Many statisticians use a semi-parametric model to examine the relationship between explanatory and response variables. In practice, a data set often contains outliers and, hence the traditional estimation methods may not be appropriate. Wu et al. (1996) provided a fuzzy-weighted estimator to reduce the influence of outliers and they discussed its asymptotic properties. However, the test performance in small sample is not discussed. In this paper, a percentile interval estimation method based on fuzzy-weighted bootstrap samples is provided and we call the improved percentile interval estimation method. We show that the fuzzy-weighted bootstrap estimator and the fuzzy-weighted estimator have the same asymptotic properties. In addition, the proposed method can reduce the influence of outliers efficiently when we make inference about the scaled regression coefficient in small sample. Hence, we provide an alternative estimation method to make inference when sample size is small.
Journal of statistics and management systems 6(3), pp.443-461