Identifying local influential observations in Liu estimator. (English) Zbl 1239.62088
Summary: 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 a the result of the research studies on the local influence of minor perturbations of the K. Liu [Commun. Stat., Theory Methods 22, No. 2, 393–402 (1993; Zbl 0784.62065)] estimator in linear regression models. 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 the Liu estimator. Two real data sets are employed to illustrate our methodologies.
MSC:
| 62J20 | Diagnostics, and linear inference and regression |
| 62J05 | Linear regression; mixed models |
| 62H12 | Estimation in multivariate analysis |
Citations:
Zbl 0784.62065References:
| [1] | Atkinson AC (1985) Plots, transformations and regression: an introduction to graphical methods of diagnostic regression analysis. Claredon Press, Oxford · Zbl 0582.62065 |
| [2] | Barnett V, Lewis T (1984) Outliers in statistical data, 2nd edn. Wiley, New York · Zbl 0638.62002 |
| [3] | Belsley DA, Kuh E, Welsch RE (1980) Regression diagnostics: identifying influence data and source of collinearity. Wiley, New York · Zbl 0479.62056 |
| [4] | Belsley DA (1991) Conditioning diagnostics: collinearity and weak data in regression. Wiley, New York · Zbl 0747.62068 |
| [5] | Chatterjee S, Hadi AS (1988) Sensitivity analysis in linear regression. Wiley, New York · Zbl 0648.62066 |
| [6] | Cook RD (1977) Detection of influential observations in linear regression. Technometrics 19: 15–18 · Zbl 0371.62096 · doi:10.2307/1268249 |
| [7] | Cook RD, Weisberg S (1982) Residuals and influence in regression. Chapman & Hall, London · Zbl 0564.62054 |
| [8] | Cook RD (1986) Assessment of local influence. J Royal Stat Assoc Ser B 48: 133–169 · Zbl 0608.62041 |
| [9] | Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation of for nonorthogonal problems. Technometrics 12: 55–67 · Zbl 0202.17205 · doi:10.1080/00401706.1970.10488634 |
| [10] | Hubert MH, Wijekoon P (2006) Improvement of the Liu estimator in linear regression model. J Stat Papers 47: 471–479 · Zbl 1125.62055 · doi:10.1007/s00362-006-0300-4 |
| [11] | Jahufer A, Chen J (2009) Assessing global influential observations in modified ridge regression. Stat Probab Lett 79: 513–518 · Zbl 1155.62051 · doi:10.1016/j.spl.2008.09.019 |
| [12] | Lawrance AJ (1988) Regression transformation diagnostics using local influence. J Am Stat Assoc 83: 1067–1072 · doi:10.1080/01621459.1988.10478702 |
| [13] | Liu K (1993) A new class of biased estimate in linear regression. Commun Stat Theory Methods 22: 393–402 · Zbl 0784.62065 · doi:10.1080/03610929308831027 |
| [14] | 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 · doi:10.1080/01621459.1967.10500896 |
| [15] | Mallows CL (1973) Some comments on C p . Technometrics 15: 661–675 |
| [16] | Mcdonald GC, Galarneau DI (1975) A Monte Carlo evaluation of some ridge-type estimators. J Am Stat Assoc 70: 407–416 · Zbl 0319.62049 · doi:10.1080/01621459.1975.10479882 |
| [17] | Shi L (1997) Local influence in principal component analysis. Biometrika 84(1): 175–186 · Zbl 0883.62060 · doi:10.1093/biomet/84.1.175 |
| [18] | Shi L, Wang X (1999) Local influence in ridge regression. Comput Stat Data Anal 31: 341–353 · Zbl 0990.62055 · doi:10.1016/S0167-9473(99)00019-5 |
| [19] | 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 · Zbl 0073.35602 |
| [20] | Sun H (1988) Macroeconomic impact of direct foreign investment in China: 1979–1996. Blackwell Publishers Ltd., UK |
| [21] | Thomas W, Cook RD (1990) Assessing the influence on predictions from generalized linear model. Technometrics 32: 59–65 · doi:10.1080/00401706.1990.10484593 |
| [22] | Wahba G, Golub GH, Heath CG (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21: 215–223 · Zbl 0461.62059 · doi:10.1080/00401706.1979.10489751 |
| [23] | Walker E, Birch JB (1988) Influence measures in ridge regression. Technometrics 30: 221–227 · doi:10.1080/00401706.1988.10488370 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
