A note about calibrated prediction regions and distributions |
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Authors: | Giovanni Fonseca Federica Giummolè Paolo Vidoni |
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Institution: | 1. Dipartimento di Scienze Economiche e Statistiche, Università di Udine, via Tomadini 30/a, I-33100 Udine, Italy;2. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca'' Foscari Venezia, San Giobbe, Cannaregio 873, I-30121 Venice, Italy |
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Abstract: | In this work we address the problem of the construction of prediction regions and distribution functions, with particular regard to the multidimensional setting. Firstly, we define a simple procedure for calculating the predictive distribution function which gives improved prediction limits. Secondly, with a multivariate generalization of a result presented in Ueki and Fueda (2007), we propose a method for correcting estimative prediction regions, to reduce their coverage error to the third-order accuracy. The improved prediction regions and the associated distribution functions are easy to calculate using a suitable bootstrap procedure. Examples of application are included, showing the good performance of the proposed method, even if we consider an approximated model for prediction purposes. |
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Keywords: | Coverage probability Estimative prediction limit Parametric bootstrap Predictive distribution Prediction region |
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