Minimum Distance Estimation and Components of Goodness-Of-Fit Statistics
William C. Parr, William R. Schucany
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1982 · Volume 44 · Issue 2
DOI: 10.1111/j.2517-6161.1982.tb01197.x
Abstract
The relationship of minimum distance (MD) estimation to components of goodness-of-fit statistics is considered.M-estimation is viewed as a special case, with interesting interpretations in terms of the defining Ψ-function as related to linear combinations of the components and modified Fourier approximations to the efficient score. The essence of the competition between efficiency and robustness is the determination of the magnitudes of the coefficients of the high frequency components. Applications to the composite and simple goodness-of-fit problems are indicated.
Keywords
efficiency, harmonic analysis, m-estimation, optimal score function, robustness
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