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变量数远超样本量时典型判别向量的同步稀疏估计AI 解读

This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when p ≫ N. Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, G − 1 canonical vectors can be considered if the number of groups is G. In the multi-group context, it is common to estimate canonical vectors in a sequential fashion. Moreover, separate prior estimation of the covariance structure is…

生物信息学数据中用于同时检验的二元模型AI 解读

We develop a novel approach for testing treatment effects in high-throughput data. Most previous works on this topic focused on testing for differences between the means, but recently it has been recognized that testing for differential variation is probably as important. We take it a step further, and introduce a bivariate model modeling strategy which accounts for both differential expression and differential variation. Our model-based approach, in which the differential…

利用目标函数与随机搜索进行聚类AI 解读

Summary A new approach to clustering multivariate data, based on a multilevel linear mixed model, is proposed. A key feature of the model is that observations from the same cluster are correlated, because they share cluster-specific random effects. The inclusion of cluster-specific random effects allows parsimonious departure from an assumed base model for cluster mean profiles. This departure is captured statistically via the posterior expectation, or best linear unbiased…

自动化 Monte Carlo EM 算法最大化广义线性混合模型似然AI 解读

Summary Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method…

广义线性混合模型中的预测标准误AI 解读

The unconditional mean squared error of prediction (UMSEP) is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in the classical normal theory mixed model. But the UMSEP is inappropriate for generalized linear mixed models where the conditional variance of the random effects depends on the data. When the random effects describe variation between independent small domains and domain-specific prediction is…

有限总体的 Bootstrap 方法AI 解读

We show that the familiar bootstrap plug-in rule of Efron has a natural analog in finite population settings. In our method a characteristic of the population is estimated by the average value of the characteristic over a class of empirical populations constructed from the sample. Our method extends that of Gross to situations in which the stratum sizes are not integer multiples of their respective sample sizes. Moreover, we show that our method can be used to generate…

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Monte Carlo 近似与迭代自助法AI 解读

We discuss optimal choice of the numbers of resamples in the two stages of the iterated bootstrap, when that technique is used to calibrate bootstrap confidence intervals. If the numbers of resamples in the first and second stages are denoted by B and C respectively, we show that it is optimal to take C to be approximately a constant multiple of B½. The value of the constant is derived, and shown to depend only on the nominal coverage level of a confidence interval. However,…

测量误差模型中线性函数关系的 Bootstrap 置信域AI 解读

We suggest bootstrap methods for constructing confidence bands (and intervals) for an unknown linear functional relationship in an errors-invariables model. It is assumed that the ratio of error variances is known to lie within an interval $\Lambda = \lbrack\lambda_1, \lambda_2\rbrack$. A confidence band is constructed for the range of possible linear relationships when $\lambda \in \Lambda$. Meaningful results are obtained even in the extreme case $\Lambda = \lbrack 0, \infty\rbrack$…

块独立性、球形性及方差协方差相等检验的鞍点近似AI 解读

SUMMARY Approximations for the null distribution of various test statistics arising in multivariate analysis using Skovgaard's saddlepoint formula are discussed. In each case an approximation is found with such accuracy as to obviate the need for exact computation.

Jackknife 分布函数估计量的一项改进AI 解读

In a recent paper, C. F. J. Wu showed that the jackknife estimator of a distribution function has optimal convergence rate $O(n^{-1/2})$, where $n$ denotes the sample size. This rate is achieved by retaining $O(n)$ data values from the original sample during the jackknife algorithm. Wu's result is particularly important since it permits a direct comparison of jackknife and bootstrap methods for distribution estimation. In the present paper we show that a very simple,…

用于自助法的平衡重要性重抽样AI 解读

We show that the method of importance resampling, introduced by Vernon Johns and Anthony Davison, may be enhanced by balancing the resamples. It is demonstrated that "balanced importance resampling" improves on both "balanced uniform resampling" and "random importance resampling", from the viewpoint of statistical efficiency. Moreover, the range of applications for which efficient resampling methods may be applied is extended to include statistics which are smooth functions…

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多元分析中 Bartlett–Nanda–Pillai 迹统计量的鞍点近似AI 解读

The null distribution of the Bartlett-Nanda-Pillai trace statistic is shown to be equivalent to the conditional distribution of canonical sufficient statistics in a multiparameter exponential family setting. As such, sequential and double saddlepoint approximations are used to approximate the distribution. The existence of tabulated percentiles for the distribution allows for comparison of the accuracy of the various saddlepoint approximations. The ability of the…