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 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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