! " ! #$% &'$ &('
!!" !!" #$ # $ !!! % & '(()* $ +
, $ -
. / 0 '
1 2 $2 $ / - 22 $ .* $ '((3 '(() 4 - - $ 5 , - . $ / / & / 1 / 6 $ 1 7 $ .
$ 1
8 '(99* 1 . - : , '((3* ; '((3* < = '((>* - - < '((3* ; 7$ !!'* :; < !!'* .* 0 7 * . ,E 5 '((>* F '((3*
5 . ; . γ Z γ $ B $ $ $ G(.) 6 m(z) = G(γ Z)
3*
. δ ∗ ν & 3* & m(z) = G ν + δ(γ Z) + ε ; ;
$$ '" & !
7 < )
# '((3 G A '(("* 8 ; 7$ !!'* 0 H0 m(Z) . θ ∈ Θ m(Z) = M(Z, θ) H1 θ $ m(Z) $ M(Xi , θ) ;
:; < !!'* H0 $ $ $ G(·) 1 $ H0 θ Gθ (m(Z)) = θ0 + D d=1 md (Zd ) Gθ θ ∈ Θ - $ < # $ * H0
. m(z) - < '((3* H0 m(z) = G(γz) γ ∈ d G(·) : → Ho Ho =
6 9
2 2 H A1= * . $ - 6 ! ; " # 5 '
. 0 1=7CC ! $ % % $ * * & * A1=
& # $ '#( & 4 & $ 4 5 6 & & # '#( ' 2 2 & $ F & $ : - ) * + * ,- . * 6 • # *
$ (
'6 # H 7
() ( .. 2.3 ./3+ ((/3 . (/ 3( /3.
(*
- /01 - 1 2 4
05 60 * 05 0 ( * 1
3 15 1 7 /*
+ = 1 - * #
= 1 -
# *89
! ! # ,&%
""#$ !'$ & ! $$ ! #'&! $&!" & #, ,,'#$
% && #&$,% "$& ##!' &', #&$ "!&% ! #& & , !'#! #% "'
# ) *
5 H 2 2 •
5 ' 0 ' , , $ , # ) [20, 45] # [0, 50]
1
½
'!
!!!%' #! $ #"# ,%, !%% #'' , %& ! % "## ''&! % $
−4
x 10
5 250 4.5
4 200
Density peak
3.5
NITRO
Mean value
3
150
2.5 100
2
1.5 50 1
0.5 0
5
10
15
20
25
30
35
40
45
50
TMEAD
- '6 / 0 (z1, z2 ) 5 . $
) " ! "
1 . 5 .
) # " ! " " ! * # "
0 $ " 0 ''
6 ) *
(*
: !
,%' #
!'
' : &
"
%
1 2 05 (
31 /
!&&&
;
: ,
: "
: ,
! " # " $% &' & γT mead " (& &% " & $&& & " "
, z1 z2 '* 5 $ .* I . A , '
'"
25 30 35 40 45 0
5
10
Tmead (%)
20
2.72 2.7 2.68 2.66 2.64 2.62 2.6 2.58 2.56 2.54
30 35 40 45 0
5
10
15
20
30 25 Nitro
Nonparametric Model 2.7 2.68 50 2.66 45 40 35 2.64 2.62 2.6 2.58
20
30 25 Nitro
2.7 2.69 2.68 2.67 2.66 2.65 2.64 2.63 2.62 2.61 2.6 2.59
2.72 2.7 2.68 2.66 2.64 2.62 2.6 2.58 2.56 2.54
25 30 35 40
25 30 35 40 45 0
10
15
20
30 25 Nitro
35
40
Additive Model 2.7 2.68 50 2.66 45 2.64 2.62 2.6 2.58
2.72 2.7 2.68 2.66 2.64 2.62 2.6 2.58 2.56 2.54
10
20
30 25 Nitro
35
Linear Model 2.7 50 2.68 2.66 2.64 2.62 2.6 45
15
40
2.58
2.6
2.62
2.64
2.66
2.68
2.7
2.72
5
H(T mead, Nitro)
Tmead (%)
20
2.72 2.7 2.68 2.66 2.64 2.62 2.6 2.58 2.56 2.54
ln(Price) (Francs)
5
45 0
H(T mead, Nitro)
Tmead (%)
20
2.72 2.7 2.68 2.66 2.64 2.62 2.6 2.58 2.56 2.54
ln(Price) (Francs)
"6 C H(z1, z2 )
7 .
15
Single Index Model 2.68 2.66 2.64 2.62 2.6 50 45 40 35
H(T mead, Nitro)
25
ln(Price) (Francs)
H(T mead, Nitro)
Tmead (%)
20
2.72 2.7 2.68 2.66 2.64 2.62 2.6 2.58 2.56 2.54
ln(Price) (Francs)
?6 7 6Y
H1 H0
% 7 . =
= β X + m(Z1 , · · · , ZL) + ε
8, H0 8, H0 H 8, H0
7
T ∗ J 3'!) Hα J >" 9( τ0 J !"">"
)$ ! 0 ? ,
)+ "& # !"
> 7 7 /$0012 ! 34 3 ) 1%/$2 '@8 '$0 , -. :6 4 /$0092 3 E 5 ) * 4 & . 5 ; 3 & ' ! 0( $@@ 5 # - . /'@@(2 3) " 6 4 & 3
-)#B /$00?2 3# ! . .3 ;! 6 -)#B $90 $0'
( (
)
6 E& /$00?2 3
