Some Remarks about Robust Estimation of the Scale Parameter in Weighted Models

Using Zieliński's (1977 Zieliński , R. ( 1977 ). Robustness: a quantitative approach . Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 25 : 1281 – 1286 . Google Scholar]) concept of robustness, B?a?ej (2007 B?a?ej , P. ( 2007 ). Robust estimation of the scale and weighted distributions . Appl. Math. (Warsaw) 34 : 39 – 45 . Google Scholar]) obtained the uniformly most bias-robust estimates (UMBREs) of the scale parameter for some statistical models, in a class of linear functions of order statistics. Violations of the models are generated by weight functions. In this article the UMBRE of the scale parameter, based on order statistics, a more general weighted model is derived. Extension of a result of B?a?ej (2007 B?a?ej , P. ( 2007 ). Robust estimation of the scale and weighted distributions . Appl. Math. (Warsaw) 34 : 39 – 45 . Google Scholar]) is given.