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  • Some aspects of differences between ▫$L_1$▫ and ▫$L_2$▫ criteria in the linear switching regression
    Tominc, Polona ; Bele-Tominc, Lada
    ǂThe ǂlast squares procedure or ▫$L_2$▫ criterion is in theory and in practice generally used to estimate the regression coefficients. It is well known that given the assumptions of the classical ... linear regression model the least squares estimates posses some ideal properties. One of the assumptions underlying the ▫$L_2$▫ criterion is that the disturbance terms are normally distributed. But there are many cases where the disturbance terms are not normally distributed. Therefore, the use of some other criteria could be legitimate. As reported in the literature (for example Narula and Korhohen, 1994) the least absolute value or ▫$L_1$▫ criterion is less sensitive to outliers than the ▫$L_2$▫ criterion. With the purpose to illustrate some aspects of differences between ▫$L_2$▫ and ▫$L_1$▫ criteria in the presence of switching regression function with a priori known switch, the Monte Carlo simulation was performed. The least absolute value criterion has another advantage, especially in the cases, where the switch is not known in advance. Using the least absolute value criterion the estimation problem can be formulated and solved as a linear mixed integer optimisation model. If the switch is known in advance the optimisation model is linear.
    Source: New approaches in applied statistics (Str. 95-106)
    Type of material - article, component part
    Publish date - 2000
    Language - english
    COBISS.SI-ID - 5182492

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