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1 No.118 (2015)

2 (c) The Institute of Statistical Mathematics 2016

3 No.118 (2015)

4

5 I i

6 II Z MS ii

7 I

8

9 (2.1) 3

10 % 45.5% (a) Z 6 (b) 2 4 (c) MS 8 3 (a) Z % 47.3%(b) % 44.7%(c) MS % 44.8%3 4

11 ,200 2, (2,000 1,000 2,000 1,000 ) 2, , () QUO (500 ) ( de )

12 2 3 (a) Z 6 (b) 2 4 (c) MS A QUO A (, 2015) () (, 2013) ( ) (, 2013) () (, 2014)

13 : Z MS Z MS , ( de ) 7

14 (a) (b) (c) Z 6 A4 3 1 Z A (A3 1 ) (A4 1 ) A4 2 (a) (b) 2 MS 8 A4 4 MS (a) Z 6 (b) 2 4 (c) MS ˆp = / wi c y i wi c (2.1) i S i S 8

15 2.3. S y i i ( 1 0) w c i i (2.1) w c i w c i = w i g i,c (2.2) w i g i,c a i w i N a 2, 000 n a M 1,0002,000 N a w i = 1, 000 2, 000 m 1,0002, (2.3) M 1,000 N a m 1, , 000 M 1,0002,000 M 1,000 m 1,0002,000 m 1,000 N a a n a a g i,c (2 ) 10 (6 ) = 12 g i,c = δ N k k i,k i δ = i,kw δ N k i k i,k (2.4) ˆN k N k 12 k δ i,k i k ˆp ŜE(ˆp) = m h h m h 1 a S h i S ha w i z i 1 w i z i m h i S ha a S h 2 (2.5) S h h PSU m h S ha h a PSU z i = 1 N { k δ i,k ( N k i y i δ )} i,kw i y i ˆN k ˆN k (2.6) 9

16 (2.1) wi c wi c = δ i,r w i g i,n g i,c (2.7) δ i,r i ( 1 0) w i (2.3) g i,n g i,c g i,n g i,c g i,n () : PSU

17 2.3. (Breiman, et al., 1984) g i,n = : () 2.2: () 11

18 g i,n g i,n = δ i,cw i i / i δ i,cδ i,r w i (2.8) δ i,c i c 1 0 g i,c 2.3 (2 ) 10 (6 ) = 12 g i,c = N k i δ i,kδ i,r w i g i,n (2.9) N k 12 k δ i,k i k 2.3: (H ) (H ) , , , , , , , , , , , , , , , , , , , , , , , , , , (2.7) ˆp 2,000 PSU 2,000 PSU PSU 1,095 1,095 r (r =1,...,1095) S h S h r PSU S r (2.3) w i w (r) i δ i,r w (r) i g (r) i,n g(r) i,c 0 i S h & i S r 12 w (r) i = C r w i w i i S h & i S r i S h (2.10)

19 2.3. S r = S \ S r S h = S \ S h S r S h K h h PSU C r = K h /(K h 1) r (2.11) ˆp (2.12) ˆp (r) = i S / δ i,r w (r) i g (r) i,n g(r) i,c y i δ i,r w (r) i g (r) i,n g(r) i,c (2.11) i S ŜE(ˆp) = (ˆp C (r) ˆp ) 2 r r=1 (2.12) 13

20 (2.2) % 45.5% 3.1: () % % (1.3) (1.4) Z % % 6 (2.0) (2.6) % % (2.2) (2.2) MS % % 8 (2.2) (2.5) MS 8 Z Z

21 % 45% 40% MS 50% 45% 40% MS 35% 35% 30% 30% 25% 25% 20% 20% 15% 15% 10% 10% 5% 5% 0% % : % 50% 100% 0% 50% 100% 3.2: ( 3.3) 48% 41% 20 12% 15

22 % 50% 100% 0% 50% 100% 3.3: % 80% 60% 40% 20% 0% 0% 20% 40% 60% 80% 100% 3.4: 16

23 % 4 20% % 50% 100% 0% 50% 100% 3.5: 17

24 A % 50% 100% 0% 50% 100% 3.6: % 50% 0% 0% 50% 100% 3.7: 4 18

25 A % 80% 60% 40% 20% 0% 0% 20% 40% 60% 80% 100% 3.8:

26 % 50% 0% 0% 50% 100% :

27 % 0% 0% 50% 50% 0% 0% 50% 3.10: % 0% 0% 100% 100% 0% 0% 100% 3.11:

28 % 0% 0% 100% 100% 0% 0% 100% 3.12:

29 % 0% 0% 100% 100% 0% 0% 100% 3.13: 60% 40% % 0% 3.14:

