Research Article
Eksik sunumlu doğrusal deterministik regresyon modelinin tahmini: genelleştirilmiş maksimum entropi ve bayesçi yaklaşım
Abstract
Regresyon modelleri; mühendislik, sosyal bilimler ve birçok bilim dalında kullanılmaktadır. Bu çalışmada, eksik sunumlu denklem sistemleriyle gösterilen regresyon modellerin çözümlerinin elde edilişi ele alınmıştır. Bu amaçla çalışmada, Genelleştirilmiş Maksimum Entropi (GME) ile GME ve Genelleştirilmiş Çapraz Entropi (GCE) yöntemlerine alternatif Bayes yaklaşımı kullanılmıştır. Gerçek veri kümesi üzerinde yapılan uygulama sonucunda elde edilen normlara göre tahmin ediciler karşılaştırılmıştır. GME’ye alternatif olarak kullanılabilecek olan Bayes yaklaşımı ile GME karşılaştırıldığında, yapılan uygulama sonucunda GME tahmin edicinin Bayes yaklaşımına göre daha etkin olduğu sonucuna ulaşılmıştır.
Keywords
Eksik sunumlu regresyon modeli genelleştirilmiş maksimum entropi alternatif bayes yaklaşımı
References
- Ciavolinoa E. ve Calcagnì A.A, Generalized Maximum Entropy (GME) estimation approach to fuzzy regression model, Applied Soft Computing, 38, 51–63, 2016.
- Al-Nasser A.D., Two steps generalized maximum entropy estimation procedure for fitting linear regression when both covariates are subject to error, Journal of Applied Statistics, 41 (8), 1708–1720, 2014.
- Grünwald P.D. ve Dawid A.P., Game theory, maximum entropy, minimum discrepancy and robust bayesian decision theory, The Annals of Statistics, 32 (4), 1367–1433, 2004.
- Macedo P. Ridge regression and generalized maximum entropy: an improved version of the ridge–gme parameter estimator. Communications in Statistics - Simulation and Computation, 46 (5), 3527-3539, 2017.
- Ciavolinoa E ve Calcagnì A.A., Generalized maximum entropy (GME) approach for crisp-input/fuzzy-output regression model. Quality & Quantity, 48, 3401–3414, 2014.
- Kamar S.H.ve Msallam B.S., Comparative study between generalized maximum entropy and bayes methods to estimate the four parameter weibull growth model, Journal of Probability and Statistics, 2020, 1-7, 2020.
- Suhartanto D., Kusdibyol L., Chen B., Dean D., Setiawatil L., Predicting consumer behaviour in tourism industry: comparing structural equation modelling (SEM) and multiple regression, Materials Science and Engineering , 830, 1-4, 2019.
- Heckelei T., Mittelhammer R., Jansson T., A Bayesian alternative to generalized cross entropy solutions for underdetermined econometric models. Discussion paper, Institute for Food and Resource Economics, University of Bonn, 2008.
- Tarkhamtham P. ve Yamaka W., High-order generalized maximum entropy estimator in kink regression model, Thai Journal of Mathematics, Special Issue: Structural Change Modeling and Optimization in Econometrics 2018, 185-200, 2019.
- Chinnakum W. ve Boonyasana P., Modelling thailand tourism demand: a dual generalized maximum entropy, Thai Journal of Mathematics, Special Issue on Entropy in Econometrics, 67–78, 2017.
- Maneejuk P., Yamaka W., Sriboonchitta S., Entropy inference in smooth transition kink regression, Communications in Statistics - Simulation and Computation, 1-24, 2020.
- Paris Q. ve Howitt R.E., An analysis of ill-posed production problems using maximum entropy. American Journal of Agricultural Economics, 80 (1), 124-138, 1998.
- Golan A., Judge G., Miller D. Maximum Entropy Econometrics: Robust Estimation with Limited Data. John Wiley & Sons, New York, A.B.D., 1996.
- Ramanathan R., Introductory Econometrics with Applications. Fourth Edition, Harcourt Brace College Publishers, 1998.
- Shannon C.E., A mathematical theory of communication. The Bell System Technical Journal, 27 (3), 379-423, 1948.
- Jaynes E.T. Information theory and statistical mechanics. Physical Review, 106 (4), 620-630, 1957.
- Jaynes E.T. Information theory and statistical mechanics II. Physics Rewiev, 108 (2), 171-190, 1957.
