Notes on Exact Power Calculations for t Tests and Analysis of Covariance

A cautionary note on robust covariance plug-in methods

Many multivariate statistical methods rely heavily on the sample covariance matrix. It is well known though that the sample covariance matrix is highly non-robust. One popular alternative approach for "robustifying" the multivariate method is to simply replace the role of the covariance matrix with some robust scatter matrix. The aim of this paper is to point out that in some situations certain properties of the covariance matrix are needed for the corresponding robust "plug-in" method to be a valid approach, and that not all scatter matrices necessarily possess these important properties. In …

A Note on Choosing the Threshold for Large Covariance Estimations in Factor Models

This note shows that for i.i.d. data, estimating large covariance matrices in factor models can be casted using a simple plug-in method to choose the threshold: $$ μ_{jl}=\frac{c_0}{\sqrt{n}}Φ^{-1}(1-\fracα{2p^2})\sqrt{\frac{1}{n}\sum_{i=1}^n\hat u_{ji}^2\hat u_{li}^2}.$$ This is motivated by the tuning parameter suggested by Belloni et al. (2012) in the lasso literature. It also leads to the minimax rate of convergence of the large covariance matrix estimator. Previously, the minimaxity is achievable only when $n=o(p\log p)$ by Fan et al. (2013), and now this condition is weakened to $n=o(p^2…

广义线性混合模型的精确后验均值与协方差

Exact Posterior Mean and Covariance for Generalized Linear Mixed Models

针对非正态响应GLMM随机效应后验含难处理积分的问题，提出SIC方法，通过优化而非Monte Carlo或后验分布计算精确后验均值与协方差。

A Note on Implementing a Special Case of the LEAR Covariance Model in Standard Software

Repeated measures analyses require proper choice of the correlation model to ensure accurate inference and optimal efficiency. The linear exponent autoregressive (LEAR) correlation model provides a flexible two-parameter correlation structure that accommodates a variety of data types in which the correlation within-sampling unit decreases exponentially in time or space. The LEAR model subsumes three classic temporal correlation structures, namely compound symmetry, continuous-time AR(1), and MA(1), while maintaining parsimony and providing appealing statistical and computational properties. It…

排列统计在多重检验问题中的协方差校正

Covariance Correction for Permutation Statistics in Multiple Testing Problems

本文提出一种更高效的协方差校正方法，恢复多重检验中排列统计的联合渐近依赖结构，适用于广泛的问题场景。

Covariance inflation in the ensemble Kalman filter: a residual nudging perspective and some implications

This note examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for the aforementioned distance to be bounded in a certain interval, some sufficient conditions are derived, indicating that the covariance inflation factor should be bounded in a certain interval, and that the inflation bounds are related to the maximum and minimum eigenvalues of certain matrices. Implications of these analytic results are discussed, and a numerical experiment is presented to verify …