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Ölçüm Hatalı Kısmi Lineer Karma Modellerde Modified Kernel Ridge Öntahmin Edicilerin Covid-19 Veri Analizi Yoluyla Performans Değerlendirmesi

Yıl 2024, Cilt: 26 Sayı: 76, 134 - 140, 23.01.2024

Özge Kuran Seçil Yalaz

https://doi.org/10.21205/deufmd.2024267615

Öz

Bu çalışmada, ölçüm hatalı kısmi lineer karma modellerde çoklu iç ilişki durumu altında yeni öntahmin ediciler tanımlanmaktadır. Bu amaca ulaşmak için, bazı ön bilgiler ele alınmıştır ve bu bilgi hesaba katılarak, ölçüm hatalı kısmi lineer karma modellerde modified Kernel ridge öntahmin edicileri önerilmiştir. Ek olarak, ölçüm hatalı kısmi lineer karma model literatüründe daha önce tanımlanan öntahmin ediciler ile yeni tanımlanan modified Kernel ridge öntahmin ediciler arasında bazı hata kareler ortalama karşılaştırmaları da yapılmıştır. Daha sonra, teorik bulgularımızı kanıtlamak için gerçek bir veri analizi ve simülasyon çalışması ile makale sonlandırılmıştır.

Anahtar Kelimeler

Lineer Karma Model Ölçüm Hatası Çoklu İç İlişki Kısmi Lineer Model Ridge Öntahmin Ediciler

Kaynakça

  • Laird, N.M., Ware, J.H. 1982. Random-Effects Models for Longitudinal Data, Biometrics, Vol. 38, No. 4 p. 963-974, DOI: 10.2307/2529876.
  • Fuller, W.A. 1987.Measurement Error Models, John Wiley and Sons, Inc., Hoboken, NJ.
  • Yalaz, S., Kuran, Ö. 2021. Kernel Estimator and Predictor of Partially Linear Mixed-Effect Errors-in-Variables Model, Journal of Statistical Computation and Simulation, Vol. 91, No. 5, p. 934–951, DOI:10.1080/00949655.2020.1836642.
  • Hoerl, A.E., Kennard, R.W. 1970. Ridge Regression Biased Estimation for Nonorthogonal Problems, Technometrics, Vol. 12, No. 1, p. 55–67, DOI: 10.2307/1267351.
  • Liu, X.Q., Hu, P. 2013. General Ridge Predictors in a Mixed Linear Model, Journal of Theoretical and Applied Statistics, Vol. 47, No. 2, p. 363-378, DOI: 10.1080/02331888.2011.592190.
  • Özkale, M.R., Can, F. 2017. An Evaluation of Ridge Estimator in Linear Mixed Models: An Example from Kidney Failure Data, Journal of Applied Statistics, Vol. 44, No. 12, p. 2251-2269, DOI: 10.1080/02664763.2016.1252732.
  • Kuran, Ö., Yalaz, S. 2022. Kernel Ridge Prediction Method in Partially Linear Mixed Measurement Error Model, Communications in Statistics - Simulation and Computation, Vol., No., p. 1–22, DOI:10.1080/03610918.2022.2075389.
  • Liu, K. 1993. A New Class of Biased Estimate in Linear Regression, Communications in Statistics - Theory and Methods,Vol. 22, No.2, p. 393–402, DOI: 10.1080/03610929308831027.
  • Swindel, B.F. 1976. Good Estimators Based on Prior Information, Communications in Statistics -Theory and Methods, Vol. 5, No.11,p. 1065-1075, DOI: 10.1080/03610927608827423.
  • Özkale, M.R., Kuran, Ö. 2020. A Further Prediction Method in Linear Mixed Models: Liu Prediction, Communications in Statistics - Simulation and Computation, Vol. 49, No. 12, p.3171–3195, DOI: 10.1080/03610918.2018.1535071.
  • Kuran, Ö., Yalaz, S. 2022. Kernel Liu Prediction Approach in Partially Linear Mixed Measurement Error Models, Statistics: A Journal of Theoretical and Applied Statistics, Vol. 56, No. 6, p. 1385-1408, DOI: 10.1080/02331888.2022.2152816.
  • Kuran, Ö. 2020. The Modified Ridge Prediction Method in the Linear Mixed Models, 3nd International Congress on Statistics, Mathematics and Analytical, 12-13 March-2020, İstanbul, Turkey, 33-43.
  • Özkale, M.R., Kaçıranlar, S. 2007. The Restricted and Unrestricted Two-Parameter Estimators, Communications in Statistics - Theory and Methods Vol. 36, No.15, p. 2707–2725, DOI: 10.1080/03610920701386877.
  • Gilmour, A.R., Thompson, R., Cullis, B.R. 1995. Average Information REML: An Efficient Algorithm for Variance Parameter Estimation in Linear Mixed Models, Biometrics, Vol. 51, No. 4, p. 1440-1450, DOI:10.2307/2533274.
  • Searle, S.R. 1982. Matrix Algebra Useful for Statistics, John Wiley and Sons, New York.
  • Pereira, L.N., Coelho, P.S. 2012. A Small Area Predictor Under Area-Level Linear Mixed Models with Restrictions, Communications in Statistics -Theory and Methods, Vol. 41, No. 13-14, p. 2524-2544, DOI:10.1080/03610926.2011.648000.
  • Robinson, G.K. 1991. That BLUP is a Good Thing: The Estimation of Random Effects (with Discussion), Statistical Science, Vol. 6, No. 1, p. 15-51, DOI: 10.1214/ss/1177011926.
  • Štulajter, F. 1997. Predictions in Nonlinear Regression Models, Acta Math Univ Comenian, Vol. LXVI, No. 1, p. 71–81.
  • European Centre for Disease Prevention and Control, COVID-19 Vaccine Tracker. Available at: https://vaccinetracker.ecdc.europa.eu/public/extensions/COVID-19/vaccine-tracker.html, 2021.
  • European Centre for Disease Prevention and Control. Download COVID-19 Datasets.Available at: https://www.ecdc.europa.eu/en/covid-19/data, 2021.
  • Bowman, A., Azzalini, A. 1997. Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-plus Illustrations, New York, Oxford.
  • McDonald, G. C., and D. I. Galarneau. 1975. A Monte Carlo Evaluation of Some Ridge-Type Estimators. Journal of the American Statistical Association, Vol. 70, No. 350, p. 407–416, DOI: 10.1080/01621459.1975.10479882.
  • Newhouse, J. P., and S. D. Oman. 1971. An Evaluation of Ridge Estimators. 1–28. Rand Corporation R-716-PR. https://www.rand.org/content/dam/rand/pubs/reports/2007/R716.pdf

Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis

Yıl 2024, Cilt: 26 Sayı: 76, 134 - 140, 23.01.2024

Özge Kuran Seçil Yalaz

https://doi.org/10.21205/deufmd.2024267615

Öz

In this article we describe new predictors under multicollinearity situation in the partially linear mixed measurement error models. In order to achieve this aim, we refer to some preliminary information and use it in order to suggest the modified Kernel ridge predictors in the partially linear mixed measurement error models. In addition, we also attain some mean square error comparisons between our new described modified Kernel ridge predictors and predictors previously described in literature for the partially linear mixed measurement error model. In conclusion, the article showcases real data analysis and a simulation study to illusrate our theoretical findings.

Anahtar Kelimeler

Linear Mixed Model Measurement Error Multicollinearity Partially Linear Model Ridge Predictor

Kaynakça

  • Laird, N.M., Ware, J.H. 1982. Random-Effects Models for Longitudinal Data, Biometrics, Vol. 38, No. 4 p. 963-974, DOI: 10.2307/2529876.
  • Fuller, W.A. 1987.Measurement Error Models, John Wiley and Sons, Inc., Hoboken, NJ.
  • Yalaz, S., Kuran, Ö. 2021. Kernel Estimator and Predictor of Partially Linear Mixed-Effect Errors-in-Variables Model, Journal of Statistical Computation and Simulation, Vol. 91, No. 5, p. 934–951, DOI:10.1080/00949655.2020.1836642.
  • Hoerl, A.E., Kennard, R.W. 1970. Ridge Regression Biased Estimation for Nonorthogonal Problems, Technometrics, Vol. 12, No. 1, p. 55–67, DOI: 10.2307/1267351.
  • Liu, X.Q., Hu, P. 2013. General Ridge Predictors in a Mixed Linear Model, Journal of Theoretical and Applied Statistics, Vol. 47, No. 2, p. 363-378, DOI: 10.1080/02331888.2011.592190.
  • Özkale, M.R., Can, F. 2017. An Evaluation of Ridge Estimator in Linear Mixed Models: An Example from Kidney Failure Data, Journal of Applied Statistics, Vol. 44, No. 12, p. 2251-2269, DOI: 10.1080/02664763.2016.1252732.
  • Kuran, Ö., Yalaz, S. 2022. Kernel Ridge Prediction Method in Partially Linear Mixed Measurement Error Model, Communications in Statistics - Simulation and Computation, Vol., No., p. 1–22, DOI:10.1080/03610918.2022.2075389.
  • Liu, K. 1993. A New Class of Biased Estimate in Linear Regression, Communications in Statistics - Theory and Methods,Vol. 22, No.2, p. 393–402, DOI: 10.1080/03610929308831027.
  • Swindel, B.F. 1976. Good Estimators Based on Prior Information, Communications in Statistics -Theory and Methods, Vol. 5, No.11,p. 1065-1075, DOI: 10.1080/03610927608827423.
  • Özkale, M.R., Kuran, Ö. 2020. A Further Prediction Method in Linear Mixed Models: Liu Prediction, Communications in Statistics - Simulation and Computation, Vol. 49, No. 12, p.3171–3195, DOI: 10.1080/03610918.2018.1535071.
  • Kuran, Ö., Yalaz, S. 2022. Kernel Liu Prediction Approach in Partially Linear Mixed Measurement Error Models, Statistics: A Journal of Theoretical and Applied Statistics, Vol. 56, No. 6, p. 1385-1408, DOI: 10.1080/02331888.2022.2152816.
  • Kuran, Ö. 2020. The Modified Ridge Prediction Method in the Linear Mixed Models, 3nd International Congress on Statistics, Mathematics and Analytical, 12-13 March-2020, İstanbul, Turkey, 33-43.
  • Özkale, M.R., Kaçıranlar, S. 2007. The Restricted and Unrestricted Two-Parameter Estimators, Communications in Statistics - Theory and Methods Vol. 36, No.15, p. 2707–2725, DOI: 10.1080/03610920701386877.
