246 Index regression function, 85 global linear estimator of, 105 least-squares estimator of, 90 linear estimator of, 104 local linear estimator of, 105 regression model simple linear, 96 simple linear through the origin, 96 additive, 197 multiple, 193 nonparametric, 101 parametric, 85 simple, 85 single-index, 199 regressogram, 133 regular deterministic design, 93 regular random design, 95 regular statistical experiment, 7 rejection of null hypothesis, 227 residual, 92 response variable, 85 response, see response variable, 85 risk, 11 risk function, 11 normalized quadratic, 12 normalized, 11 sample mean, 5 scaled spline, 158 scatter plot, 86 separation between hypotheses, 228 sequence space, 146 sequential estimation, 65, 69, 78 sequential estimator, 69, 78 shifted B-splines, 155 sigma-algebra, see σ-algebra, 65 signal-to-noise ratio, 51 simple alternative hypothesis, 227 simple linear regression model, 96 simple linear regression through the origin, 96 simple regression model, 85 single-index regression model, 199 smoothing kernel, 107 smoothing kernel estimator, 107 optimal, 109 smoothness of H¨ older class of functions, 101 spline B-spline, 152 power, 156 scaled, 158 shifted B-spline, 155 standard B-spline, 153 standard B-spline, 153 statistical experiment, 3 regular, 7 asymptotically exponential, 46 irregular, 43 stopping time, 66 sup-norm loss function, 102 supereﬃcient estimator, 22 supereﬃcient point, 22 test function, 123, 168 time, 65 random, 68 total Fisher score function, 6 tri-cube kernel function, 112 triangular kernel function, 105 trigonometric basis, 142 two-sided Gaussian random walk, 52 type I error, 227 type II error, 228 unbiased estimator, 5 uniform design, 94 uniform kernel function, 105 vector of regression coeﬃcients, 87 vector of regression coeﬃcients least-squares estimator of, 89 Wald’s first identity, 66 Wald’s second identity, 83 weight function, 185 weighted posterior density, 14 weighted posterior mean, 14

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