ÖLÇÜM HATALI LiNEER OLMAYAN MODELLER ve EN KÜÇÜK KARELER KESTİRİMİ

Öz

Bu çalışmada, ve için gözlemleri yapıldığında, ölçüm hatalı lineer olmayan Y=f(x; ) fonksiyonel ilişkisine sahip regresiyon modelinin parametreleri hata vektörünün sıfır ortalamaya ve pozitif tanımlı singuler olmayan kovaryans hata matrisi ile normal dağılıma sahip olduğunu kabul ederek hata matrisinin bilindiği veya bilinmediği durumlarda ’nin tamamen türeve dayalı en küçük kareler kestirimi incelenmiştir.

Anahtar Kelimeler

• En küçük kareler,kestirim,lineer olmama,ölçüm hastalı modeller

The Nonlinear Models with Measurement Error and Least Squares Estimation

Öz

In this study , it has been purposed to estimate parameters of nonlineer regression model Y=f(x; ) with functional relationships, where Yt and Xt are both subject to measurement error , when we consider observe ( Yt , Xt ) for and there for it is assumed that the error vector has zero mean value and covariance error matrix with normal distibuted , that is positive defined and nonsinguler . In cases whether covariance error matrix known or unknown, we give least squares estimation about that depend on diferantation .

Anahtar Kelimeler

• Least Squares,Estimaton,Non Linear,Measurement Error Models

Kaynakça

1. Britt H.I. and Lucke R.H. The estimation of parameters in nonlinear implicit model. Tecnometrics, (1973)15, 233-247.
2. Donald W. Marquart.; An algorithm for least squares setimation of nonlinear parameters. J.Soc.Indust. Appl.Math. 11. 2- (1963)
3. Dolby. G.R.; Generalized least squares and Maksimum likelihood Estimation of Nonlinear Fonctional Relationships, J.R. Stat. 25,157-162-(1972).
4. Fuller A.Wayne.; Estimating a Nonlinear errors in variables model with singular error Covairance matrix. procedings of the business and Econometric statistics section. Amer Statist. Assoc. (1975).
5. Fuller A.W. and Wolter. M.K.;Estimation of nonlinear errors in variables models. The. Ann. of statistics. 10.2, 539-548. (1982-a)
6. Seber, G.A.F. and Wild, C.J.; Nonlinear Regression. John Wiley and Sons. Newyork. (1988).
7. DEMİNG, W.E.; The application of least squares. Philosophical magazine series 7,11, 146- 158(1931