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This approach is feasible when the number of covariates is small and if the covariates are discrete. When the number of covariates is large or if covariates are continuous, then the methods described in Beach and Davidson (1983)are impractical. , a semiparametric method). C. SemiparametricMethods The idea behind any semiparametric method is to put enough structure on the distribution of Y given X equals x so as to reduce the curse of dimensionality that arises in nonparametric methods. In this section, we focus on one particularly useful approach (that of Donald, Green, and Paarsch 1995)to estimating GLCs semiparametrically.

The authors are also grateful to Gordon Anderson and Charles M. Beach as well as two anonymous referees for useful comments and helpful suggestions. REFERENCES Anderson, G. (1996), Nonparametric Tests for Stochastic Dominance in Income Distributions, Econometrica, 64, 1183-1193. (1970), On the Measurement of Inequality, Journal ofEconomic Theory, 2,244- 263. Atkinson, A. (1975), The Economics ofhequality, Oxford University Press, Oxford. , K. Chow, J. Formby, and G. Slotsve, (1994), Statistical Inference for Decile Means, Economics Letters, 45, 161-167.

Wolak, F. (1989),Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models, Econometric Theory, 5, 1-35. Wolak, F. (1991), The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models, Econometrica, 59,981-995. , G. Fisher, and D. Willson (1995),New Distribution-Free Tests for Stochastic Dominance, Department of Economics, Dalhousie University, Working Paper 9502. Measurement of Inequality WaIte r Kriime r University of Dortmund, Dortmund, Germany 1.

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Business Statistics by Geis

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