Janusz Wywiał
ARTICLE

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ABSTRACT

The problem of choosing the appropriate predictor is being considered. Generally, in this paper the analysis is focused on the problem of unbiasedness of the predictors. Several tests attempting to verify the unbiasedness of three predictors of the linear trend are proposed. They are based on some modifications of the well-known Janus quotient being a ratio of the variance of prediction errors and the residual variance. In general each of the considered test statistic can be represented as the ratio of two quadratic forms of normal vectors. These two quadratic forms can be dependent, so its distribution function has to be approximated. An example of testing hypothesis on unbiasedness is presented. The obtained results can be generalized in the case of prediction on the basis of regression models.

KEYWORDS

test statistic, prediction error, unbiasednees, Janus quotient, quadratic form of normally distributed vector, approximation of distribution function, residual variance, prediction variance

REFERENCES

[1] Azzalini A., Bowman A., [1993], On nonparametric regression for checking linear relationships, „The Journal of the Royal Statistical Society”, B55(2), s. 549-557.

[2] Gadd A., Wold H., [1964], The Janus quotient; a measure for the accuracy of prediction, In Econometric Model Building, Amsterdam.

[3] Mathai A.M., Provost S.B., [1992], Quadratic Forms in Random Variables (Theory and Applications), Marcel Decker, Inc., New York-Basel-Hong Kong.

[4] Pearson E.S., [1959], Note on an approximation to the distribution of noncentral c2, „Biometrika”, 46, pp. 346-346.

[5] Rao C.R., Mitra S.K., [1971], Generalized inverse of matrices and its applications, John Wiley and Sons, New York-London-Sydney-Toronto.

[6] Wywiał J., [1995], Weryfikacja hipotez o błędach predykcji adaptacyjnej, Ossolineum, Wrocław-Warszawa-Kraków.

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