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En este trabajo se pretende desarrollar por primera vez un test completamente no paramétrico para contrastar el crecimiento de la función de regresión. Para ello se propone un estadístico basado en la L-distancia de un estimador no suavizado de la regresión al conjunto de todas las funciones crecientes. Se prueba que el test es asintóticamente del nivel prefijado y que su potencia bajo normalidad es la misma que las de los usuales contrastes chi-cuadrado.
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