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Comparison of the r- (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function

Year 2015, Volume: 7 Issue: 1, 1 - 12, 01.04.2015
https://doi.org/10.33818/ier.278037

Abstract

In the case of ill-conditioned design matrix in linear regression model, the r - (k, d) class estimator was proposed, including the ordinary least squares (OLS) estimator, the principal component regression (PCR) estimator, and the two-parameter class estimator. In this paper, we opted to evaluate the performance of the r - (k, d) class estimator in comparison to others under the weighted quadratic loss function where the weights are inverse of the variance-covariance matrix of the estimator, also known as the Mahalanobis loss function using the criterion of average loss. Tests verifying the conditions for superiority of the r - (k, d) class estimator have also been proposed. Finally, a simulation study and also an empirical illustration have been done to study the performance of the tests and hence verify the conditions of dominance of the r - (k, d) class estimator over the others under the Mahalanobis loss function in artificially generated data sets and as well as for a real data. To the best of our knowledge, this study provides stronger evidence of superiority of the r - (k, d) class estimator over the other competing estimators through tests for verifying the conditions of dominance, available in literature on multicollinearity.

References

  • Baye, M.R. and D.F. Parker (1984). Combining ridge and principal components regression: a money demand illustration. Communications in Statistics-Theory and Methods, 13 (2), 197-205.
  • Draper, N.R. and A. Smith (1981). Applied Regression Analysis. (II edition) New York: Wiley.
  • Hald, A. (1952). Statistical Theory with Engineering Applications. New York: Wiley, 647.
  • Hoerl, A.E. and R.W. Kennard (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55-67.
  • Johnson, N.L., S. Kotz and N. Balakrishnan (2004). Continuous Univariate Distributions. Vol 2 (II edition) New York: Wiley.
  • Massy, M.F. (1965). Principal component regression in explanatory research. Journal of the American Statistical Association, 60, 234-266.
  • Montgomery, D.C. and E.A. Peck (1982). Introduction to linear regression analysis. New York: Wiley.
  • Newhouse, J.P. and S.D. Oman (1971). An evaluation of ridge estimators. Rand corporation, 1-29.
  • Nomura, M. and T. Okhuba (1985). A note on combining ridge and principal component regression. Communications in Statistics-Theory and Methods, 14, 489-2493.
  • Özkale, M.R. and S. Kaçiranlar (2007). The restricted and unrestricted two parameter estimators. Communications in Statistics-Theory and Methodsi 36 (15), 2707-2725.
  • Özkale M.R. (2012). Combining the unrestricted estimators into a single estimator and a simulation study on the unrestricted estimators. Journal of Statistical Computation and Simulation, 62 (4), 653-688.
  • Peddada, S.D., A.K. Nigam and A.K. Saxena (1989). On the inadmissibility of ridge estimator in a linear model. Communications in Statistics-Theory and Methods, 18 (10), 3571- 3585.
  • Piepel, G. and T. Redgate (1998). A mixture experiment analysis with Hald Cement data. Journal of the American Statistical Association, 52 (1), 23-30.
  • Sarkar, N. (1992). A new estimator combining the ridge regression and the restricted least squares methods of estimation. Communications in Statistics-Theory and Methods, 21, 1987-2000.
  • Sarkar, N. (1996). Mean square error matrix comparison of some estimators in linear regression with multicollinearity. Statistics and Probability Letters, 30, 133-138.
  • Üstündaǧ-Şiray, G. and S. Sakallioğlu (2012). Superiority of the r-k class estimator over some estimators in a linear model. Communications in Statistics-Theory and Methods, 41 (15), 2819-2832.
Year 2015, Volume: 7 Issue: 1, 1 - 12, 01.04.2015
https://doi.org/10.33818/ier.278037

