Regresión por mínimos cuadrados parciales PLS con datos de intervalo
Partial least squares regression PLS on interval data
DOI:
https://doi.org/10.15446/rev.fac.cienc.v5n1.54616Keywords:
Regresión por componentes principales, mínimos cuadrados parciales PLS, optimización intervalo-valuada, intervalo valores y vectores propios (es)Principal components regression, partial least squares regression PLS, interval-valued optimization, interval eigen values and eigen vectors (en)
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La incertidumbre en los datos puede ser considerada mediante un intervalo numérico en el cual una variable puede asumir sus posibles valores, esto se conoce como datos de intervalo. En este artículo se extiende la metodología de regresión PLS al caso donde tanto las variables explicativas como las variables respuesta y los coeficientes de regresión son del tipo intervalo. De ésta manera se propone una metodología de regresión que resuelve tres problemas que se presentan con los datos de tipo real: en primer lugar problemas de multicolinealidad tanto en las variables explicativas como en las variables respuesta, en segundo lugar problemas cuando los datos no pertenecen a un espacio Euclídeo y por último problemas cuando la incertidumbre en los datos se representa por medio de intervalos. Hoy en día existen tareas del común, tales como planificación y operación de sistemas eléctricos, planificación de producción, logística del transporte, inventarios, gestión de carteras de valores, entre otras, que involucran incertidumbre. De ésta manera se requieren modelos que tengan en cuenta dicha incertidumbre y puedan dar la posibilidad de tomar decisiones para resultados óptimos desde una gama de posibilidades o escenarios posibles. Por otro lado, el análisis de datos reales a menudo se ve afectado por diferentes tipos de errores tales como: errores de medición, errores de cálculo e impresición relacionada con el método adoptado para la estimación de los datos. Este trabajo es una propuesta metodológica de tipo teórico y está fundamentada en los desarrollos teóricos sobre optimización matemática sobre los conjuntos de multi-intervalos y multi-matrices.
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