MINIMUM DISPARITY ESTIMATION IN LINEAR REGRESSION MODELS: DISTRIBUTION AND EFFICIENCY

RO JIN PAK^{1} AND AYANENDRANATH BASU^{2}

1Department of Statistics, Taejon University, Taejon 300-716, Korea

2Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700 035, India

(Received January 13, 1997; revised July 22, 1997)

Abstract. This paper deals with the minimum disparity estimation in linear regression models. The estimators are defined as statistical quantities which minimize the blended weight Hellinger distance between a weighted kernel density estimator of errors and a smoothed model density of errors. It is shown that the estimators of the regression parameters are asymptotic normally distributed and efficient at the model if the weights of the density estimators are appropriately chosen.

Key words and phrases: Asymptotic efficiency, blended weight Hellinger distance, kernel density estimator, linear regression model.