# Heritability estimation in high dimensional sparse linear mixed models

@article{Bonnet2015HeritabilityEI, title={Heritability estimation in high dimensional sparse linear mixed models}, author={Anna Bonnet and Elisabeth Gassiat and C{\'e}line L{\'e}vy-Leduc}, journal={Electronic Journal of Statistics}, year={2015}, volume={9}, pages={2099-2129} }

Motivated by applications in genetic fields, we propose to estimate the heritability in high-dimensional sparse linear mixed models. The heritability determines how the variance is shared between the different random components of a linear mixed model. The main novelty of our approach is to consider that the random effects can be sparse, that is may contain null components, but we do not know either their proportion or their positions. The estimator that we consider is strongly inspired by the…

## 19 Citations

### Optimal Estimation of Genetic Relatedness in High-Dimensional Linear Models

- MathematicsJournal of the American Statistical Association
- 2018

ABSTRACT Estimating the genetic relatedness between two traits based on the genome-wide association data is an important problem in genetics research. In the framework of high-dimensional linear…

### Improving heritability estimation by a variable selection approach in sparse high dimensional linear mixed models

- Computer Science
- 2015

A novel methodology to estimate heritability, which corresponds to the proportion of phenotypic variance that can be explained by genetic factors, is proposed and implemented in the R package EstHer and applied on neuroanatomical data from the project IMAGEN.

### Estimation of variance components, heritability and the ridge penalty in high-dimensional generalized linear models

- Computer Science, MathematicsCommun. Stat. Simul. Comput.
- 2022

This work reviews and compares several estimators of variances and of the random slopes and errors of high-dimensional linear regression models and demonstrates the superior accuracy of the resulting MML estimator of λ as compared to CV.

### Boosting heritability: estimating the genetic component of phenotypic variation with multiple sample splitting

- BiologyBMC Bioinform.
- 2021

This paper proposes a generic strategy for heritability inference, termed as “boosting heritability”, by combining the advantageous features of different recent methods to produce an estimate of the heritability with a high-dimensional linear model.

### The Mahalanobis kernel for heritability estimation in genome-wide association studies: fixed-effects and random-effects methods

- Computer Science
- 2019

It is shown that reliance on the Euclidean distance kernel contributes to several unresolved modeling inconsistencies in heritability estimation for GWAS and is proposed a new definition of partitioned heritability -- the heritability attributable to a subset of genes or single nucleotide polymorphisms -- using the Mahalanobis GRM, and it inherits many of the nice consistency properties identified in the original analysis.

### Heritability estimation in case-control studies

- Biology
- 2018

The main result is the proof of the consistency of this estimator, under several assumptions that will state and discuss, and a numerical study to compare two approximations leading to two heritability estimators.

### Statistical Inference for Genetic Relatedness Based on High-Dimensional Logistic Regression

- Computer ScienceStatistica Sinica
- 2022

The ability to obtain novel insights about the shared genetic architecture between ten pediatric autoimmune diseases is demonstrated to show the superiority of the proposed methods and their applicability to the analysis of real genetic data.

### Fixed Effects Testing in High-Dimensional Linear Mixed Models

- MathematicsJournal of the American Statistical Association
- 2020

A hypothesis test and the corresponding p-value for testing for the significance of the homogeneous structure in linear mixed models are developed and a robust matching moment construction is used for creating a test that adapts to the size of the model sparsity.

### EigenPrism: inference for high dimensional signal‐to‐noise ratios

- Mathematics, Computer ScienceJournal of the Royal Statistical Society. Series B, Statistical methodology
- 2017

A novel procedure is derived, called EigenPrism, which is asymptotically correct when the covariates are multivariate Gaussian and produces valid confidence intervals in finite samples as well and applies to a genetic data set to estimate the genetic signal‐to‐noise ratio for a number of continuous phenotypes.

### A Unified Approach to Robust Inference for Genetic Covariance

- Biology
- 2021

The asymptotic properties of the proposed estimator are provided and it is shown that the proposal is robust under certain model misspecification and robust inference for the narrow-sense genetic covariance, even when both linear models are mis-specified.

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