Index 245 model, 86 linear span-space, 87 Lipschitz condition, 102 Lipschitz function, 102 local asymptotic normality (LAN) condition, 29 local linear estimator of regression function, 105 local polynomial approximation, 115 local polynomial estimator, 118 location parameter, 4 log-likelihood function, 4 log-likelihood ratio, 24 loss function, 11 absolute, 11 bounded, 11 quadratic, 11 sup-norm, 102 lower bound asymptotically minimax, 23 Cram´ er-Rao, 7 minimax, 18 Markov stopping time, see stopping time, 66 maximum likelihood estimator (MLE), 4, 33 maximum normalized risk, 16, 103 mean integrated squared error (MISE), 90 mean squared error (MSE), 90 mean squared risk at a point, see mean squared error (MSE), 90 measurable event, see Ft-measurable event, 65 up to random time, 68 minimax estimator, 16 minimax lower bound, 18 minimax risk, 16 of detection, 69 minimax risk of detection, 69 minimax separation rate, 229 more eﬃcient estimator, 12 multiple regression model, 193 Nadaraya-Watson kernel estimator, 106 non-linear functional, 188 non-linear integral functional, 188 nonparametric hypotheses testing, 228 nonparametric regression model, 101 normal equations, 88 normalized quadratic risk, 12 normalized risk, 11 maximum, 16 normalized risk function, see normalized risk, 11 null hypothesis, 227 on-line detection problem, 69 on-line detector, 69 on-line estimation, 78 on-line estimator, 78 optimal bandwidth, 108, 118 optimal smoothing kernel estimator, 109 orthogonal series, see projection estimator, 147 orthonormal basis, 141 parametric hypotheses testing, 227 parametric regression model, 85 linear, 86 random error in, 86 partition of unity, 153 pixel, 208 point estimator, see estimator, 4 polynomial regression, 86 posterior density, 14 weighted, 14 posterior mean, 14 non-weighted, 14 weighted, 14 power spline, 156 predicted, see fitted response vector, 87 predictor variable, see explanatory variable, 85 prior density, 13 prior distribution, 13 conjugate, 15 projection, see orthogonal series estimator, 147 quadratic loss function, 11 random error, 85 random regular design, 95 random time, 68 random walk, two-sided Gaussian, 52 rate of convergence, 23 regression coeﬃcient, 85 least-squares estimator of, 88 regression equation, 85, 101

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2011 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.