Optimal Estimation of Genetic Relatedness in High-Dimensional Linear Models

References

• Belloni, A., Chernozhukov, V., and Wang, L. (2011), “Square-Root Lasso: Pivotal Recovery of Sparse Signals Via Conic Programming,” Biometrika, 98, 791–806.
   Web of Science ®Google Scholar
• Bloom, J. S., Ehrenreich, I. M., Loo, W. T., Lite, T.-L. V., and Kruglyak, L. (2013), “Finding the Sources of Missing Heritability in a Yeast Cross,” Nature, 494, 234–237.
   PubMed Web of Science ®Google Scholar
• Bonnet, A., Gassiat, E., and Lévy-Leduc, C. (2015), “Heritability Estimation in High Dimensional Sparse Linear Mixed Models,” Electronic Journal of Statistics, 9, 2099–2129.
   Web of Science ®Google Scholar
• Bulik-Sullivan, B., Finucane, H. K., Anttila, V., Gusev, A., Day, F. R., Loh, P.-R., Duncan, L., Perry, J. R. B., Patterson, N., Robinson, E. B., Daly, M. J., Price, A. L., Neale, B. M., ReproGen Consortium, Psychiatric Genomics Consortium, and Genetic Consortium for Anorexia Nervosa of the Wellcome Trust Case Control Consortium (2015), “An Atlas of Genetic Correlations Across Human Diseases and Traits,” Nature Genetics, 47, 1236–1241.
   Google Scholar
• Cai, T. T., and Guo, Z. (2017), “Accuracy Assessment for High-dimensional Linear Regression,” The Annals of Statistics, 46, 1807–1836.
   Google Scholar
• Cai, T. T., and Low, M. G. (2005), “Nonquadratic Estimators of a Quadratic Functional,” The Annals of Statistics, 33, 2930–2956.
   Web of Science ®Google Scholar
• ——— (2006), “Optimal Adaptive Estimation of a Quadratic Functional,” The Annals of Statistics, 34, 2298–2325.
   Web of Science ®Google Scholar
• Collier, O., Comminges, L., and Tsybakov, A. B. (2015), “Minimax Estimation of Linear and Quadratic Functionals on Sparsity Classes,” The Annals of Statistics, 45, 923–958.
   Web of Science ®Google Scholar
• Donoho, D. L., and Nussbaum, M. (1990), “Minimax Quadratic Estimation of a Quadratic Functional,” Journal of Complexity, 6, 290–323.
   Google Scholar
• Efromovich, S., and Low, M. (1996), “On Optimal Adaptive Estimation of a Quadratic Functional,” The Annals of Statistics, 24, 1106–1125.
   Web of Science ®Google Scholar
• Fan, J., Han, X., and Gu, W. (2012), “Estimating False Discovery Proportion Under Arbitrary Covariance Dependence,” Journal of the American Statistical Association, 107, 1019–1035.
   PubMed Web of Science ®Google Scholar
• Golan, D., and Rosset, S. (2011), “Accurate Estimation of Heritability in Genome Wide Studies Using Random Effects Models,” Bioinformatics, 27, i317–i323.
   PubMed Web of Science ®Google Scholar
• Guo, Z., Kang, H., Cai, T. T., and Small, D. S. (2016), “Confidence Intervals for Causal Effects with Invalid Instruments Using Two-stage Hard Thresholding with Voting,” arXiv:1603.05224.
   Google Scholar
• Janson, L., Barber, R. F., and Candes, E. (2016), “Eigenprism: Inference for High Dimensional Signal-to-Noise Ratios,” Journal of the Royal Statistical Society, Series B, 79, 1037–1065.
   Google Scholar
• Javanmard, A., and Montanari, A. (2014), “Confidence Intervals and Hypothesis Testing for High-dimensional Regression,” The Journal of Machine Learning Research, 15, 2869–2909.
   Web of Science ®Google Scholar
• Laurent, B., and Massart, P. (2000), “Adaptive Estimation of a Quadratic Functional by Model Selection,” The Annals of Statistics, 28, 1302–1338.
   Web of Science ®Google Scholar
• Lee, S. H., Ripke, S., Neale, B. M., Faraone, S. V., Purcell, S. M., Perlis, R. H., Mowry, B. J., Thapar, A., Goddard, M. E., and Witte, J. S. (2013), “Genetic Relationship Between Five Psychiatric Disorders Estimated from Genome-Wide SNPS,” Nature Genetics, 45, 984–994.
