Geodesic
Minmax estimation of the empirical distribution function
Mathematica Applicanda, Tome 8 (1980) no. 16, pp. 115-123.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Let X1,⋯,Xm and Y1,⋯,Yn be two independent samples from the same distribution. The problem is to predict the empirical distribution function, F^(t)=∑ni=1δ(Yi,t), from the second sample using the first sample, where δ(Yi,t)=1 if Yi≤t, and δ(Yi,t)=0 otherwise. The class of predictors φ(t)=a+∑mi=1biδ(Xi,t), a≥0, bi≥0, is considered and the minimax solution under the loss function L(F^,φ)=∫[F(t)−φ(t)]2[F(t)]γ−1[1−F(t)]δ−1dW(t) is constructed; here γ and δ are each either 0 or 1, and W is a given nonnull, finite measure. A method developed by E. G. Phadia [Ann. Statist. 1 (1973), 1149–1157; MR0348872] is used.
DOI : 10.14708/ma.v8i16.1472
Classification : 62G05(62C20)
Mots-clés : Estimation,Minimax procedures 
@article{10_14708_ma_v8i16_1472,
     author = {Magdalena Rutkowska},
     title = {Minmax estimation of the empirical distribution function},
     journal = {Mathematica Applicanda},
     pages = { 115--123},
     publisher = {mathdoc},
     volume = {8},
     number = {16},
     year = {1980},
     doi = {10.14708/ma.v8i16.1472},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/ma.v8i16.1472/}
}
TY  - JOUR
AU  - Magdalena Rutkowska
TI  - Minmax estimation of the empirical distribution function
JO  - Mathematica Applicanda
PY  - 1980
SP  -  115
EP  - 123
VL  - 8
IS  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14708/ma.v8i16.1472/
DO  - 10.14708/ma.v8i16.1472
LA  - pl
ID  - 10_14708_ma_v8i16_1472
ER  - 
%0 Journal Article
%A Magdalena Rutkowska
%T Minmax estimation of the empirical distribution function
%J Mathematica Applicanda
%D 1980
%P  115-123
%V 8
%N 16
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14708/ma.v8i16.1472/
%R 10.14708/ma.v8i16.1472
%G pl
%F 10_14708_ma_v8i16_1472
Magdalena Rutkowska. Minmax estimation of the empirical distribution function. Mathematica Applicanda, Tome 8 (1980) no. 16, pp.  115-123. doi : 10.14708/ma.v8i16.1472. http://geodesic.mathdoc.fr/articles/10.14708/ma.v8i16.1472/

Cité par Sources :