| Title:
|
Combining forecasts using the least trimmed squares (English) |
| Author:
|
Víšek, Jan Ámos |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
[183]-204 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Employing recently derived asymptotic representation of the least trimmed squares estimator, the combinations of the forecasts with constraints are studied. Under assumption of unbiasedness of individual forecasts it is shown that the combination without intercept and with constraint imposed on the estimate of regression coefficients that they sum to one, is better than others. A numerical example is included to support theoretical conclusions. (English) |
| Keyword:
|
regression coefficients |
| MSC:
|
62F30 |
| MSC:
|
62F35 |
| MSC:
|
62J05 |
| MSC:
|
62M10 |
| MSC:
|
62M20 |
| MSC:
|
65C60 |
| idZBL:
|
Zbl 1264.62087 |
| idMR:
|
MR1835816 |
| . |
| Date available:
|
2009-09-24T19:38:27Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135400 |
| . |
| Reference:
|
[1] Bates J. M., Granger C. W. J.: The combination of forecasts.Oper. Res. Quarterly 20 (1969), 451–468 10.1057/jors.1969.103 |
| Reference:
|
[2] Bickel P. J.: One-step Huber estimates in the linear model.J. Amer. Statist. Assoc. 70 (1975), 428–433 Zbl 0322.62038, MR 0386168, 10.1080/01621459.1975.10479884 |
| Reference:
|
[3] Clemen R. T.: Linear constraints and efficiency of combined forecasts.J. of Forecasting 6 (1986), 31–38 10.1002/for.3980050104 |
| Reference:
|
[4] Hampel F. R., Ronchetti E. M., Rousseeuw P. J., Stahel W. A.: Robust Statistics – The Approach Based on Influence Functions.Wiley, New York 1986 Zbl 0733.62038, MR 0829458 |
| Reference:
|
[5] Peel K. Holdenand D. A.: Unbiasedness, efficiency and the combination of economic forecasts.J. of Forecasting 8 (1989), 175–188 10.1002/for.3980080304 |
| Reference:
|
[6] Huber P. J.: Robust Statistics.Wiley, New York 1981 MR 0606374 |
| Reference:
|
[7] Jurečková J., Sen P. K.: Regression rank scores scale statistics and studentization in linear models.In: Proceedings of the Fifth Prague Symposium on Asymptotic Statistics, Physica Verlag, Heidelberg 1993, pp. 111–121 MR 1311932 |
| Reference:
|
[8] Rao R. C.: Linear Statistical Inference and Its Applications.Wiley, New York 1973 Zbl 0256.62002, MR 0346957 |
| Reference:
|
[9] Rubio A. M., Aguilar L. Z., Víšek J. Á.: Combining the forecasts using constrained $M$-estimators.Bull. Czech Econometric Society 4 (1996), 61–72 |
| Reference:
|
[10] Rubio A. M., Víšek J. Á.: Estimating the contamination level of data in the framework of linear regression analysis.Qűestiió 21 (1997), 9–36 Zbl 1167.62388, MR 1476149 |
| Reference:
|
[11] Varadarajan V. S.: A useful convergence theorem.Sankhyã 20 (1958), 221–222 Zbl 0088.11303, MR 0107290 |
| Reference:
|
[12] Víšek J. Á.: Stability of regression model estimates with respect to subsamples.Computational Statistics 7 (1992), 183–203 Zbl 0775.62182, MR 1178353 |
| Reference:
|
[13] Víšek J. Á.: Statistická analýza dat.(Statistical Data Analysis – a textbook in Czech.) Publishing House of the Czech Technical University Prague 1997 |
| Reference:
|
[14] Víšek J. Á.: Robust constrained combination of forecasts.Bull. Czech Econometric Society 5 (1998), 8, 53–80 |
| Reference:
|
[15] Víšek J. Á.: Robust instruments.In: Robust’98 (J. Antoch and G. Dohnal, eds.), Union of the Czech Mathematicians and Physicists, Prague 1998, pp. 195–224 |
| Reference:
|
[16] Víšek J. Á.: Robust specification test.In: Proceedings of Prague Stochastics’98 (M. Hušková, P. Lachout and J. Á. Víšek, eds.), Union of Czech Mathematicians and Physicists 1998, pp. 581–586 |
| Reference:
|
[17] Víšek J. Á.: Robust estimation of regression model.Bull. Czech Econometric Society 9 (1999), 57–79 |
| Reference:
|
[18] Víšek J. Á.: The least trimmed squares – random carriers.Bull. Czech Econometric Society 10 (1999), 1–30 |
| Reference:
|
[19] Víšek J. Á.: Robust instrumental variables and specification test.In: PRASTAN 2000, Proceedings of the conference “Mathematical Statistics and Numerical Mathematics and Their Applications”, (M. Kalina, J. Kalická, O. Nanásiová and A. Handlovičová, eds.), Comenius University, pp. 133–164 |
| Reference:
|
[20] Víšek J. Á.: Regression with high breakdown point.In: Proceedings of ROBUST 2000, Nečtiny, Union of the Czech Mathematicians and Physicists and The Czech Statistical Society. Submitted |
| Reference:
|
[21] Víšek J. Á.: A new paradigm of point estimation.In: Proceedings of seminar “Data Processing”, TRYLOBITE, Pardubice 2000. Submitted |
| Reference:
|
[22] Wald A., Wolfowitz J.: Statistical tests based on permutations of the observations.Ann. Math. Statist. 15 (1944), 358–372 Zbl 0063.08124, MR 0011424, 10.1214/aoms/1177731207 |
| Reference:
|
[23] Yohai V. J., Maronna R. A.: Asymptotic behaviour of $M$-estimators for the linear model.Ann. Statist. 7 (1979), 258–268 MR 0520237, 10.1214/aos/1176344610 |
| . |