- Campbell L.L., Minimum cross entropy estimation with inaccurate side information. IEEE Transactions on Information Theory, 45 (7), 2650-2652, 1999.
- Zellner A., Introduction to Bayesian Inference in Econometrics. John Wiley & Sons, New York, A.B.D., 1971.
- Hill R.C., Griffihts W.E., Judge G.G., Undergraduate Econometrics, John Wiley & Sons. New York, A.B.D., 2001.
Year 2022,
Volume: 37 Issue: 2, 815 - 824, 28.02.2022
Abstract
References
- Ciavolinoa E. ve Calcagnì A.A, Generalized Maximum Entropy (GME) estimation approach to fuzzy regression model, Applied Soft Computing, 38, 51–63, 2016.
- Al-Nasser A.D., Two steps generalized maximum entropy estimation procedure for fitting linear regression when both covariates are subject to error, Journal of Applied Statistics, 41 (8), 1708–1720, 2014.
- Grünwald P.D. ve Dawid A.P., Game theory, maximum entropy, minimum discrepancy and robust bayesian decision theory, The Annals of Statistics, 32 (4), 1367–1433, 2004.
- Macedo P. Ridge regression and generalized maximum entropy: an improved version of the ridge–gme parameter estimator. Communications in Statistics - Simulation and Computation, 46 (5), 3527-3539, 2017.
- Ciavolinoa E ve Calcagnì A.A., Generalized maximum entropy (GME) approach for crisp-input/fuzzy-output regression model. Quality & Quantity, 48, 3401–3414, 2014.
- Kamar S.H.ve Msallam B.S., Comparative study between generalized maximum entropy and bayes methods to estimate the four parameter weibull growth model, Journal of Probability and Statistics, 2020, 1-7, 2020.
- Suhartanto D., Kusdibyol L., Chen B., Dean D., Setiawatil L., Predicting consumer behaviour in tourism industry: comparing structural equation modelling (SEM) and multiple regression, Materials Science and Engineering , 830, 1-4, 2019.
- Heckelei T., Mittelhammer R., Jansson T., A Bayesian alternative to generalized cross entropy solutions for underdetermined econometric models. Discussion paper, Institute for Food and Resource Economics, University of Bonn, 2008.
- Tarkhamtham P. ve Yamaka W., High-order generalized maximum entropy estimator in kink regression model, Thai Journal of Mathematics, Special Issue: Structural Change Modeling and Optimization in Econometrics 2018, 185-200, 2019.
- Chinnakum W. ve Boonyasana P., Modelling thailand tourism demand: a dual generalized maximum entropy, Thai Journal of Mathematics, Special Issue on Entropy in Econometrics, 67–78, 2017.
- Maneejuk P., Yamaka W., Sriboonchitta S., Entropy inference in smooth transition kink regression, Communications in Statistics - Simulation and Computation, 1-24, 2020.
- Paris Q. ve Howitt R.E., An analysis of ill-posed production problems using maximum entropy. American Journal of Agricultural Economics, 80 (1), 124-138, 1998.
- Golan A., Judge G., Miller D. Maximum Entropy Econometrics: Robust Estimation with Limited Data. John Wiley & Sons, New York, A.B.D., 1996.
- Ramanathan R., Introductory Econometrics with Applications. Fourth Edition, Harcourt Brace College Publishers, 1998.
- Shannon C.E., A mathematical theory of communication. The Bell System Technical Journal, 27 (3), 379-423, 1948.
- Jaynes E.T. Information theory and statistical mechanics. Physical Review, 106 (4), 620-630, 1957.
- Jaynes E.T. Information theory and statistical mechanics II. Physics Rewiev, 108 (2), 171-190, 1957.
- Campbell L.L., Minimum cross entropy estimation with inaccurate side information. IEEE Transactions on Information Theory, 45 (7), 2650-2652, 1999.
- Zellner A., Introduction to Bayesian Inference in Econometrics. John Wiley & Sons, New York, A.B.D., 1971.
- Hill R.C., Griffihts W.E., Judge G.G., Undergraduate Econometrics, John Wiley & Sons. New York, A.B.D., 2001.
There are 20 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | February 28, 2022 |
| Submission Date | March 15, 2021 |
| Acceptance Date | August 20, 2021 |
| Published in Issue | Year 2022 Volume: 37 Issue: 2 |