Asymptotic Properties of a Family of Minimum Quantile Distance Estimators Academic Article uri icon

abstract

  • A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M approaches infinity. The asymptotic relative efficiency is computed for various sets of quantiles and various parameter values of the three-parameter lognormal distribution. The small-sample properties and robustness of the optimal M-quantile estimator for the three-parameter lognormal distribution are investigated in Monte Carlo studies. 1976 Taylor & Francis Group, LLC.

published proceedings

  • Journal of the American Statistical Association

author list (cited authors)

  • Lariccia, V. N., & Wehrly, T. E.

citation count

  • 11

complete list of authors

  • Lariccia, Vincent N||Wehrly, Thomas E

publication date

  • September 1985