The existence of data with different dependence structures motivates the development of models which can capture several types of dependence. In this paper we consider a stationary sequence of moving maxima vectors <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\{{\mathbf {X}}_n=(X_{n1},\ldots ,X_{nd})\}_{n\ge 1}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mrow> <mo stretchy="false">{</mo> <msub> <mi mathvariant="bold">X</mi> <mi>n</mi> </msub> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow> <mi>n</mi>...</mn></mrow></msub></mrow></mrow></msub></math></equationsource></equationsource></inlineequation>

Multiplicative regression models are useful for analyzing data with positive responses, such as wages, stock prices and lifetimes, that are particularly common in economic, financial, epidemiological and social studies. Recently, the least absolute relative error (LARE) estimation was proposed...