You are here

Nonlinear Least Squares Estimation of the Shifted Gompertz Distribution

Journal Name:

Publication Year:

AMS Codes:

Abstract (2. Language): 
The focus of this paper is the existence of the best nonlinear least squares estimate for the shifted Gompertz distribution. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the lp norm (1 < p < OO).
157
166

REFERENCES

References: 

[1] A. Atieg, G.A. Watson. Use of 1p norms in fitting curves and surfaces to data. ANZIAM J., 45(E):C187-C200, 2004.
[2] D.M. Bates, D.G. Watts. Nonlinear regression analysis and its applications. Wiley, New York, 1988.
[3] A.C. Bemmaor. Modelling the diffusion of new durable goods: Word-of-mouth effect versus consumer heterogeneity. In G. Laurent, G.L. Lilien, B. Pras, editors, Research Traditions in Marketing., pages 201-229, Boston, 1994., Kluwer.
[4] A.C. Bemmaor, J. Lee. The impact of heterogeneity and ill-conditioning on diffusion model parameter estimates. Marketing Sci., 21:209-220, 2002.
[5] A. Björck. Numerical Methods for Least Squares Problems. SIAM, Philadelphia, 1996.
[6] E.Z. Demidenko. Criteria for unconstrained global optimization. J. Optim. Theory
Appl., 136:375-395, 2008.
REFERENCES 166
[7] E.Z. Demidenko. Criteria for global minimum of sum of squares in nonlinear regres¬sion. Comput. Statis. Data Anal., 51:1739-1753, 2006.
[8] E.Z. Demidenko. Is this the least squares estimate?. Biometrika, 87:437-452, 2000.
[9] J.E. Dennis, R.B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, 1996.
[10] P.E. Gill, W. Murray, M.H. Wright. Practical Optimization. Academic Press, London,
1981.
[11] R. Gonin, A.H. Money. Nonlinear Lp-Norm Estimation. Marcel Dekker, New York,
1989.
[12] F. Jimenez, P. Jodra. A note on the moments and computer generation of the shifted Gompertz distribution. Commun. Stat. Theory Methods, 38:75-89, 2009.
[13] F. Jimenez Torres. Estimation of parameters of the shifted Gompertz distribution using least squares, maximum likelihood and moments methods. J. Comput. Appl.
Math., 255:867-877, 2014.
[14] D. Jukic. A simple proof of the existence of the best estimator in a quasilinear re¬gression model. J. Optim. Theory Appl., 162:293-302, 2014.
[15] J.F. Lawless. Statistical models and methods for lifetime data. Wiley, New York, 1982.
[16] D. Markovic, D. Jukic. On parameter estimation in the Bass model by nonlinear least squares fitting the adoption curve. Int. J. Appl. Math. Comput. Sci., 23:145-155, 2013.
[17] D. Markovic, D. Jukic, M. BensiC Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start. J. Comput. Appl. Math.,
228:304-312, 2009.
[18] W. Nelson. Applied life data analysis. Wiley, New York, 1982.
[19] G.J.S. Ross. Nonlinear Estimation. Springer, New York, 1990.
[20] G.A.F. Seber, C.J. Wild. Nonlinear Regression. Wiley, New York, 1989.
[21] V. Srinivasan, C.H. Mason. Nonlinear least squares estimation of new product diffu¬sion models. Marketing Sci., 5:169-178, 1986.

Thank you for copying data from http://www.arastirmax.com