Index

additive model
see AM | 5.1.3 | 8.
backfitting
8.1
bandwidth choice
8.3.1
derivative
8.2.2
equivalent kernel weights
8.3.3
finite sample behavior
8.3
hypotheses testing
9.4
interaction terms
8.2.3
marginal effect
8.2.1
marginal integration
8.2
MASE
8.3.2
additive partial linear model
see APLM
ADE
6.2 | 6.2.3
AMISE
histogram
2.2.4
kernel density estimation
3.2.4
kernel regression
4.1.2.3
AMSE
local polynomial regression
4.1.3
APLM
9.1
ASH
2.4
asymptotic MISE
see AMISE
asymptotic MSE
see AMSE
asymptotic properties
histogram
2.2
kernel density estimation
3.2
average derivative estimator
see ADE
average shifted histogram
see ASH
averaged squared error
see ASE
backfitting
8.1
classical
8.1.1
GAM
9.2.1
GAPLM
9.3.1
GPLM
7.2.3
local scoring
9.2.1
modified
8.1.2
smoothed
8.1.3
bandwidth
canonical
3.4.1
kernel density estimation
3.1.2
rule of thumb
3.3.1
bandwidth choice
additive model
8.3.1
kernel density estimation
3.3 | 3.3.4
kernel regression
4.3
Silverman's rule of thumb
3.3.1
bias
histogram
2.2.1
kernel density estimation
3.2.1
kernel regression
4.1.2.3
multivariate density estimation
3.6.1
multivariate regression
4.5.1
bin
2.1.1
binary response
1.2.3 | 5.1
binwidth
2.1.1 | 2.1.3
optimal choice
2.2.5
rule of thumb
2.2.5
canonical bandwidth
3.4.1
canonical kernel
3.4.1
canonical link function
5.2.2
CHARN model
4.4.2
conditional expectation
1.2.3 | 4.1.1.1
conditional heteroscedastic autoregressive nonlinear
see CHARN
confidence bands
kernel density estimation
3.5
kernel regression
4.4.2
confidence intervals
kernel density estimation
3.5
kernel regression
4.4.1
cross-validation
see CV
bandwidth choice
4.3
biased
3.6.3
kernel density estimation
3.3.2
kernel regression
4.3.2
multivariate density estimation
3.6.2.2
pseudo-likelihood
3.6.3
smoothed
3.6.3
curse of dimensionality
1.2 | 4.5.2 | 5. | 6. | 8.1.1 | 8.3.3
density estimation
1.1
histogram
2.
kernel estimation
3.1.2
nonparametric
1.1 | 3.
derivative estimation
additive function
8.2.2
regression
4.1.3
design
fixed
4.1.1.2
random
4.1.1.2
deviance
5.2.3
dimension reduction
5.1
Engel curve
1.2.2
equivalent kernel
3.4.1
equivalent kernel weights
8.3.3
explanatory variable
1.2
exponential family
5.2.1
finite prediction error
4.3.3
Fisher scoring algorithm
5.2.3
fixed design
4.1.1.2 | 4.1.2.2
Gasser-Müller estimator
4.1.2.2
Fourier coefficients
4.2.4
Fourier series
4.2.4
frequency polygon
2.4
GAM
5.1.3 | 9. | 9.2
backfitting
9.2.1
hypotheses testing
9.4
marginal integration
9.2.2
GAPLM
5.1.3 | 9.3
backfitting
9.3.1
hypotheses testing
9.4
marginal integration
9.3.2
Gasser-Müller estimator
4.1.2.2
Gauss-Seidel algorithm
8.1
generalized additive model
see GAM
generalized additive partial linear model
see GAPLM
generalized cross-validation
4.3.3
generalized linear model
see GLM
generalized partial linear model
see GPLM
approximate LR test
7.3.1
modified LR test
7.3.2
GLM
5.2
estimation
5.2.3
exponential family
5.2.1
Fisher scoring
5.2.3
hypotheses testing
5.2.3
IRLS
5.2.3
link function
5.2.2
Newton-Raphson
5.2.3
GPLM
5.1.3 | 7.
backfitting
7.2.3
hypotheses testing
7.3
profile likelihood
7.2.1
Speckman estimator
7.2.2
gradient
3.6.1
Hessian matrix
3.6.1
histogram
2.
ASH
2.4
asymptotic properties
2.2
bias
2.2.1
binwidth choice
2.2.5
construction
2.1.1
dependence on binwidth
2.1.3
dependence on origin
2.3
derivation
2.1.2
MSE
2.2.3
variance
2.2.2
hypotheses testing
GPLM
7.3
regression
4.4
i.i.d
2.1
identification
5.2.3
AM
8.1.1
SIM
6.
independent and identically distributed
see i.i.d.
index
1.2.3 | 5.1.3 | 6.
semiparametric
5.1.3
integrated squared error
see ISE
interaction terms
8.2.3
IRLS
5.2.3
iteratively reweighted least squares
see IRLS
kernel density estimation
3.