30 ( ) % 50% 0% 0% 50% 100% 3.15: % 50% 100% 0% 50% 100% 3.16: 24

31 % 50% 0% 0% 50% 100% 3.17:

32 % 50% 0% 0% 50% 100% 3.18: % 50% 100% 0% 50% 100% 3.19: 10 25% 4 3 ( 3.19) 26

33 % 50% 100% 0% 50% 100% 3.20:

34 % 50% 100% 0% 50% 100% 3.21: 11 ( 0 10) % 20% 0% 0% 20% 40% :

35 % 50% 100% % 50% 100% : % 50% 0% 0% 50% 100% 3.24: 29

36 4 Breiman, L., Friedman, J.H., Olshen, R.A., & Stone, C.J. (1984) Classification and Regression Trees, Wadsworth. (2014) (2014), No.115. (2013) (2013), No.112. (2013) (2012), No.108. (2015) 13, No

37 II

38

39 # D.K. N (2012) (2012)2012 (, 2013) (2013) (2013)2013 (, 2013) (2014)2014 (, 2014) (2013) (, 2015) (2.1) (2.12) 100%

40 D. N K ,045 (1.6) (1.5) (1.2) (1.6) (0.5) (2.4) (2.3) (1.8) (2.1) (0.8) (2.2) (1.8) (1.5) (2.4) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 34

41 D. N K ,045 (1.7) (1.6) (1.1) (0.8) (0.8) (0.5) (2.4) (2.1) (1.4) (1.2) (1.2) (0.8) (2.4) (2.4) (1.7) (0.8) (1.1) (0.5) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 35

42 D. N K ,045 (1.7) (1.9) (1.6) (0.8) ( ) (0.1) (2.5) (2.6) (2.4) (1.0) ( ) ( ) (2.2) (2.8) (2.0) (1.3) ( ) (0.2) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 36

43 D. N K ,045 (0.9) (1.9) (1.9) (1.1) (0.5) (0.3) (1.3) (2.7) (2.8) (1.5) (0.3) (0.4) (1.4) (2.6) (2.7) (1.6) (1.0) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 37

44 D. N K ,045 (1.9) (2.0) (1.5) (1.0) (0.1) (0.2) (2.7) (3.1) (2.2) (1.2) (0.1) (0.3) (2.5) (2.4) (1.9) (1.5) ( ) ( ) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 38

45 D. N K ,045 (1.7) (1.8) (1.3) (0.6) (0.2) (0.2) (2.5) (2.6) (1.7) (0.8) (0.2) (0.3) (2.1) (2.5) (1.9) (0.9) (0.4) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 39

46 D. N K ,045 (1.9) (1.7) (1.8) (1.0) (0.1) (0.2) (2.8) (2.5) (2.7) (1.5) (0.1) (0.4) (2.6) (2.3) (2.2) (1.1) (0.3) (0.2) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 40

47 D. N K ,045 (1.1) (2.0) (2.0) (1.5) (0.1) (0.2) (1.4) (2.7) (2.9) (2.0) ( ) (0.3) (1.8) (3.0) (2.6) (2.4) (0.3) (0.1) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 41

48 D. N K ,045 (1.9) (2.1) (1.3) (0.8) (0.2) (0.2) (2.8) (3.2) (2.0) (1.3) (0.3) (0.3) (2.6) (2.7) (1.7) (0.7) (0.3) (0.3) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 42

49 D. N K ,045 (1.6) (1.9) (1.2) (1.2) (0.2) (2.4) (2.6) (1.0) (1.7) (0.1) (2.1) (2.7) (2.2) (1.6) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 43

50 5 4-A D. N K (1.9) (1.2) (0.9) (1.3) (0.5) (2.6) (1.8) (1.1) (1.8) (0.7) (2.8) (1.2) (1.7) (1.6) (0.6) (2012) (2012) (2013) (2013) (2014) (2013) 44

51 D. N K ,045 (0.6) (1.0) (1.2) (0.7) (1.0) (1.5) (1.7) (0.8) (0.8) (1.3) (1.7) (1.2) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 45

52 D. N K ,045 (0.5) (1.2) (1.3) (0.7) (0.7) (1.7) (2.0) (0.9) (0.7) (1.7) (1.8) (1.2) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 46

53 D. N K ,045 (0.8) (1.3) (1.5) (0.6) (1.3) (2.0) (2.3) (0.7) (1.0) (1.4) (1.9) (1.1) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 47

54 D. N K ,045 (0.8) (1.6) (1.6) (0.7) (1.3) (2.1) (2.3) (0.8) (0.8) (2.3) (2.3) (1.1) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 48

