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高维线性回归中 Lasso 变量选择的稀疏性与偏差AI 解读

Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436–1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of greater order than the sample size. Zhao and Yu [(2006) J. Machine Learning Research 7 2541–2567] formalized the neighborhood stability condition in the context of linear regression as a strong irrepresentable condition. That paper showed…

稀疏高维回归模型中桥估计量的渐近性质AI 解读

We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero. We show that under appropriate conditions, bridge estimators correctly select covariates with nonzero coefficients with…

用于 cDNA 微阵列归一化与分析的双向半线性模型AI 解读

A basic question in analyzing cDNA microarray data is normalization, the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve across the whole dynamic range. A proper normalization procedure ensures that the normalized intensity ratios provide meaningful measures of relative expression levels. We propose a two-way semilinear model (TW–SLM) for normalization and analysis of microarray data. This method does not…

最大得分估计量的 BootstrapAI 解读

This paper shows that the bootstrap does not consistently estimate the asymptotic distribution of the maximum score estimator. The theory developed also applies to other estimators within a cube-root convergence class. For some single-parameter estimators in this class, the results suggest a simple method for inference based upon the bootstrap.

部分线性可加 Cox 模型的有效估计AI 解读

The partly linear additive Cox model is an extension of the (linear) Cox model and allows flexible modeling of covariate effects semiparametrically. We study asymptotic properties of the maximum partial likelihood estimator of this model with right-censored data using polynomial splines. We show that, with a range of choices of the smoothing parameter (the number of spline basis functions) required for estimation of the nonparametric components, the estimator of the…

区间删失比例优势失效时间回归模型的筛估计AI 解读

Estimation of the proportional-odds failure-time regression model with interval censoring is considered. Conditions that allow for positive information for the regression parameter are discussed. The efficient score is characterized by a Fredholm equation of the second kind. The sieve maximum likelihood estimator for the finite-dimensional regression parameter is shown to be asymptotically normal with √n convergence rate and to achieve the information bound. Data analysis…

基于排序集样本的分布函数非参数最大似然估计的渐近性质AI 解读

We show that the nonparametric maximum likelihood estimator (NPMLE) of a distribution function based on balanced ranked set samples is consistent, converges weakly to a Gaussian process and is asymptotically efficient. The covariance function of the limiting process is described in terms of the solution to a Fredholm integral equation of the second kind.

序约束下生存曲线非参数估计的渐近理论AI 解读

We consider two problems in nonparametric survival analysis under the restriction of stochastic ordering. The first problem is that of estimating a survival function $\overline{F}(t)$ under the restriction $\overline{F}(t) \geq $\overline{F}_0 (t)$, all t, where $\overline{F}_0 (t)$ is known. The second problem consists of estimating two unknown survival functions $\overline{F}^{(1)}(t)$ and $\overline{F}^{(2)}(t)$ when it is known that $\overline{F}^{(1)}(t) \geq…

区间删失比例风险模型的有效估计AI 解读

The maximum likelihood estimator (MLE) for the proportional hazards model with "case 1" interval censored data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with $\sqrt{n}$ convergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at $n^{1/3}$ rate. Estimation of the asymptotic variance matrix for the MLE of the regression parameter is also considered. To…