Recent results in ridge regression methods
Tóm tắt
Necessary and sufficient conditions for superiority of the restricted ridge estimator over the restricted least squares estimator are derived when the set of a prior restrictions on parameters are assumed to be incorrect (as well as when the restrictions are assumed to hold). Condition number and trace of mean square error criteria are used to gauge the goodness of some new and some known ridge parameters in rectifying the collinearity problem in three well known real life data sets and a Monte Carlo simulation. Tables 1, 2, 3, 4 and 5 reveal the superiority of the newly formed ridge parameters over some known ridge parameters by means of the foregoing criteria.
Tài liệu tham khảo
Alkhamisi, M.A.: Ridge estimation in linear models with heteroskedatic errors. Sankhy\(\bar{\rm a}\) B 74(2), 302–314 (2012)
Alkhamisi, M.A.: Ridge estimation in linear models with autocorrelated errors. Commun. Stat. Theor. Meth. 39, 2630–2644 (2010)
Andrews, D.F.: A robust method for multiple linear regression. Technometrics 16(4), 523–531 (1974)
Belsley, D.A.: Conditioning Diagnostics. Collinearity and Weak Data in Regression. Wiley, NY (1991)
Chen, J., Gupta, A.K.: Parametric Statistical Change Point Analysis. Birkh\(\ddot{a}\)user, Boston (2000)
Daniel, C., Wood, F.S.: Fitting Equations to Data. Wiley, NY (1971)
Dodge, Y.: The guinea pig of multiple regression. In: Rieder, H. (ed.) Lecture Notes in Statistics, vol. 109, pp. 91–118 (1996)
Draper, N.R., Smith, H.: Applied Regression Analysis. Wiley, NY (1998)
Edelman, A.: Eigenvalues and condition numbers of random matrices. SIAM J. Matrix Anal. Appl. 9, 543–560 (1988)
Greene, W.: Econometric Analysis, 6th edn. Prentice Hall, NJ (2008)
Groß, J.: Restricted ridge estimation. Stat. Probab. Lett. 65, 57–64 (2003)
Gruber, M.H.J.: Improving Efficiency by Shrinkage. Marcel Dekke, NY (1998)
Hinkley, D.V.: Inference about the change point in a sequence of random variables. Biometrika 57, 1–17 (1970)
Hocking, R.R., Speed, F.M., Lynn, M.J.: A class of biased estimators in linear regression. Technometrics 18, 425–438 (1976)
Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for non-orthogonal problems. Technometrics 12, 55–67 (1970)
Hoerl, A.E., Kennard, R.W., Baldwin, K.F.: Ridge regression: some simulation. Commun. Stat. Theor. Meth. 4(2), 105–123 (1975)
Horn, R.A., Johnson, C.A.: Matrix Analysis. Cambridge University Press, New York (1985)
Kibria, B.M.G.: Performance of some new ridge regression estimators. Commun. Stat. Simul. Comput. 32(2), 419–435 (2003)
Liu, K.: Using Liu-type estimator to combat collinearity. Commun. Stat. Theor. Meth. 32(5), 1009–1020 (2003)
MacNeill, I.B.: Tests for change of parameter at unknown time and distributions of some related functionals on Brownian motion. Ann. Stat. 2, 950–962 (1974)
Magnus, J.R., Neudecker, H.: Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley, NY (1999)
Page, E.S.: A test for change in a parameter occurring at an unknown point. Biometrika 42, 532–526 (1955)
Rao, C.R.: Linear Statistical Inferences and its Applications. Wiley, NY (1973)
Vinod, H.D., Ullah, A.: Recent Advances in Regression Methods. Marcel Dekker, NY (1980)
Zhong, Z., Yang, H.: Ridge estimation to the restricted linear model. Commun. Stat. Theor. Meth. 36, 2099–2115 (2007)