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

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