Index

B-spline

standard, 153

B-splines, 152

shifted, 155

Ft-measurable event, 65

σ-algebra, 65

absolute loss function, 11

acceptance of null hypothesis, 227

adaptation, 211

adaptive estimator, 211

adaptive risk, 212

additive regression model, 197

anisotropic H¨ older class of functions,

209

asymptotically exponential

statistical experiment, 46

asymptotically Fisher

eﬃcient estimator, 22

asymptotically minimax

estimator, 103

lower bound, 23

rate of convergence, 23, 103

estimator, 33

asymptotically sharp minimax

bounds, 23

asymptotically unbiased

estimator, 21

autoregression coeﬃcient, 75

autoregression, see autoregressive

model, 75

coeﬃcient, 75

autoregressive model, 75

balance equation, 108

bandwidth, 105

optimal, 108

basis

complete, 142

orthonormal, 141

trigonometric, 142

Bayes estimator, 13

Bayes risk, 13

bi-square kernel function, 105

bias, 5

bin, 132

bounded loss function, 11

change point, 51

change-point problem, 51

complete basis, 142

composite alternative hypothesis, 228

conjugate family of distributions, 15

conjugate prior distribution, 15

covariance matrix, 90

limiting, 94

Cram´ er-Rao inequality, 7

Cram´ er-Rao lower bound, 7

decision rule, 227

design, 86

regular deterministic, 93

regular random, 95

uniform, 94

design matrix, 87

detection, see on-line detection

problem, 69

243