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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