Geodesic
Goodness-of-fit test with modified statistics chi-square
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 4, pp. 52-63

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we continue the research on possibility of using parametric functions that allow unbiased estimates to test a null hypothesis about a kind of distribution by the chi-square test. Based on Wald's method a new asymptotic test is proposed for testing hypothesis according to which the distribution of random value belongs to a one-parameter exponential family. According to a level of complexity this test occupies an intermediate position between the Nikulin-Rao-Robson’s test and the test of moment conditions. Two examples are mentioned as corollaries for the main statement of the paper. Corollary 2.1 contains the result connecting the proposed test statistic with one-dimensional version of the Nikulin-Rao-Robson’s statistic. Corollary 2.2 contains test statistic for testing a null hypothesis about the kind of distribution with a special additional restriction on a hypothetical distribution.
Keywords: exponential family of functions, unbiased estimate, fitting criterion, power. 
@article{SVMO_2016_18_4_a6,
     author = {M. V. Radionova and V. V. Chichagov},
     title = {Goodness-of-fit test with modified statistics chi-square},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {52--63},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a6/}
}
TY  - JOUR
AU  - M. V. Radionova
AU  - V. V. Chichagov
TI  - Goodness-of-fit test with modified statistics chi-square
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2016
SP  - 52
EP  - 63
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a6/
LA  - ru
ID  - SVMO_2016_18_4_a6
ER  - 
%0 Journal Article
%A M. V. Radionova
%A V. V. Chichagov
%T Goodness-of-fit test with modified statistics chi-square
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2016
%P 52-63
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a6/
%G ru
%F SVMO_2016_18_4_a6
M. V. Radionova; V. V. Chichagov. Goodness-of-fit test with modified statistics chi-square. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 4, pp. 52-63. http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a6/