Abstract

References

  • Baye, M.R. and D.F. Parker (1984). Combining ridge and principal components regression: a money demand illustration. Communications in Statistics-Theory and Methods, 13 (2), 197-205.
  • Draper, N.R. and A. Smith (1981). Applied Regression Analysis. (II edition) New York: Wiley.
  • Hald, A. (1952). Statistical Theory with Engineering Applications. New York: Wiley, 647.
  • Hoerl, A.E. and R.W. Kennard (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55-67.
  • Johnson, N.L., S. Kotz and N. Balakrishnan (2004). Continuous Univariate Distributions. Vol 2 (II edition) New York: Wiley.
  • Massy, M.F. (1965). Principal component regression in explanatory research. Journal of the American Statistical Association, 60, 234-266.
  • Montgomery, D.C. and E.A. Peck (1982). Introduction to linear regression analysis. New York: Wiley.
  • Newhouse, J.P. and S.D. Oman (1971). An evaluation of ridge estimators. Rand corporation, 1-29.
  • Nomura, M. and T. Okhuba (1985). A note on combining ridge and principal component regression. Communications in Statistics-Theory and Methods, 14, 489-2493.
  • Özkale, M.R. and S. Kaçiranlar (2007). The restricted and unrestricted two parameter estimators. Communications in Statistics-Theory and Methodsi 36 (15), 2707-2725.
  • Özkale M.R. (2012). Combining the unrestricted estimators into a single estimator and a simulation study on the unrestricted estimators. Journal of Statistical Computation and Simulation, 62 (4), 653-688.
  • Peddada, S.D., A.K. Nigam and A.K. Saxena (1989). On the inadmissibility of ridge estimator in a linear model. Communications in Statistics-Theory and Methods, 18 (10), 3571- 3585.
  • Piepel, G. and T. Redgate (1998). A mixture experiment analysis with Hald Cement data. Journal of the American Statistical Association, 52 (1), 23-30.
  • Sarkar, N. (1992). A new estimator combining the ridge regression and the restricted least squares methods of estimation. Communications in Statistics-Theory and Methods, 21, 1987-2000.
  • Sarkar, N. (1996). Mean square error matrix comparison of some estimators in linear regression with multicollinearity. Statistics and Probability Letters, 30, 133-138.
  • Üstündaǧ-Şiray, G. and S. Sakallioğlu (2012). Superiority of the r-k class estimator over some estimators in a linear model. Communications in Statistics-Theory and Methods, 41 (15), 2819-2832.
There are 16 citations in total.

Details

Subjects Business Administration
Other ID JA95HY53YV
Journal Section Articles
Authors

Shalini Chandra This is me

Nityananda Sarkar This is me

Publication Date April 1, 2015
Submission Date April 1, 2015
Published in Issue Year 2015 Volume: 7 Issue: 1

Cite

APA Chandra, S., & Sarkar, N. (2015). Comparison of the r- (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function. International Econometric Review, 7(1), 1-12. https://doi.org/10.33818/ier.278037
AMA Chandra S, Sarkar N. Comparison of the r- (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function. IER. June 2015;7(1):1-12. doi:10.33818/ier.278037
Chicago Chandra, Shalini, and Nityananda Sarkar. “Comparison of the R- (k, D) Class Estimator With Some Estimators for Multicollinearity under the Mahalanobis Loss Function”. International Econometric Review 7, no. 1 (June 2015): 1-12. https://doi.org/10.33818/ier.278037.
EndNote Chandra S, Sarkar N (June 1, 2015) Comparison of the r- (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function. International Econometric Review 7 1 1–12.
IEEE S. Chandra and N. Sarkar, “Comparison of the r- (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function”, IER, vol. 7, no. 1, pp. 1–12, 2015, doi: 10.33818/ier.278037.
ISNAD Chandra, Shalini - Sarkar, Nityananda. “Comparison of the R- (k, D) Class Estimator With Some Estimators for Multicollinearity under the Mahalanobis Loss Function”. International Econometric Review 7/1 (June 2015), 1-12. https://doi.org/10.33818/ier.278037.
JAMA Chandra S, Sarkar N. Comparison of the r- (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function. IER. 2015;7:1–12.
MLA Chandra, Shalini and Nityananda Sarkar. “Comparison of the R- (k, D) Class Estimator With Some Estimators for Multicollinearity under the Mahalanobis Loss Function”. International Econometric Review, vol. 7, no. 1, 2015, pp. 1-12, doi:10.33818/ier.278037.
Vancouver Chandra S, Sarkar N. Comparison of the r- (k, d) class estimator with some estimators for multicollinearity under the Mahalanobis loss function. IER. 2015;7(1):1-12.