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
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