Abstract
In this article, we proposed a new estimator namely, modified jackknifed generalized Liu-type estimator (MJGLE). It is based on the criterion that it combines the ideas underlying both the generalized Liu estimator (GLE) and jackknifed generalized Liu estimator (JGLE). The performance of this estimator (MJGLE) is compared to that of the GLE and the JGLE. The ideas in the article are illustrated and evaluated using a real data example and simulations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akdeniz F (2004) New biased estimators under the LINEX loss function. Stat Papers 45: 175–190
Akdeniz F, Erol H (2003) Mean squared error comparisons of some biased estimators in linear regression. Commun Stat Theory Methods 32(12): 2391–2415
Akdeniz F, Kaçıranlar S (1995) On the almost unbiased generalized Liu estimator and unbiased estimation of the Bias and MSE. Commun Stat Theory Methods 24(7): 1789–1797
Akdeniz F, Akdeniz Duran E (2009) Liu-type estimator in semiparametric regression Model. J Stat Comput Simul. doi:10.1080/00949650902821699
Batah F, Ramanathan TK, Gore SD (2008) The efficiency of modified jackknife and ridge type regression estimators: a comparison. Surv Math Appl 3: 111–122
Belsley DA (1991) Conditioning diagnostics: collinearity and weak data in regression. Wiley, New York
Farebrother RW (1976) Further results on the mean square error of ridge regression. J R Stat Soc B 38: 248–250
Gross J (2003) Linear regression. Springer, Berlin
Hinkley DV (1977) Jackknifing in unbalanced situations. Technometrics 19: 285–292
Hoerl AE, Kennard RW (1970) Ridge regression: applications to nonorthogonal problems. Technometrics 12: 69–82
Hubert MH, Wijekoon P (2006) Improvement of the Liu estimation in linear regression model. Stat Papers 47(3): 471–479
Liu KJ (1993) A new class of biased estimate in linear regression. Commun Stat Theory Methods 22(2): 393–402
Liu KJ (2003) Using Liu type estimator to combat multicollinearity. Commun Stat Theory Methods 32(5): 1009–1020
McDonald GC, Galarnaeu DI (1975) A Monte Carlo evaluation of some ridge-type estimators. J Am Stat Assoc 20: 407–416
Nyquist H (1988) Applications of the jackknife procedure in ridge regression. Comput Stat Data Anal 6: 177–183
Singh B, Chaubey YP, Dwivedi TD (1986) An almost unbiased ridge estimator. Sankhya Indian J Stat Ser B 48: 342–346
Stein C (1956) Inadmissibility of the usual estimator fort he mean of a multivariate normal distribution. In: Proceedings of the third Berkeley symposium on mathematical statistics and probability, vol 1, pp 197–206
Torigoe N, Ujiie K (2006) On the restricted Liu estimator in the Gauss–Markov model. Commun Stat Theory Methods 35: 1713–1722
Yang H, Xu J (2008) Tuning parameters selection and various good fitting characteristics for the Liu-type estimators in linear regression. Commun Stat Theory Methods 37: 3204–3215
Yang H, Xu J (2009) An alternative stochastic restricted Liu estimator in linear regression. Stat Papers 50(3): 639–647
Yang H, Chang XF, Liu D (2009) Improvement of the Liu estimator in weighted mixed regression. Commun Stat Theory Methods 38: 285–292
Yatchew A (2003) Semiparametric regression for the applied econometrican. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Akdeniz Duran, E., Akdeniz, F. Efficiency of the modified jackknifed Liu-type estimator. Stat Papers 53, 265–280 (2012). https://doi.org/10.1007/s00362-010-0334-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-010-0334-5
Keywords
- Almost unbiased Liu estimator
- Jackknifed estimator
- Liu-type estimator
- Multicollinearity
- Ridge regression estimator