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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 23, Fasc. 1,
pages 61 - 76
 

ALMOST SURE PROPERTIES OF WEIGHTED VECTORIAL MARTINGALES TRANSFORMS WITH APPLICATIONS TO PREDICTION FOR LINEAR REGRESSION MODELS

Peggy Cénac

Abstract: We establish new almost sure properties for powers of weighted martingale transforms. It allows us to deduce useful asymptotic results for cumulative prediction and estimation errors associated with linear regression models. We also provide two examples of applications on the linear and functional autoregressive models.

2000 AMS Mathematics Subject Classification: 62J12, 62H12, 60G25, 60G42.

Key words and phrases: Linear regression models; martingales transforms; least squares estimators; cumulative prediction and estimation errors.

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