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Year 2020, Volume: 41 Issue: 3, 571 - 579, 30.09.2020

Özge Kuran , Seçil Yalaz

https://doi.org/10.17776/csj.671812

Abstract

References

  • Laird, N. M. and Ware, J. H., Random-effects models for longitudinal data. Biometrics, 38 (1982) 963–974.
  • Engle, R. F., Granger, C. W. J., Rice, J. and Weiss, A., Semiparametric estimates of the relation between weather and electricity sales. Journal of the American Statistical Association, 81 (1986) 310-320.
  • Severini, T. A. and Staniswalis, J. G., Quasi-likelihood estimation in semi-parametric models. Journal of the American Statistical Association, 89 (1994) 510-512.
  • Lin, X. and Carroll, R. J., Semiparametric regression for clustered data using generalised estimating equations. Journal of the American Statistical Association, 96 (2001) 1045–1056.
  • Wang, N,. Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika, 90 (2003) 43–52.
  • Rice, J. A., Convergence rates for partially splined models. Statistics & Probability Letters 4 (1986) 204–208.
  • Speckman, P. E., Regression analysis for partially linear models. Journal of the Royal Statistical Society: Series B, 50 (1988) 413–436.
  • Opsomer, J. D. and Ruppert, D., A root-n consistent backfitting estimator for semiparametric additive modeling. Journal of Computational and Graphical Statistics, 8 (1999) 715–732.
  • Zeger, S. L. and Diggle, P. J., Semi-parametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics, 50 (1994) 689–699.
  • Qin, G. Y. and Zhu, Z. Y., Robust estimation in generalized semiparametric mixed models for longitudinal data. Journal of Multivariate Analysis, 98 (2007) 1658–1683.
  • Qin, G. Y. and Zhu, Z. Y., Robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data. Biometrics, 65 (2009) 52–59.
  • Li, Z. and Zhu, L., On variance components in semiparametric mixed models for longitudinal data. Scandinavian Journal of Statistics, 37 (2010) 442–457.
  • Zhang, D., Generalized linear mixedmodels with varying coefficients for longitudinal data. Biometrics, 60 (2004) 8–15.
  • Liang, H., Generalized partially linear mixed-effects models incorporating mismeasured covariates. Annals of the Institute of Statistical Mathematics, 61 (2009) 27–46.
  • Taavoni, M. and Arashi, M., Kernel estimation in semiparametric mixed effect longitudinal modeling. Statistical Papers, https://doi.org/10.1007/s00362-019-01125-8.
  • Henderson, C. R., Estimation of genetic parameters. Annals of the Institute of Statistical Mathematics, 21 (1950) 309–310 (abstract).
  • Henderson, C. R., Kempthorne, O., Searle, S. R., and Von Krosig, C. N., Estimation of environmental and genetic trends from records subject to culling. Biometrics, 15 (1959) 192–218.
  • Gilmour, A. R., Thompson, R., and Cullis, B. R., Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models. Biometrics, 51 (1995) 1440–1450.
  • Searle, S. R., Matrix Algebra Useful for Statistics. John Wiley and Sons, New York, 1982.
  • Newhouse, J. P. and S. D. Oman., An evaluation of ridge estimators. Rand Corporation R-716-PR, (1971) 1–28.

Henderson's method approach to Kernel prediction in partially linear mixed models

Year 2020, Volume: 41 Issue: 3, 571 - 579, 30.09.2020

Özge Kuran , Seçil Yalaz

https://doi.org/10.17776/csj.671812

Abstract

In this article, we propose Kernel prediction in partially linear mixed models by using Henderson's method approach. We derive the Kernel estimator and the Kernel predictor via the mixed model equations (MMEs) of Henderson's that they give the best linear unbiased estimation (BLUE) of the fixed effects parameters and the nonparametric function computationally easier and the best linear unbiased prediction (BLUP) of the random effects parameters as by-products. Additionally, asymptotic property of the Kernel estimator is investigated. A Monte Carlo simulation study is supported to illustrate the performance of Kernel prediction in partially linear mixed models and then, we finalize the article with the help of conclusion and discussion part to summarize the findings.

