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Abstract:
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Least-squares estimation treats underestimation and overestimation by the same amount equally. Thus, if it is worse to underestimate the response variable in a regression model, least-squares is not appropriate to use. The LINEX loss function is well-suited to handle this type of scenario because it can place an exponentially increasing loss on underestimation and linearly increasing loss on overestimation. Due to the LINEX loss function’s complexity, there is no closed-form solution for the estimators, so we must use an unconstrained optimization method to estimate the parameters. The amount of overestimation and underestimation depends on the choice of the shape parameter. We suggest a data-driven method to select its value. We examined the LINEX regression model’s properties using simulated data with various error distributions. Results show that the LINEX estimators for the model parameters are biased and their distributions are not necessarily normal. The LINEX loss function works well in reducing the percentage of positive residuals or negative residuals compared to the least-squares method.
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