Inference for mixed models of ANOVA type with high-dimensional data

Abstract

a b s t r a c tInference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes to infinity. In this paper, existing tests are extended to handle this problem with a sparse model structure. To avoid the impact from insignificant fixed effects, the proposed tests are post-selection-based with an orthogonality-based selection of SCAD type applied to selecting significant fixed effects into working model. The selection and estimation of fixed effects are under the assumption on the existence of second order moments for errors. Two types of tests for random effects are considered and some new insights are obtained. The proposed tests are distribution-free, though they request the existence of the fourth moments of random effects and errors. The proposed methods are illustrated by simulation studies and a real data analysis.

Model selection in linear mixed-effect models

“…Fan et al (2014) demonstrate that their proposed robust estimator enjoy all the properties defined by Liski and Lisk (2008). Chen et al (2015) demonstrate only the validity of the Oracle property of only sparsity and consistency, but not the asymptotical distribution. Li et al (2018) show the "sparsistency" property which ensures the selection consistency for the true signals of both fixed and random effects; hence, they provide analytical proofs about the validity of consistency and sparsity, but nothing about the distributional form.…”

“…It is worth noting that, all simulations are applied with a moderate number of random effects (for both the full and the true model) and of variance-covariance parameters, except for that of Li et al (2018) and Ahn et al (2012). A large amount of fixed effects occur in the full model of Chen et al (2015), Ghosh and Thoresen (2018) and Rohart et al (2014).…”

A Method of Local Influence Analysis in Sufficient Dimension Reduction

“…The relationship between the ambient nitrate concentration and predictors is of interest; see, for example, Bondell et al (2010) and Chen et al (2015). Here, we conduct sliced inverse regression for the visualization.…”

“…The original data are obtained from the Clean Air Status and Trends Network (www.epa.gov/castnet) provided by the United States Environmental Protection Agency, which are seasonal for y, x 1 and x 2 and hourly for x 3 -x 7 . The hourly data are transformed to be seasonal via the method used in Chen et al (2015) and all the predictors are standardized. We use the data from BEL116 and BWR139, two sites that are both in Maryland, from 2001 to 2009.…”

Predicting the Types of Ion Channel-Targeted Conotoxins Based on AVC-SVM Model

“…SS b ( u ) is the sum of the squares between the groups. And SS w ( u ) is the sum of squares within the groups [20]. The calculation methods are shown in (6) and (7), respectively:$\begin{array}{c}T19S{S}_b\left(u\right)\\ =\underset{i=\mathrm{normal1}}{\overset{K}{{\displaystyle false\sum }}}{m}_i{\left(\frac{{\sum }_{j=\mathrm{normal1}}^{m_i}{a}_u\left(i,j\right)}{m_i}-\frac{{\sum }_{i=\mathrm{normal1}}^K{\sum }_{j=\mathrm{normal1}}^{m_i}{a}_u\left(i,j\right)}{{\sum }_{i=\mathrm{normal1}}^K{m}_i}\right)}^{\mathrm{2}},\end{array}$$\begin{array}{c}S{S}_w\left(u\right)=\underset{i=\mathrm{normal1}\hspace{0.17em}}{\overset{K}{{\displaystyle false\sum }}}\underset{j=\mathrm{normal1}}{\overset{m_i}{{\displaystyle false\sum }}}{\left(a_u\left(i,j\right)-\frac{{\sum }_{j=\mathrm{normal1}}^{m_i}{a}_u\left(i,j\right)}{m_i}\right)}^{\mathrm{2}},\end{array}$where m i denotes the total of samples in the i th group (here m 1 = 24, m 2 = 45...…”