  • Gilmour, A.R., Thompson, R., Cullis, B.R. 1995. Average Information REML: An Efficient Algorithm for Variance Parameter Estimation in Linear Mixed Models, Biometrics, Vol. 51, No. 4, p. 1440-1450, DOI:10.2307/2533274.
  • Searle, S.R. 1982. Matrix Algebra Useful for Statistics, John Wiley and Sons, New York.
  • Pereira, L.N., Coelho, P.S. 2012. A Small Area Predictor Under Area-Level Linear Mixed Models with Restrictions, Communications in Statistics -Theory and Methods, Vol. 41, No. 13-14, p. 2524-2544, DOI:10.1080/03610926.2011.648000.
  • Robinson, G.K. 1991. That BLUP is a Good Thing: The Estimation of Random Effects (with Discussion), Statistical Science, Vol. 6, No. 1, p. 15-51, DOI: 10.1214/ss/1177011926.
  • Štulajter, F. 1997. Predictions in Nonlinear Regression Models, Acta Math Univ Comenian, Vol. LXVI, No. 1, p. 71–81.
  • European Centre for Disease Prevention and Control, COVID-19 Vaccine Tracker. Available at: https://vaccinetracker.ecdc.europa.eu/public/extensions/COVID-19/vaccine-tracker.html, 2021.
  • European Centre for Disease Prevention and Control. Download COVID-19 Datasets.Available at: https://www.ecdc.europa.eu/en/covid-19/data, 2021.
  • Bowman, A., Azzalini, A. 1997. Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-plus Illustrations, New York, Oxford.
  • McDonald, G. C., and D. I. Galarneau. 1975. A Monte Carlo Evaluation of Some Ridge-Type Estimators. Journal of the American Statistical Association, Vol. 70, No. 350, p. 407–416, DOI: 10.1080/01621459.1975.10479882.
  • Newhouse, J. P., and S. D. Oman. 1971. An Evaluation of Ridge Estimators. 1–28. Rand Corporation R-716-PR. https://www.rand.org/content/dam/rand/pubs/reports/2007/R716.pdf
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Sayısal Analiz
Bölüm Araştırma Makalesi
Yazarlar

Özge Kuran 0000-0001-5632-001X

Seçil Yalaz 0000-0001-7283-9225

Erken Görünüm Tarihi 22 Ocak 2024
Yayımlanma Tarihi 23 Ocak 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 26 Sayı: 76

Kaynak Göster

APA Kuran, Ö., & Yalaz, S. (2024). Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, 26(76), 134-140. https://doi.org/10.21205/deufmd.2024267615
AMA Kuran Ö, Yalaz S. Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis. DEUFMD. Ocak 2024;26(76):134-140. doi:10.21205/deufmd.2024267615
Chicago Kuran, Özge, ve Seçil Yalaz. “Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi 26, sy. 76 (Ocak 2024): 134-40. https://doi.org/10.21205/deufmd.2024267615.
EndNote Kuran Ö, Yalaz S (01 Ocak 2024) Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 26 76 134–140.
IEEE Ö. Kuran ve S. Yalaz, “Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis”, DEUFMD, c. 26, sy. 76, ss. 134–140, 2024, doi: 10.21205/deufmd.2024267615.
ISNAD Kuran, Özge - Yalaz, Seçil. “Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 26/76 (Ocak 2024), 134-140. https://doi.org/10.21205/deufmd.2024267615.
JAMA Kuran Ö, Yalaz S. Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis. DEUFMD. 2024;26:134–140.
MLA Kuran, Özge ve Seçil Yalaz. “Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, c. 26, sy. 76, 2024, ss. 134-40, doi:10.21205/deufmd.2024267615.
Vancouver Kuran Ö, Yalaz S. Performance Assessment of the Modified Kernel Ridge Predictors in the Partially Linear Mixed Measurement Error Models via Covid-19 Data Analysis. DEUFMD. 2024;26(76):134-40.

Dokuz Eylül Üniversitesi, Mühendislik Fakültesi Dekanlığı Tınaztepe Yerleşkesi, Adatepe Mah. Doğuş Cad. No: 207-I / 35390 Buca-İZMİR.