Minmax estimation of the empirical distribution function

• Autorzy: Magdalena Rutkowska
• Języki publikacji: EN

Abstrakty

PL

.

EN

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.

Słowa kluczowe

EN

Estimation,Minimax procedures

• Wydawca: Polish Mathematical Society
• Czasopismo: Mathematica Applicanda
• Rocznik: 1980
• Tom: 8
• Numer: 16

Daty

wydano

1980

online

1981-02-01

Twórcy

autor

Magdalena Rutkowska

Identyfikatory

DOI

10.14708/ma.v8i16.1472