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http://dx.doi.org/10.5351/KJAS.2004.17.3.489

Generalized Weighted Linear Models Based on Distribution Functions - A Frequentist Perspective  

여인권 (숙명여자대학교 이과대학 수학통계학부)
Publication Information
The Korean Journal of Applied Statistics / v.17, no.3, 2004 , pp. 489-498 More about this Journal
Abstract
In this paper, a new form of linear models referred to as generalized weighted linear models is proposed. The proposed models assume that the relationship between the response variable and explanatory variables can be modelled by a distribution function of the response mean and a weighted linear combination of distribution functions of covariates. This form addresses a structural problem of the link function in the generalized linear models in which the parameter space may not be consistent with the space derived from linear predictors. The maximum likelihood estimation with Lagrange's undetermined multipliers is used to estimate the parameters and resampling method is applied to compute confidence intervals and to test hypotheses.
Keywords
Conjugate family; Exponential family; Mixture of beta distributions; Parametric transformation;
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1 Yeo, I. K. and Johnson, R. A. (2000), A new family of power transformations to improve normality or symmetry, Biometrika, 87, 954-959   DOI   ScienceOn
2 Yeo, I. K. (2001), Goodness of link tests for binaary response data, <한국통계학회논문집>, 8, 357-366
3 Arando-Ordaz, F. J. (1981), On two families of transformations to additivity for binary response data, Biometrika, 68, 357-363   DOI   ScienceOn
4 Cheng, K. F. and Wu, J. W. (1994), Testing goodness of fit for a parametric family of link function, Journal of the American Statistical Association, 89, 657-664   DOI   ScienceOn
5 Guerrero, V. M. and Johnson, R. A. (1982), Use of the Box-Cox transformation with binary response models, Biometrika, 69, 309-314   DOI   ScienceOn
6 John, J. A. and Draper, N. R. (1980), An alternative family of transformations, Applied Statistics, 29, 190-197   DOI   ScienceOn
7 Lehmann, E. L. and Casella, G. (1998), Theory of Point Estimation (revised edition), Springer-Verlag, New York
8 Mallick, B. K. and Gelfand, A. E. (1994), Generalized linear models with unknown link functions, Biometrika, 81, 237-245   DOI   ScienceOn
9 McCullagh, P. and Nelder, J. A. (1989), Generalized Linear Models 2nd Ed. Chapman & IIall, New York
10 Milicer, H. and Szczoka, F. (1966), Age at menarche in Warsaw girls in 1965, Human Biology, 38, 199-203
11 Nolder, J. A. and Wedderburn, R. W. M. (1972), Generalized linear models, Journal of the Royal Statistical Society, Series A, 135, 370-384   DOI   ScienceOn
12 Stukel, T. (1988), Generalized logistic models, Journal of the American Statistical Association, 83, 426-431   DOI   ScienceOn
13 Taylor, J. (1988), The cost of generalized logistic regression, Journal of the American Statistical, Association, 83, 1078-1083   DOI   ScienceOn