244 Index
detector, see on-line detector, 69
deterministic regular design, 93
differentiable functional, 188
efficient estimator, 8
Epanechnikov kernel function, 105
estimator, 4
asymptotically unbiased, 21
maximum likelihood (MLE), 4, 33
projection, 147
adaptive, 211
asymptotically Fisher
efficient, 22
Bayes, 13
efficient, 8
Fisher efficient, see efficient, 8
global linear, 105
linear, 104
local linear, 105
minimax, 16
more efficient, 12
on-line, 78
orthogonal series, 147
sequential, 69, 78
smoothing kernel, 107
superefficient, 22
unbiased, 5
expected detection delay, 69
explanatory variable, 85
false alarm probability, 69
filter, 66
first-order autoregressive
model, 75
Fisher efficient estimator, see
efficient estimator, 8
Fisher information, 6, 7
Fisher score function, 6
total, 6
fitted response vector, 87
functional
differentiable, 188
integral quadratic, 188
linear, 186
linear integral, 185
non-linear, 188
non-linear integral, 188
global linear estimator of regression
function, 105
older class of functions, 101
anisotropic, 209
Lipschitz condition, 102
smoothness, 101
Hellinger distance, 31
Hodges’ example, 22
hypotheses testing
parametric, 227
acceptance of null hypothesis, 227
composite alternative hypothesis, 228
decision rule, 227
minimax separation rate, 229
nonparametric, 228
null hypothesis, 227
rejection of null hypothesis, 227
separation between hypotheses, 228
simple alternative hypothesis, 227
type I error, 227
type II error, 228
hypothesis
simple alternative, 227
composite alternative, 228
null, 227
integral functional, 185
integral quadratic functional, 188
irregular statistical experiment, 43
kernel estimator
Nadaraya-Watson, 106
optimal smoothing, 109
smoothing, 107
kernel function, 105
Epanechnikov, 105
bi-square, 105
tri-cube, 112
triangular, 105
uniform, 105
kernel, see kernel function, 105
Kullback-Leibler information
number, 58
LAN, see local asymptotic
normality condition, 29
least-squares estimator
of regression coefficient, 88
of regression function, 90
of vector of regression coefficients, 89
likelihood ratio, 45
limiting covariance matrix, 94
linear estimator, 104
linear functional, 186
linear integral functional, 185
linear parametric regression
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