Skip to main content
SpringerLink
Log in

Identifying local influential observations in Liu estimator

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

Identifying influential observations is an important step in the right direction of the linear regression model building process. Various influence measures based on different motivational arguments are designed to measure the influence of observations through different aspects of various regression models. This paper is on the result of the research studies on the local influence of minor perturbation on the Liu estimator in linear regression model. The diagnostics under the perturbations of constant variance, individual explanatory variables and assessing the influence on the selection of Liu estimator biasing parameter are derived for Liu estimator. Two real data sets are employed to illustrate our methodologies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Atkinson AC (1985) Plots, transformations and regression: an introduction to graphical methods of diagnostic regression analysis. Claredon Press, Oxford

    MATH  Google Scholar 

  • Barnett V, Lewis T (1984) Outliers in statistical data, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Belsley DA, Kuh E, Welsch RE (1980) Regression diagnostics: identifying influence data and source of collinearity. Wiley, New York

    Book  Google Scholar 

  • Belsley DA (1991) Conditioning diagnostics: collinearity and weak data in regression. Wiley, New York

    MATH  Google Scholar 

  • Chatterjee S, Hadi AS (1988) Sensitivity analysis in linear regression. Wiley, New York

    Book  MATH  Google Scholar 

  • Cook RD (1977) Detection of influential observations in linear regression. Technometrics 19: 15–18

    Article  MathSciNet  MATH  Google Scholar 

  • Cook RD, Weisberg S (1982) Residuals and influence in regression. Chapman & Hall, London

    MATH  Google Scholar 

  • Cook RD (1986) Assessment of local influence. J Royal Stat Assoc Ser B 48: 133–169

    MATH  Google Scholar 

  • Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation of for nonorthogonal problems. Technometrics 12: 55–67

    Article  MATH  Google Scholar 

  • Hubert MH, Wijekoon P (2006) Improvement of the Liu estimator in linear regression model. J Stat Papers 47: 471–479

    Article  MathSciNet  MATH  Google Scholar 

  • Jahufer A, Chen J (2009) Assessing global influential observations in modified ridge regression. Stat Probab Lett 79: 513–518

    Article  MathSciNet  MATH  Google Scholar 

  • Lawrance AJ (1988) Regression transformation diagnostics using local influence. J Am Stat Assoc 83: 1067–1072

    Article  MathSciNet  Google Scholar 

  • Liu K (1993) A new class of biased estimate in linear regression. Commun Stat Theory Methods 22: 393–402

    Article  MATH  Google Scholar 

  • Longley JW (1967) An appraisal of least squares programs for electronic computer from the point of view of the user. J Am Stat Assoc 62: 819–841

    Article  MathSciNet  Google Scholar 

  • Mallows CL (1973) Some comments on C p . Technometrics 15: 661–675

    Article  MATH  Google Scholar 

  • Mcdonald GC, Galarneau DI (1975) A Monte Carlo evaluation of some ridge-type estimators. J Am Stat Assoc 70: 407–416

    Article  MATH  Google Scholar 

  • Shi L (1997) Local influence in principal component analysis. Biometrika 84(1): 175–186

    Article  MathSciNet  MATH  Google Scholar 

  • Shi L, Wang X (1999) Local influence in ridge regression. Comput Stat Data Anal 31: 341–353

    Article  MATH  Google Scholar 

  • Stein C (1956) Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution. Proc Third Berkeley Symp Math Stat Probab 1: 197–206

    Google Scholar 

  • Sun H (1988) Macroeconomic impact of direct foreign investment in China: 1979–1996. Blackwell Publishers Ltd., UK

    Google Scholar 

  • Thomas W, Cook RD (1990) Assessing the influence on predictions from generalized linear model. Technometrics 32: 59–65

    Article  MathSciNet  Google Scholar 

  • Wahba G, Golub GH, Heath CG (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21: 215–223

    Article  MathSciNet  MATH  Google Scholar 

  • Walker E, Birch JB (1988) Influence measures in ridge regression. Technometrics 30: 221–227

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Applied Sciences, South Eastern University of Sri Lanka, Sammanthurai, 32200, Sri Lanka

    Aboobacker Jahufer

  2. Department of Planning and Statistics, School of Economics, Xiamen University, Xiamen, 361005, Peoples Republic of China

    Jianbao Chen

Authors
  1. Aboobacker Jahufer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianbao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aboobacker Jahufer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jahufer, A., Chen, J. Identifying local influential observations in Liu estimator. Metrika 75, 425–438 (2012). https://doi.org/10.1007/s00184-010-0334-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-010-0334-4

Keywords

Search

Navigation