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