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A Study on the Use of Jackknife Method in Biased Estimates

Yıl 2019, , 886 - 892, 31.08.2019
https://doi.org/10.18185/erzifbed.500442

Öz

In the regression analysis, the most widely used method for estimating
the coefficients of the ordinary least squares (OLS) method. For this method to
be used, there should be no relationship between variables. In cases where
explanatory variables are related to each other, the use of OLS estimation
method will lead to incorrect model findings and usage. Different-sided estimators
were developed to analyze with such interdependent independent variables. In
the literature, commonly used biased estimators are compared among themselves
by performing real data and Monte Carlo simulation.

Kaynakça

  • Akdeniz, F.and Kaçıranlar, S. 1995. “On the Almost Unbiased Generalized Liu Estimator and Unbiased Estimation of the Bias and MSE”, Comm. Statist. Theory Methods, 24, 1789-1797.
  • Crouse, R. H., Jin, C., Hanumara, R. C. 1995. “Unbiased Ridge Estimation with Prior Information and Ridge Trace”, Comm. Statist. Theory Methods, 24 9, 2341-2354.
  • Farrar, D. E. and Glauber, R. R. 1967. “Multicollinearity in regression analysis: the problem revisited”, Rev. Econ. Statist. 49(1):92–107.
  • Gruber, M. H. J. (1998) “Improving Efficiency by Shrinkage: The James-Stein and Ridge Regression Estimators”, Marcell Dekker, Inc. New York.
  • Hinkley, D.V. 1977. “Jackknifing in unbalanced situations”, Technometrics, 19, 285–292.
  • Hoerl, A. and Kennard, R. 1970. “Ridge regression: biased estimation for nonorthogonal problems”, Technometrics, 12: 55–67.
  • Hongchang, H. and Yuhe, X. 2013. “Jackknifed Liu estimator İn Linear regresiion Models”, Wuhan University Journal of Natural Sciences, 18, 331-336.
  • Kibria, B.M.G. 2003. “Performance of some new ridge regression estimators”, Commun. Stat. Simul Comput. 32:2389-2413.
  • Liu, K. 1993. “A New Class of Biased Estimate in Linear Regression”, Comm. Statist. Theory Methods, 22, 2, 393-402.
  • Liu, K. 2003. “Using Liu-type estimator to combat collinearity”, Commun. Stat. Theor Meth. 32(5):1009–1020.
  • Montgomery, C.D., Peck, E.A. and Vining, G.G. (2010). “Introduction to Linear Regresssion Analysis” 5 th, Wiley. NewYork.
  • Nomura, M. and Ohkubo, T. 1985. “A Note on Combining Ridge and Principal Component Regression”, Comm. Statist. Theory Methods, 14, 10, 2489-2493.
  • Parker, D. F. And Baye, M. R. 1984. “Combining Ridge and Principal component Regression: A Money Demand Illustration”, Commun. Statist.-Theor. Meth. 13(2), 197-205
  • Sarkar, N.1992. “A New Estimator Combining the Ridge Regression and the Restricted Least Squares Methods for Estimation”, Comm. Statist. Theory Methods, 21, 7, 1987-2000.
  • Sarkar, N. 1996. “Mean Square Error Comparison of Some Estimators in Linear Regressions with Multicollinearity”, Statistics and Probability Letters, 30, 133- 138.
  • Stein, C.1956. “Inadmissibility of Usual Estimator for the Mean of a Multivariate Normal Distribution”, Proceeding of the Third Berkeley Symposium on Mathematical Statistics and Probability. Univeristy of California Press, Berkeley, 197-206.
  • Swindel, F. F. 1976. “Good Ridge Estimators Based on Prior Information”, Comm. Statist. Theory Methods, A5 (11), 1065-1075.
  • Quenouille, M. H. 1956. “Notes on bias in estimation”, Biometrika 43:353–360.
  • Tukey, J. W. 1958. “Bias and confidence in not quite large samples (Abstract)”, Ann. Mathemat. Statist. 29:614.
  • Yıldız, N. 2018. “On the performance of the Jackknified Liu-type estimator in linear regression model”, Comm. Statist. Theory Methods 47 (9), 2278–2290.

