The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a finite partition. The asymptotic behavior of the raking-ratio empirical process indexed by a class of functions is studied when the auxiliary information is given by estimates. These estimates are supposed to result from the learning of the probability of sets of partitions from another sample larger than the sample of the statistician, as in the case of two-stage sampling surveys. Under some metric entropy hypothesis and conditions on the size of the information source sample, the strong approximation of this process and in particular the weak convergence are established. Under these conditions, the asymptotic behavior of the new process is the same as the classical raking-ratio empirical process. Some possible statistical applications of these results are also given, like the strengthening of the Z-test and the chi-square goodness of fit test.
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ps/2020017
Keywords: Uniform central limit theorems, nonparametric statistics, empirical processes, raking ratio process, auxiliary information, learning
@article{PS_2020__24_1_435_0,
author = {Albertus, Mickael},
title = {Raking-ratio empirical process with auxiliary information learning},
journal = {ESAIM: Probability and Statistics},
pages = {435--453},
year = {2020},
publisher = {EDP Sciences},
volume = {24},
doi = {10.1051/ps/2020017},
mrnumber = {4158668},
zbl = {1453.62461},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2020017/}
}
TY - JOUR AU - Albertus, Mickael TI - Raking-ratio empirical process with auxiliary information learning JO - ESAIM: Probability and Statistics PY - 2020 SP - 435 EP - 453 VL - 24 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2020017/ DO - 10.1051/ps/2020017 LA - en ID - PS_2020__24_1_435_0 ER -
Albertus, Mickael. Raking-ratio empirical process with auxiliary information learning. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 435-453. doi: 10.1051/ps/2020017
[1] and , Auxiliary information: the raking-ratio empirical process. Electron. J. Stat. 13 (2019) 120–165. | MR | Zbl | DOI
[2] , Estimators based on several stratified samples with applications to multiple frame surveys. J. Am. Stat. Assoc. 81 (1986) 1074–1079. | Zbl | DOI
[3] and , Revisiting two strong approximation results of Dudley and Philipp. JSTOR 51 (2006) 155–172. | MR | Zbl
[4] and , Estimating the variance of raking-ratio estimators. Canad. J. Statist. 16 (1988) 47–55. | MR | Zbl | DOI
[5] and , Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 (1998) 329–375. | MR | Zbl | DOI
[6] and , An investigation of raking ratio estimators. Indian J. Stat. 41 (1979) 97–114. | Zbl
[7] and , Variance estimation for the canadian labour force survey. Survey Methodol. 13 (1987) 147–161.
[8] and , On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Ann. Math. Stat. 11 (1940) 427–444 | MR | JFM | Zbl | DOI
[9] and , Contingency tables with given marginals. Biometrika 55 (1968) 179–188. | MR | Zbl | DOI
[10] , Biases, variances and covariances of raking ratio estimators for marginal and cell totals and averages of observed characteristics. Metrika 28 (1981) 109–121. | MR | Zbl | DOI
[11] , Asymptotics via empirical processes. Statist. Sci. 4 (1989) 341–366. | MR | Zbl
[12] , A relationship between arbitrary positive matrices and doubly stochastic matrices. Ann. Math. Statist. 35 (1964) 876–879. | MR | Zbl | DOI
[13] , An iterative method of adjusting sample frequency tables when expected marginal totals are known. Ann. Math. Stat. 13 (1942) 166–178. | MR | Zbl | DOI
[14] , Sharper bounds for Gaussian and empirical processes. Ann. Probab. 22 (1994) 28–76. | MR | Zbl | DOI
[15] and , Weak convergence and empirical processes. Springer Series in Statistics (Springer-Verlag, New York, 1996). With applications to statistics. | MR | Zbl
Cité par Sources :
