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Theory and Methods

Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability

Pages 407-422 | Received 01 Oct 2013, Published online: 05 May 2016

REFERENCES

  • Antoniadis, A., Sapatinas, T. (2007), Estimation and Inference in Functional Mixed-Effects Models, Computational Statistics and Data Analysis, 51, 4793–4813.
  • Aston, J. A.D., Chiou, J.-M., Evans, J.P. (2006), Linguistic Pitch Analysis Using Functional Principal Component Mixed Effect Models, Journal of the Royal Statistical Society, Series C, 68, 837–857.
  • Bosq, D. (2000), Linear Processes in Function Spaces, New York: Springer.
  • Brown, K. (1976), Asymptotic Behavior of MINQUE-Type Estimators of Variance Components, The Annals of Statistics, 4, 746–754.
  • Chen, K., Müller, H. (2012), Conditional Quantile Analysis When Covariates are Functions, With Application to Growth Data, Journal of the Royal Statistical Society, Series B, 74, 67–89.
  • Chen, X., White, H. (1998), Central Limit and Functional Central Limit Theorems for Hilbert-Valued Dependent Heterogeneous Arrays with Applications, Econometric Theory, 14, 260–284.
  • Costafreda, S., Barker, G., Brammer, M. (2009), Bayesian Wavelet-based Analysis of Functional Magnetic Resonance Time Series, Magnetic Resonance Imaging, 27, 460–469.
  • Gamazon, E., Im, H., Liu, C., Nicolae, D., Cox, N. (2013), The Convergence of eQTL Mapping, Heritability Estimation and Polygenic Modeling: Emerging Spectrum of Risk Variation in Bipolar Disorder, arXiv:1303.6227.
  • Gromenko, O., Kokoszka, P. (2013), Nonparametric Inference in Small Data Sets of Spatially Indexed Curves with Application to Ionospheric Trend Determination, Computational Statistics and Data Analysis, 59, 82–94.
  • Gromenko, O., Kokoszka, P., Zhu, L., Sojka, J. (2012), Estimation and Testing for Spatially Indexed Curves With Application to Ionospheric and Magnetic Field Trends, The Annals of Applied Statistics, 6, 669–696.
  • Guo, W. (2002), Functional Mixed Effects Models, Biometrics, 58, 121–128.
  • Horváth, L., and Kokoszka, P. (2012), Inference for Functional Data with Applications, New York: Springer.
  • Isserlis, L. (1918), On a Formula for the Product-Moment Coefficient of Any Order of a Normal Frequency Distribution in Any Number of Variables, Biometrika, 12, 134–139.
  • Ivanescu, A., Staicu, A., Scheipl, F., Greven, S. (2013), Penalized Function-on-Function Regression, Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 254.
  • Kokoszka, P., Reimherr, M. (2012), Determining the Order of the Functional Autoregressive Model, Journal of Time Series Analysis, 34, 116–129.
  • Kokoszka, P., and Reimherr, M. (2013), Predictability of Shapes of Intraday Price Curves, The Econometrics Journal, 16, 285--308.
  • Kostem, E., Eskin, E. (2013), Improving the Accuracy and Efficiency of Partitioning Heritability into the Contributions of Genomic Regions, American Journal of Human Genetics, 92, 558–564.
  • LaMotte, L. (1973a), On Non-Negative Quadratic Unbiased Estimation of Variance Components, Journal of the American Statistical Association, 68, 728–730.
  • ——— (1973b), Quadratic Estimation of Variance Components, Biometrics, 29, 311–330.
  • Li, Y., Wang, N., Carroll, R.J. (2010), Generalized Functional Linear Models with Semiparametric Single-Index Interactions, Journal of the American Statistical Association, 105, 621–633.
  • Luo, L., Zhu, Y., Xiong, M. (2012), Quantitative Trait Locus Analysis for Next–Generation Sequencing with the Functional Linear Models, Journal of Medical Genetics, 49, 513–524.
  • McCullagh, P. (1987), Tensor Methods in Statistics, New York: Chapman & Hall.
  • Morris, J., Carroll, R.J. (2006), Wavelet-Based Functional Mixed Models, Journal of the Royal Statistical Society, Series B, 68, 179–199.