Regresyon Analizinde Kullanılan Yanlı Tahmin Edicilerin Etkinliklerinin Karşılaştırılması

Yıl 2019, , 886 - 892, 31.08.2019
https://doi.org/10.18185/erzifbed.500442

Öz

Regresyon analizinde,
katsayıları tahmin etmek için en yaygın olarak kullanılan yöntem, En küçük
kareler (EKK) yöntemidir. Bu yönteminin kullanılabilmesi için değişkenler
arasında ilişki olmaması gerekir. Açıklayıcı değişkenlerin birbirleriyle
ilişkili olduğu durumlarda EKK tahmin yönteminin kullanılması yanlış model
bulgularına ve kullanımına neden olur. Bu tür birbiriyle bağımlılık gösteren
bağımsız değişkenlerle analiz yapmak için farklı yanlı tahmin ediciler
geliştirilmiştir. Literatürde, yaygın olarak kullanılan yanlı tahmin ediciler,
gerek gerçek veri gerekse Monte Carlo simülasyonu yapılarak kendi aralarında
karşılaştırılmıştır.

Kaynakça

  • Akdeniz, F.and Kaçıranlar, S. 1995. “On the Almost Unbiased Generalized Liu Estimator and Unbiased Estimation of the Bias and MSE”, Comm. Statist. Theory Methods, 24, 1789-1797.
  • Crouse, R. H., Jin, C., Hanumara, R. C. 1995. “Unbiased Ridge Estimation with Prior Information and Ridge Trace”, Comm. Statist. Theory Methods, 24 9, 2341-2354.
  • Farrar, D. E. and Glauber, R. R. 1967. “Multicollinearity in regression analysis: the problem revisited”, Rev. Econ. Statist. 49(1):92–107.
  • Gruber, M. H. J. (1998) “Improving Efficiency by Shrinkage: The James-Stein and Ridge Regression Estimators”, Marcell Dekker, Inc. New York.
  • Hinkley, D.V. 1977. “Jackknifing in unbalanced situations”, Technometrics, 19, 285–292.
  • Hoerl, A. and Kennard, R. 1970. “Ridge regression: biased estimation for nonorthogonal problems”, Technometrics, 12: 55–67.
  • Hongchang, H. and Yuhe, X. 2013. “Jackknifed Liu estimator İn Linear regresiion Models”, Wuhan University Journal of Natural Sciences, 18, 331-336.
  • Kibria, B.M.G. 2003. “Performance of some new ridge regression estimators”, Commun. Stat. Simul Comput. 32:2389-2413.
  • Liu, K. 1993. “A New Class of Biased Estimate in Linear Regression”, Comm. Statist. Theory Methods, 22, 2, 393-402.
  • Liu, K. 2003. “Using Liu-type estimator to combat collinearity”, Commun. Stat. Theor Meth. 32(5):1009–1020.
  • Montgomery, C.D., Peck, E.A. and Vining, G.G. (2010). “Introduction to Linear Regresssion Analysis” 5 th, Wiley. NewYork.
  • Nomura, M. and Ohkubo, T. 1985. “A Note on Combining Ridge and Principal Component Regression”, Comm. Statist. Theory Methods, 14, 10, 2489-2493.
  • Parker, D. F. And Baye, M. R. 1984. “Combining Ridge and Principal component Regression: A Money Demand Illustration”, Commun. Statist.-Theor. Meth. 13(2), 197-205
  • Sarkar, N.1992. “A New Estimator Combining the Ridge Regression and the Restricted Least Squares Methods for Estimation”, Comm. Statist. Theory Methods, 21, 7, 1987-2000.
  • Sarkar, N. 1996. “Mean Square Error Comparison of Some Estimators in Linear Regressions with Multicollinearity”, Statistics and Probability Letters, 30, 133- 138.
  • Stein, C.1956. “Inadmissibility of Usual Estimator for the Mean of a Multivariate Normal Distribution”, Proceeding of the Third Berkeley Symposium on Mathematical Statistics and Probability. Univeristy of California Press, Berkeley, 197-206.
  • Swindel, F. F. 1976. “Good Ridge Estimators Based on Prior Information”, Comm. Statist. Theory Methods, A5 (11), 1065-1075.
  • Quenouille, M. H. 1956. “Notes on bias in estimation”, Biometrika 43:353–360.
  • Tukey, J. W. 1958. “Bias and confidence in not quite large samples (Abstract)”, Ann. Mathemat. Statist. 29:614.
  • Yıldız, N. 2018. “On the performance of the Jackknified Liu-type estimator in linear regression model”, Comm. Statist. Theory Methods 47 (9), 2278–2290.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Nilgün Yıldız 0000-0002-4084-1969

Yayımlanma Tarihi 31 Ağustos 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Yıldız, N. (2019). Regresyon Analizinde Kullanılan Yanlı Tahmin Edicilerin Etkinliklerinin Karşılaştırılması. Erzincan University Journal of Science and Technology, 12(2), 886-892. https://doi.org/10.18185/erzifbed.500442