2013
,
1(22)
512.2
.. , ..

.
: , , .
, (., , [1-6]). , . . , () [4, 5]. [6] (), . , ( ), ( ).
() [7, 8] .
1. ()
1,..., - ... () /(). : 0(, 9), g(, 9) - ; 9 - ; () - (...).
- 9
( , 9) - .
[3] , [7] ( , 9)
(1.1)
(, 9) = 1 g(, 9) + ^ (, 9),
(1.2)
I - , - , , = 0 [7].
(1.2) gl (, 9) : I = 0 (), I = 0,5 - (), I = 1 - () [3]. I » , , .
() = (1 -)(, 9) + - (, 9)
4-1
W (, 0) = =|, +.
- h( , 9) f () I (1 -) g (, 9)
l
ln f ()
l =
(1 -)--
ln g (, 9) _
(1.2) . , H(, 9) W(, 9) . l. , (1.2) , [3].
2.
- 9N 9 , [7], [11]
j ( , 9 N, TN (, 9 N )dFN () = 0,
T = (Ti,...,Tk)T ; T =|(,t,9)dF(t); = jSt(,t,9)dFv(t).

- d l-1
9n-9= j(,9,T)dF() -y(t,9)dF(t),
L 59 J
k d
y(t, 9) = (t, 9, T(t, 9)) + V Sj (, t, 9)-^, 9, T(t, 9))dF().
,=! dT,
/N(9N - 9) -

2 =
j(, 9, T)dF() -jv2(t, 9)dF(t).
59
(1.2) (St = 0)
( , 9) =
_5_
50
g (, 9)
gl-1( , 9).
(2.1)
(2.2)
^1 (2.1), (2.2) ( -) I = 0 (2.1) , I = 1 [3].
, ,
(, 0,71,72) = (, 0) 21 -1 (, 0),
X (,/,0) = | 20~ - I, 52(,/,0) = 51 (,/,0).
' 1 2 50 '
(2.1) I.
. () = (1 -)(, 0) + - (, 0) ,
»: (), , , () () [11]. ,
I () = 1
\/2
-2 -(-5)2 I
0,9 2 +0,1 2
; (2.3)
\ /
I () = 1
\/2
2 2
- 0 1 -
0,9 2 + ^ 18 3
V
. (2.4)
[11]. (2.1) (2.3), (2.4), . (2.3) , (2.4), .
g (, , X) :
I( -) ^ (, , s)dFN () = 0. (2.5)

| 2 g 21 (, 0, s)dF ()
2
II 12-1 I gl (,0, 5^() I
2 =
5
1. I (2.5) =0 (. . 1)
1
(2.5) = 0
(1 = 0.5) (1 = 1)
( 1 . 1, 2) 1 1,193 1,54
1 0,832 0,649
.
2. l (. . 3, 4; . 1, 2) (2.3), (2.4).
. 1. l . 2. l
(2.3) (2.4)
. 1, 2: 1 - = 0; 2 - ; 3 - ; 4 - ; 5 - .
2
(2.3)

2.5)
O,3O3 O O O,48!
1,303 ,939 3,4O2 ,376
1 O,672 O,383 O,947
3
(2.4)

2.5)
O,^ O O O,532
1,273 U8O3 3,4O2 U5O2
1 O,7O6 O,474 O,848
( ). , .
3. (2.5) (. . 4, 5) (2.3), (2.4).
(2.5) , * - ().
(). (). . , , .
4
(2.5) (2.3)


3,5 1,303 1,364 1,72
0.372 1 0,955 0,758
5
(2.5) (2.4)


1,8 1,273 1,4 1,782
0,707 1 0,909 0,714
3.
( g (, 0) ), g (, 0) (1.2) - gN (, 0) :
20- -t

dFN (1).
(3.1)
, 0 X [7], [8]:
1 N N
1 XX
N (N -1)
1
7+1
(3.2)

1( 1) = --
(0N 21])
X N
(0 N 2 )
7-1
= ( + }-) / 2 - .
- (3.1) 0(, 0). . (3.2) 7, » , , . (3.2) 7. -. - ]1» 7 (0 <7 < 1) (3.2).
4.
(3.2) - » - » - - ^ = 100). . 6, 7 .
, 2 ( (2)). , 3 ( (3.2)). , (2) , (3.2) . - .
6


(. 2) (3.2) -
0,0149 0,0132 0,0145 0,0200 0,0426
0,88590 1,0000 0,91 0,6600 0,3099
7


(. 2) (3.2) -
4,4959 1,3416 1,4304 4,8568 1,7537
0,3009 1,0000 0,9379 0,2762 0,7650
(3.2) [6] N = 39+1 ). . 3 ( ) (Jackknife) - 7 (0 <7 < 1).
. 3. ^ = 39+1 ) 1 - ; 2 - = 5; 3 - = 11

. , . [9] [10].

1. ., ., ., . . .: , 1989. 512 .
2. . . .: , 1984. 303 .
3. .. . . . . .: , 2000. 223 .
4. Basu A., Harris I.R., Hjort N.L., Jones M.C. Robust and efficient estimation by minimising a density power divergence // Biometrika. 1998. V. 85. P. 549-559.
5. Hogg V., Horn P.S., Lenth R.V. On adaptive estimation // J. Statistical Planning and Inference. 1984. V. 9. P. 333-1343.
6. Beran R. An efficient and robust adaptive estimator of location // Ann. Stat. 1978. V. 6. . 2. P. 292-313.
7. .. . . II. . : - , 2004. 163 .
8. RymarI.V., Simakhin V.A. Nonparametric robust estimates of the shift and scale parameters // Proc. SPIE. 2005. V. 6160. P. 230-239.
9. Simakhin V.A. Nonparametric robust regression estimate // Proceedings SPIE. 2006. P. 130-139.
10. Simakhin V.A. Nonparametric robust prediction algorithms // Proc. International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations management. Beer Sheva, Israel, 2010. P. 1017-1030.
11. .. . LAMBERT Academic Publishing, Germany, 2011. 292 .



E-mail: sva_full@mail.ru, ocherepanov@inbox.ru 2 2012 .
Simakhin Valerii A., Cherepanov Oleg S. (Kurgan State University). Adaptive estimation of location parameter.
Keywords: Adaptive; robust; nonparametric; estimation.
There are proposed adaptive robust estimates of location parameter on the basis of weighted maximum likelihood method. The effectiveness of the proposed estimates in the case of symmetrical and asymmetrical outliers is studied. The robust nonparametric estimates appeared to be are effective and adaptive both to the kind of distribution and clogging sample degree.