  • Müller, H.-G., Stadtmüller, U. (2005), Generalized Functional Linear Models, The Annals of Statistics, 33, 774–805.
  • Paige, C.C., Saunders, M.A. (1975), Solution of Sparse Indefinite Systems of Linear Equations, SINUM, 12, 617–629.
  • Ramsay, J.O., Altman, N., Bock, R.D. (1994), Variation in Height Acceleration in the Fels Growth Data, The Canadian Journal of Statistics, 22, 89–102.
  • Rao, C. (1971a), Estimation of Variance and Covariance Components–MINQUE Theory, Journal of Multivariate Analysis, 1, 257–275.
  • ——— (1971b)Minimum Variance Quadratic Unbiased Estimation of Variance Components, Journal of Multivariate Analysis 1, 445–456.
  • Reimherr, M., Nicolae, D. (2014), A Functional Data Analysis Approach for Association Studies, Annals of Applied Statistics, 8, 406–429.
  • Reiss, P., Mennes, M., Petkova, E., Huang, L., Hoptman, M., Biswal, B., Colcombe, S., Zuo, X.-N., Milham, M. (2011), Extracting Information From Functional Connectivity Maps via Function-on-Scalar Regression, NeuroImage, 56, 140–148.
  • Scheipl, F., Staicu, A.-M., Greven, S. (2014), Functional Additive Mixed Models, Journal of Computational and Graphical Statistics, 24, 477–501.
  • Searle, S.R., Casella, G., and McCulloch, C.E. (1992), Variance Components, New York: Wiley.
  • Stefanescu, M. V., Serban, F., and Dedu, S. (2010), Portfolio Optimization Using Data Analysis Techniques, Proceedings of the 12th WSEAS International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems, Stevens Point, Wisconsin World: Scientific and Engineering Academy and Society (WSEAS), pp. 146–151
  • Tang, R., Müller, H. (2009), Time-Synchronized Clustering of Gene Expression Trajectories, Biostatistics, 10, 32–45.
  • (1999), The Childhood Asthma Management Program (CAMP): Design, Rationale, and Methods, Controlled Clinical Trials, 20, 91–120.
  • (2000), Long-Term Effects of Budesonide or Nedocromil in Children With Asthma, New England Journal of Medicine, 343, 1054–1063.
  • Vattikuti, S., Guo, J., Chow, C.C. (2012), Heritability and Genetic Correlations Explained by Common SNPs for Metabolic Syndrome Traits, PLoS Genetics, 8, e1002637.
  • Verzelen, N., Tao, W., Müller, H.-G. (2012), Inferring Stochastic Dynamics from Functional Data, Biometrika, 99, 533–550.
  • Yang, J., Benyamin, B., McEvoy, B.P., Gordon, S., Henders, A.K., Nyholt, D.R., Madden, P.A., Heath, A.C., Martin, N.G., Montgomery, G.W., Goddard, M.E., Visscher, P.M. (2010), Common SNPs Explain a Large Proportion of the Heritability for Human Height, Nature Genetics, 42, 565–569.
  • Yang, J., Lee, S., Goddard, M., and Visscher, P. (2011), GCTA: A Tool for Genome-Wide Complex Trait Analysis. American Journal of Human Genetics, 88, 76–82.
  • Yang, J., Manolio, T., Pasquale, L., Boerwinkle, E., Caporaso, N., Cunningham, J., de Andrade, M., Feenstra, B., Feingold, E., Hayes, M., Hill, W., Landi, M., Alonso, A., Lettre, G., Lin, P., Ling, H., Lowe, W., Mathias, R., Melbye, M., Pugh, E., Cornelis, M., Weir, B., Goddard, M., Visscher, P. (2011), Genome Partitioning of Genetic Variation for Complex Traits Using Common SNPs, Nature Genetics, 43, 519–525.
  • Yao, F., Müller, H.-G., Wang, J.-L. (2005), Functional Data Analysis for Sparse Longitudinal Data, Journal of the American Statistical Association, 100, 577–590.
  • Zhou, X., Carbonetto, P., Stephens, M. (2013), Polygenic Modeling with BAyesian Sparse Linear Mixed Models, PLOS Genetics, 9, e1003264.
  • Zhou, X., Stephens, M. (2012), Genome-Wide Efficient Mixed-Mmodel Analysis for Association Studies, Nature Genetics, 44, 821–826.
  • Zipunnikov, V., Caffo, B., Yousem, D., Davatzikos, C., Schwartz, B., Crainiceanu, C. (2011), Functional Principal Component Model for High-Dimensional Brain Imaging, NeuroImage, 58, 772–784.

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