Geodesic
Transformations to symmetry based on the probability weighted characteristic function
Kybernetika, Tome 51 (2015) no. 4, pp. 571-587
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis et al. [10] and use this PWECF in order to estimate the parameters of arbitrary transformations to symmetry. The almost sure consistency of the resulting estimators is shown. Finite-sample results for i.i.d. data are presented and are subsequently extended to the regression setting. A real data illustration is also included.
We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis et al. [10] and use this PWECF in order to estimate the parameters of arbitrary transformations to symmetry. The almost sure consistency of the resulting estimators is shown. Finite-sample results for i.i.d. data are presented and are subsequently extended to the regression setting. A real data illustration is also included.
DOI : 10.14736/kyb-2015-4-0571
Classification : 62G10, 62G20
Keywords: characteristic function; empirical characteristic function; probability weighted moments; symmetry transformation 
@article{10_14736_kyb_2015_4_0571,
     author = {Meintanis, Simos G. and Stupfler, Gilles},
     title = {Transformations to symmetry based on the probability weighted characteristic function},
     journal = {Kybernetika},
     pages = {571--587},
     year = {2015},
     volume = {51},
     number = {4},
     doi = {10.14736/kyb-2015-4-0571},
     mrnumber = {3423188},
     zbl = {06530334},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-4-0571/}
}
TY  - JOUR
AU  - Meintanis, Simos G.
AU  - Stupfler, Gilles
TI  - Transformations to symmetry based on the probability weighted characteristic function
JO  - Kybernetika
PY  - 2015
SP  - 571
EP  - 587
VL  - 51
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-4-0571/
DO  - 10.14736/kyb-2015-4-0571
LA  - en
ID  - 10_14736_kyb_2015_4_0571
ER  - 
%0 Journal Article
%A Meintanis, Simos G.
%A Stupfler, Gilles
%T Transformations to symmetry based on the probability weighted characteristic function
%J Kybernetika
%D 2015
%P 571-587
%V 51
%N 4
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-4-0571/
%R 10.14736/kyb-2015-4-0571
%G en
%F 10_14736_kyb_2015_4_0571
Meintanis, Simos G.; Stupfler, Gilles. Transformations to symmetry based on the probability weighted characteristic function. Kybernetika, Tome 51 (2015) no. 4, pp. 571-587. doi: 10.14736/kyb-2015-4-0571

[1] Bickel, P. J.: On adaptive estimation. Ann. Statist. 10 (1982), 647-671. | DOI | MR | Zbl

[2] Bickel, P. J., Doksum, K. A.: An analysis of transformations revisited. J. Amer. Statist. Assoc. 76 (1981), 296-311. | DOI | MR | Zbl

[3] Box, G. E. P., Cox, D. R.: An analysis of transformations. J. Roy. Statist. Soc. B 26 (1964), 211-243. | MR | Zbl

[4] Burbidge, J. B., Magee, L., Robb, A. L.: Alternative transformations to handle extreme values of the dependent variable. J. Amer. Statist. Assoc. 83 (1988), 123-127. | DOI | MR

[5] Chen, G., Lockhart, R., Stephens, M. A.: Box-Cox transformations in linear models: large sample theory and tests for normality (with discussion). Canad. J. Statist. 30 (2002), 1-59. | DOI | MR

[6] González-Rivera, G., Drost, F. C.: Efficiency comparisons of maximum-likelihood-based estimators in GARCH models. J. Econometr. 93 (1999), 93-111. | DOI | MR | Zbl

[7] Horowitz, J. L.: Semiparametric and Nonparametric Methods in Econometrics. Springer-Verlag, New York 2009. | DOI | MR | Zbl

[8] John, J. A., Draper, N. R.: An alternative family of transformations. J. Roy. Statist. Soc. C 29 (1980), 190-197. | DOI | Zbl

[9] Manly, B. F. J.: Exponential data transformations. J. Roy. Statist. Soc. D 25 (1976), 37-42.

[10] Meintanis, S. G., Swanepoel, J., Allison, J.: The probability weighted characteristic function and goodness-of-fit testing. J. Statist. Plann. Infer. 146 (2014), 122-132. | DOI | MR | Zbl

[11] Newey, W. K.: Adaptive estimation of regression models via moment restrictions. J. Econometr. 38 (1988), 301-339. | DOI | MR | Zbl

[12] Newey, W. K., Steigerwald, D. G.: Asymptotic bias for quasi-maximum-likelihood estimators in conditional heteroskedasticity models. Econometrica 65 (1997), 587-599. | DOI | MR | Zbl

[13] Parzen, E.: On estimation of a probability density function and mode. Ann. Math. Statist. 33 (1962), 1065-1076. | DOI | MR | Zbl

[14] Pólya, G., Szegő, G.: Problems and Theorems in Analysis, Volume I. Springer-Verlag, Berlin 1998.

[15] Rosenblatt, M.: Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27 (1956), 832-837. | DOI | MR | Zbl

[16] Savchuk, O. Y., Schick, A.: Density estimation for power transformations. J. Nonparametr. Statist. 25 (2013), 545-559. | DOI | MR

[17] Sen, P. K.: Estimates of the regression coefficient based on Kendall's tau. J. Amer. Statist. Assoc. 63 (1968), 1379-1389. | DOI | MR | Zbl

[18] Theil, H.: A rank-invariant method of linear and polynomial regression analysis. I, II, III. Nederl. Akad. Wetensch. Proc. 53 (1950), 386-392, 521-525, 1397-1412. | MR

[19] Yeo, I.-K., Johnson, R. A.: A new family of power transformations to improve normality or symmetry. Biometrika 87 (2000), 954-959. | DOI | MR | Zbl

[20] Yeo, I.-K., Johnson, R. A.: A uniform law of large numbers for $U$-statistics with application to transforming to near symmetry. Statist. Probab. Lett. 51 (2001), 63-69. | DOI | MR

[21] Yeo, I.-K., Johnson, R. A.: An empirical characteristic function approach to selecting a transformation to symmetry. In: Contemporary Developments in Statistical Theory (S. Lahiri, A. Schick, A. SenGupta and T. Sriram, eds.), Springer International Publishing 2014, pp. 191-202. | DOI | MR

[22] Yeo, I.-K., Johnson, R. A., Deng, X. W.: An empirical characteristic function approach to selecting a transformation to normality. Commun. Stat. Appl. Methods 21 (2014), 213-224. | DOI | Zbl

Cité par Sources :