains n1/2-consistency without undersmoothing; (b) it is efficient when…

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…

风险集抽样下比例风险模型的统计估计AI 解读

Thomas’ partial likelihood estimator of regression parameters is widely used in the analysis of nested case-control data with Cox’s model. This paper proposes a new estimator of the regression parameters, which is consistent and asymptotically normal. Its asymptotic variance is smaller than that of Thomas’ estimator away from the null. Unlike some other existing estimators, the proposed estimator does not rely on any more data than strictly necessary for Thomas’ estimator…

广义病例—队列抽样AI 解读

Summary A class of cohort sampling designs, including nested case–control, case–cohort and classical case–control designs involving survival data, is studied through a unified approach using Cox’s proportional hazards model. By finding an optimal sample reuse method via local averaging, a closed form estimating function is obtained, leading directly to the estimators of the regression parameters that are relatively easy to compute and are more efficient than some commonly…

响应偏倚抽样下的参数模型AI 解读

Summary Suppose that subjects in a population follow the model f(y*|x*;θ) where y* denotes a response, x* denotes a vector of covariates and θ is the parameter to be estimated. We consider response-biased sampling, in which a subject is observed with a probability which is a function of its response. Such response-biased sampling frequently occurs in econometrics, epidemiology and survey sampling. The semiparametric maximum likelihood estimate of θ is derived, along with its…

再捕获与移除研究的参数和半参数模型：似然方法AI 解读

Summary Capture–recapture processes are biased samplings of recurrent event processes, which can be modelled by the Andersen–Gill intensity model. The intensity function is assumed to be a function of time, covariates and a parameter. We derive the maximum likelihood estimators of both the parameter and the population size and show the consistency and asymptotic normality of the estimators for both recapture and removal studies. The estimators are asymptotically efficient…

病例对照研究的最优序贯设计AI 解读

Fixed case-control studies separately collect a case sample and a control sample withthe two sample sizes being fixed prior to studies and sometimes arbitrarily chosen. This often results in loss of efficiency of case-control designs in terms of cost-saving or time-saving of the studies. We study sequential case-control designs and, in connection with treatment allocation and stochastic approximation, derive a simple sampling rule that leads to optimal case-control designs.…

固定与自适应设计下广义线性模型最大拟似然估计的强一致性AI 解读

Strong consistency for maximum quasi-likelihood estimators of regression parameters in generalized linear regression models is studied. Results parallel to the elegant work of Lai, Robbins and Wei and Lai and Wei on least squares estimation under both fixed and adaptive designs are obtained. Let $y_1,\dots, y_n$ and $x_1,\dots, x_n$ be the observed responses and their corresponding design points ($p \times 1$ vectors), respectively. For fixed designs, it is shown that if the…

By approximating the classical product-limit estimator of a distribution function with an average of iid random variables, we derive sufficient and necessary conditions for the rate of (both strong and weak) uniform convergence of the product-limit estimator over the whole line. These findings somehow fill a longstanding gap in the asymptotic theory of survival analysis. The result suggests a natural way of estimating the rate of convergence. We also prove a related…

关于 Hall–Wellner 置信带猜想的反例AI 解读

Hall and Wellner proposed a natural extension of the Kolmogorov-Smirnov simultaneous confidence band for survival curve using the Kaplan-Meier estimator. They and Gill conjectured that the confidence band holds for all t up to the last observed failure time. A counterexample is given herein, showing that this may not always be true.

删失数据下自助法的近似精度AI 解读

In survival analysis with censored data, we consider three closely related survival function estimators: the Kaplan-Meier, Nelson and moment estimators. We derive the Edgeworth expansions for these three estimators with Studentization. Edgeworth expansions for the corresponding bootstrap statistics are also given. It is found that the bootstrap approximation is better than the normal approximation for the Studentized Kaplan-Meier and Nelson estimators, but not so for the…

截断数据 Lynden–Bell 估计量的强一致收敛AI 解读

In this paper, we prove that the Lynden-Bell estimator of a distribution function in the random truncation model is uniformly strong consistent over the whole half line, a problem left open by Woodroofe.