Keywords

Henderson's method Kernel estimator Kernel predictor Partially linear mixed model Semiparametric models

References

  • Laird, N. M. and Ware, J. H., Random-effects models for longitudinal data. Biometrics, 38 (1982) 963–974.
  • Engle, R. F., Granger, C. W. J., Rice, J. and Weiss, A., Semiparametric estimates of the relation between weather and electricity sales. Journal of the American Statistical Association, 81 (1986) 310-320.
  • Severini, T. A. and Staniswalis, J. G., Quasi-likelihood estimation in semi-parametric models. Journal of the American Statistical Association, 89 (1994) 510-512.
  • Lin, X. and Carroll, R. J., Semiparametric regression for clustered data using generalised estimating equations. Journal of the American Statistical Association, 96 (2001) 1045–1056.
  • Wang, N,. Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika, 90 (2003) 43–52.
  • Rice, J. A., Convergence rates for partially splined models. Statistics & Probability Letters 4 (1986) 204–208.
  • Speckman, P. E., Regression analysis for partially linear models. Journal of the Royal Statistical Society: Series B, 50 (1988) 413–436.
  • Opsomer, J. D. and Ruppert, D., A root-n consistent backfitting estimator for semiparametric additive modeling. Journal of Computational and Graphical Statistics, 8 (1999) 715–732.
  • Zeger, S. L. and Diggle, P. J., Semi-parametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics, 50 (1994) 689–699.
  • Qin, G. Y. and Zhu, Z. Y., Robust estimation in generalized semiparametric mixed models for longitudinal data. Journal of Multivariate Analysis, 98 (2007) 1658–1683.
  • Qin, G. Y. and Zhu, Z. Y., Robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data. Biometrics, 65 (2009) 52–59.
  • Li, Z. and Zhu, L., On variance components in semiparametric mixed models for longitudinal data. Scandinavian Journal of Statistics, 37 (2010) 442–457.
  • Zhang, D., Generalized linear mixedmodels with varying coefficients for longitudinal data. Biometrics, 60 (2004) 8–15.
  • Liang, H., Generalized partially linear mixed-effects models incorporating mismeasured covariates. Annals of the Institute of Statistical Mathematics, 61 (2009) 27–46.
  • Taavoni, M. and Arashi, M., Kernel estimation in semiparametric mixed effect longitudinal modeling. Statistical Papers, https://doi.org/10.1007/s00362-019-01125-8.
  • Henderson, C. R., Estimation of genetic parameters. Annals of the Institute of Statistical Mathematics, 21 (1950) 309–310 (abstract).
  • Henderson, C. R., Kempthorne, O., Searle, S. R., and Von Krosig, C. N., Estimation of environmental and genetic trends from records subject to culling. Biometrics, 15 (1959) 192–218.
  • Gilmour, A. R., Thompson, R., and Cullis, B. R., Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models. Biometrics, 51 (1995) 1440–1450.
  • Searle, S. R., Matrix Algebra Useful for Statistics. John Wiley and Sons, New York, 1982.
  • Newhouse, J. P. and S. D. Oman., An evaluation of ridge estimators. Rand Corporation R-716-PR, (1971) 1–28.
There are 20 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Özge Kuran 0000-0001-5632-001X

Seçil Yalaz 0000-0001-7283-9225

Publication Date September 30, 2020
Submission Date January 7, 2020
Acceptance Date June 15, 2020
Published in Issue Year 2020Volume: 41 Issue: 3

Cite

APA Kuran, Ö., & Yalaz, S. (2020). Henderson’s method approach to Kernel prediction in partially linear mixed models. Cumhuriyet Science Journal, 41(3), 571-579. https://doi.org/10.17776/csj.671812