   PubMed Web of Science ®Google Scholar
• Lee, S. H., Yang, J., Goddard, M. E., Visscher, P. M., and Wray, N. R. (2012), “Estimation of Pleiotropy Between Complex Diseases Using Single-Nucleotide Polymorphism-Derived Genomic Relationships and Restricted Maximum Likelihood,” Bioinformatics, 28, 2540–2542.
   PubMed Web of Science ®Google Scholar
• Lee, S. H., and van der Wer, J. H. (2016), “Mtg2: An Efficient Algorithm for Multivariate Linear Mixed Model Analysis Based on Genomic Information,” Bioinformatics, 32, 1420–1422.
   PubMed Web of Science ®Google Scholar
• Maier, R., Moser, G., Chen, G.-B., Ripke, S., Coryell, W., Potash, J. B., Scheftner, W. A., Shi, J., Weissman, M. M., Hultman, C. M., Landen, M., Levinosn, D. F., Kendler, K. S., Smoller, J. W., Wray, N. R., Lee. S. H., and Cross-Disorder Working Group of the Psychiatric Genomics Consortium (2015), “Joint Analysis of Psychiatric Disorders Increases Accuracy of Risk Prediction for Schizophrenia, Bipolar Disorder, and Major Depressive Disorder,” The American Journal of Human Genetics, 96, 283–294.
   Google Scholar
• Manolio, T. A. (2010), “Genomewide Association Studies and Assessment of the Risk of Disease,” New England Journal of Medicine, 363, 166–176.
   PubMed Web of Science ®Google Scholar
• McCarthy, M. I., Abecasis, G. R., Cardon, L. R., Goldstein, D. B., Little, J., Ioannidis, J. P. A., and Hirschhorn, J. N. (2008), “Genome-Wide Association Studies for Complex Traits: Consensus, Uncertainty and Challenges,” Nature Reviews Genetics, 9, 356–369.
   PubMed Web of Science ®Google Scholar
• Purcell, S. M., Wray, N. R., Stone, J. L., Visscher, P. M., O’Donovan, M. C., Sullivan, P. F., Sklar, P., Ruderfer, D. M., McQuillin, A., Morris, D. W., and International Schizophrenia Consortium (2009), “Common Polygenic Variation Contributes to Risk of Schizophrenia and Bipolar Disorder,” Nature, 460, 748–752.
   Google Scholar
• Sun, T., and Zhang, C.-H. (2012), “Scaled Sparse Linear Regression,” Biometrika, 101, 269–284.
   Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection Via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• van de Geer, S., Bühlmann, P., Ritov, Y., and Dezeure, R. (2014), “On Asymptotically Optimal Confidence Regions and Tests for High-Dimensional Models,” The Annals of Statistics, 42, 1166–1202.
   Web of Science ®Google Scholar
• Vershynin, R. (2012), “Introduction to the Non-asymptotic Analysis of Random Matrices,” in Compressed Sensing: Theory and Applications, eds. Y. Eldar, and G. Kutyniok, Cambridge, UK: Cambridge University Press, pp. 210–268.
   Google Scholar
• Verzelen, N., and Gassiat, E. (2016), “Adaptive Estimation of High-Dimensional Signal-to-Noise Ratios,” Bernoulli, 24, 3683–3710.
   Google Scholar
• Wray, N. R., Goddard, M. E., and Visscher, P. M. (2007), “Prediction of Individual Genetic Risk to Disease from Genome-wide Association Studies,” Genome Research, 17, 1520–1528.
   PubMed Web of Science ®Google Scholar
• Wu, T. T., Chen, Y. F., Hastie, T., Sobel, E., and Lange, K. (2009), “Genome-wide Association Analysis by Lasso Penalized Logistic Regression,” Bioinformatics, 25, 714–721.
   PubMed Web of Science ®Google Scholar
• Yang, L., Neale, B. M., Liu, L., Lee, S. H., Wray, N. R., Ji, N., Li, H., Qian, Q., Wang, D., Li, J., Faraone, S. V., Wang, Y., and Psychiatric GWAS Consortium: ADHD Subgroup (2013), “Polygenic Transmission and Complex Neuro Developmental Network for Attention Deficit Hyperactivity Disorder: Genome-Wide Association Study of Both Common and Rare Variants,” American Journal of Medical Genetics Part B: Neuropsychiatric Genetics, 162, 419–430.
   Google Scholar
• Zhang, C.-H., and Zhang, S. S. (2014), “Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models,” Journal of the Royal Statistical Society, Series B, 76, 217–242.
   Google Scholar
• Zhernakova, A., van Diemen, C. C., and Wijmenga, C. (2009), “Detecting Shared Pathogenesis from the Shared Genetics of Immune-related Diseases,” Nature Reviews Genetics, 10, 43–45.
   PubMed Web of Science ®Google Scholar