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Title: Accounting for asymmetry in M-estimation: A Julia package Authors:  Manuel Stapper - WWU Muenster (Germany) [presenting]
Abstract: A software package is presented that enables the user to carry out M-Estimation in different univariate settings. Besides location estimation, it provides methods for parameter estimation for i.i.d. samples, regression, and fitting time series models. A focus is put on asymmetric distributions, in which estimates are potentially biased when using symmetric loss functions. It is accounted for in two ways: an established consistency correction and an adaptive estimation procedure based on asymmetric loss functions. The latter enables the user to estimate parameters of an i.i.d. sample with a selected relative asymptotic efficiency compared to Maximum Likelihood Estimation. The package includes not only four frequently used loss functions (Huber, Tukey's Biweight, Hampel and Andrew's Wave) but also allows applying the methods with self-defined loss functions. By utilising Julia's Multiple Dispatch, parameter estimates are computed fast for more than 30 common distributions in the Distributions.jl package. Fallback functions allow carrying out parameter estimation for any other univariate distribution with a known probability (density) function. The extension to time series applications is discussed and showcased by fitting a count data model to real-world data.