as a sum of bumps
3.1.5
asymptotic properties
3.2
bandwidth choice
3.3.4
bias
3.2.1
confidence bands
3.5
confidence intervals
3.5
dependence on bandwidth
3.1.3
dependence on kernel
3.1.4
derivation
3.1.2
multivariate
3.6
multivariate rule-of-thumb bandwidth
3.6.2.1
optimal bandwidth
3.2.4
rule-of-thumb bandwidth
3.3.1
variance
3.2.2
kernel function
3.1.2
canonical
3.4.1 | 3.4.1
efficiency
3.4.3
equivalent
3.4.1
kernel regression
4.1.2
bandwidth choice
4.3
bias
4.1.2.3
confidence bands
4.4.2
confidence intervals
4.4.1
cross-validation
4.3.2
fixed design
4.1.2.2
Nadaraya-Watson estimator
4.1.2.1
penalizing functions
4.3.3
random design
4.1.2.1
statistical properties
4.1.2.3
univariate
4.1.2
variance
4.1.2.3
$ k$-NN
see $ k$-nearest-neighbor
least squares
see LS
likelihood ratio
see LR
linear regression
1.2
link function
1.2.3 | 5.1 | 5.2.2
canonical
5.2.2
nonparametric
5.1.2
power function
5.2.2
local constant
4.1.3
local linear
4.1.3
local polynomial
derivative estimation
4.1.3
regression
4.1.3 | 4.1.3
local scoring
9.2.1
log-likelihood
GLM
5.2.1
pseudo likelihood
6.2.2
quasi-likelihood
5.2.3
marginal effect
8.2.1
derivative
8.2.2
marginal integration
8.2
GAM
9.2.2
GAPLM
9.3.2
maximum likelihood
see ML
maximum likelihood estimator
see MLE
mean averaged squared error
see MASE
mean integrated squared error
see MISE
mean squared error
see MSE
median smoothing
4.2.2
MISE
histogram
2.2.4
kernel density estimation
3.2.4
regression
4.3
ML
5.2.1 | 5.2.3
MLE
5.2.1 | 5.2.3
MSE
histogram
2.2.3
kernel density estimation
3.2.3
multivariate density estimation
3.6 | 3.6
bias
3.6.1
computation
3.6.3
graphical representation
3.6.3
variance
3.6.1
multivariate regression
4.5
asymptotics
4.5.1
bias
4.5.1
computation
4.5.2
curse of dimensionality
4.5.2
variance
4.5.1
Nadaraya-Watson estimator
4.1.2.1
$ k$-nearest-neighbor
4.2.1 | 4.2.1 | 4.2.1
Newton-Raphson algorithm
GLM
5.2.3
nonparametric regression
4.
multivariate
4.5
univariate
4.1
origin
2.1.1
orthogonal series
Fourier series
4.2.4
orthogonal series regression
4.2.4
orthonormality
4.2.4
partial linear model
see PLM
pdf
1.1 | 1.1 | 2.1 | 3.1.1
multivariate
3.6
penalizing functions
4.3.3
Akaike's information criterion
4.3.3
finite prediction error
4.3.3
generalized cross-validation
4.3.3
Rice's $ T$
4.3.3
Shibata' s model selector
4.3.3
penalty term
bandwidth choice
4.3
spline
4.2.3
spline smoothing
4.2.3
PLM
5.1.3 | 7.1
estimation
7.2
plug-in method
3.3.3
refined
3.6.3
Silverman's rule of thumb
3.3.1
PMLE
6.2
probability density function
see pdf
profile likelihood
7.2.1
pseudo likelihood
6.2.2
pseudo maximum likelihood estimator
see PMLE
quasi-likelihood
5.2.3
random design
4.1.1.2 | 4.1.2.1 | 4.1.2.3
regression
1.2
conditional expectation
4.1.1.1
confidence bands
4.4
confidence intervals
4.4
fixed design
4.1.1.2 | 4.1.2.3
generalized
5.
hypotheses testing
4.4
kernel regression
4.1.2
linear
1.2 | 1.2.1
local polynomial
4.1.3
median smoothing
4.2.2
$ k$-nearest-neighbor
4.2.1
nonparametric
1.2.2 | 4.
nonparametric univariate
4.1
orthogonal series
4.2.4
parametric
1.2.1
random design
4.1.1.2 | 4.1.2.3
semiparametric
1.2.3 | 5.
spline smoothing
4.2.3
residual sum of squares
see RSS
RSS
4.2.3
rule of thumb
histogram
2.2.5
kernel density estimation
3.3.1
multivariate density estimation
3.6.2.1
semiparametric least squares
see SLS
Shibata' s model selector
4.3.3
Silverman's rule of thumb
3.3.1
SIM
6.
estimation
6.2
hypotheses testing
6.3
identification
6.1
PMLE
6.2.2
SLS
6.2.1
WADE
6.2.3
single index model
see SIM
SLS
6.2
smoothing spline
4.2.3
Speckman estimator
7.1 | 7.2.2
spline kernel
4.2.3
spline smoothing
4.2.3
subset selection
5.1.1
Taylor expansion
first order
2.2.1
multivariate
3.6.1
test
AM, GAM, GAPLM
9.4
approximate LR test
7.3.1
LR test
5.2.3
modified LR test
7.3.2
SIM
6.3
time series
nonparametric
4.4.2
variable selection
5.1.1
variance
histogram
2.2.2
kernel density estimation
3.2.2
kernel regression
4.1.2.3
multivariate density estimation
3.6.1
multivariate regression
4.5.1
WADE
6.2 | 6.2.3
wage equation
1.2
WARPing
2.4
wavelets
4.2.4
weighted average derivative estimator
see WADE
weighted semiparametric least squares
see WSLS
XploRe
Preface