55 A D. N K (2.3) (3.0) (2.3) (1.2) (1.2) (3.0) (4.3) (3.2) (1.6) (0.9) (3.7) (4.1) (3.3) (1.7) (2.6) (2012) (2012) (2013) (2013) (2014) (2013) 49

56 5 5-A D. N K (0.8) (2.7) (2.8) (1.8) (1.0) (1.2) (3.3) (3.4) (2.4) (0.7) (1.1) (4.5) (4.9) (2.7) (2.4) (2012) (2012) (2013) (2013) (2014) (2013) 50

57 A D. N K (1.8) (3.0) (2.5) (1.6) (1.3) (2.1) (4.1) (3.3) (2.2) (1.2) (3.1) (4.5) (3.8) (2.0) (2.7) (2012) (2012) (2013) (2013) (2014) (2013) 51

58 5 5-A D. N K (1.3) (2.5) (2.7) (1.8) (1.2) (1.6) (3.3) (3.6) (2.6) (0.7) (2.2) (4.0) (4.1) (2.5) (2.7) (2012) (2012) (2013) (2013) (2014) (2013) 52

59 A D. N K (1.0) (2.2) (2.8) (2.1) (1.1) (1.6) (2.8) (4.0) (2.7) (0.7) (0.9) (3.4) (3.9) (3.3) (2.6) (2012) (2012) (2013) (2013) (2014) (2013) 53

60 5 5-A D. N K (1.4) (2.6) (2.7) (1.5) (1.1) (1.7) (3.4) (3.7) (1.9) (0.7) (2.5) (3.9) (3.8) (2.6) (2.6) (2012) (2012) (2013) (2013) (2014) (2013) 54

61 D. N K ,045 (1.3) (1.4) (0.6) (2.1) (2.2) (0.7) (1.3) (1.5) (0.9) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 55

62 D. N K ,045 (0.9) (1.1) (0.5) (1.5) (1.6) (0.7) (1.1) (1.3) (0.8) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 56

63 D. N K ,045 (1.3) (1.4) (0.6) (2.2) (2.4) (0.8) (1.4) (1.5) (0.8) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 57

64 D. N K ,045 (1.0) (1.1) (0.6) (1.5) (1.5) (0.7) (1.4) (1.5) (0.9) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 58

65 D. N K ,044 (0.9) (1.1) (0.6) (1.4) (1.6) (0.8) (1.2) (1.4) (0.9) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 59

66 D. N K ,045 (1.9) (1.7) (1.6) (0.4) (2.8) (2.5) (2.4) (0.6) (2.5) (2.3) (2.1) (0.7) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 60

67 D. N K ,045 (1.8) (1.8) (0.3) (2.4) (2.5) (0.5) (2.6) (2.6) (0.4) (2012) (2012) (2013) (2013) (2014) (2013) 61

68 D. N K ,045 (1.7) (1.7) ( ) (0.3) (2.5) (2.5) ( ) (0.4) (2.3) (2.3) ( ) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) 62

69 D. N K ,045 (1.7) (1.8) (0.6) (2.4) (2.5) (1.0) (2.5) (2.4) (0.7) (2012) (2012) (2013) (2013) (2014) (2013) 63

70 5 #2.3h D. N K ,045 (1.6) (1.9) (1.3) (1.0) (0.4) (0.2) (2.4) (2.8) (1.9) (1.5) (0.5) (0.3) (2.0) (2.4) (1.8) (1.5) (0.6) (0.1) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 64

71 5.2. #2.3d D. N K ,045 (1.0) (1.6) (1.6) (1.4) (0.4) (0.1) (1.6) (2.4) (2.2) (2.0) (0.6) (0.1) (1.2) (2.1) (2.3) (1.9) (0.5) (0.3) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 65

72 5 #2.3c D. N K ,045 (1.7) (1.8) (1.1) (0.8) (0.6) (0.2) (2.6) (2.7) (1.8) (1.1) (0.9) (0.3) (2.0) (2.2) (1.3) (1.3) (0.8) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 66

73 5.2. #2.3l D. N K ,045 (1.6) (1.7) (1.5) (0.9) (0.4) (0.2) (2.6) (2.4) (2.2) (1.3) (0.5) (0.3) (1.8) (2.5) (2.2) (1.2) (0.6) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 67

74 5 # D. N K ,045 (1.3) (1.7) (1.8) (1.1) (0.3) (0.2) (1.9) (2.6) (2.8) (1.6) (0.5) (0.3) (1.7) (2.0) (2.2) (1.6) (0.3) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 68

75 5.2. #2.30c D. N K ,045 (0.9) (1.2) (1.8) (1.6) (0.3) (0.3) (1.2) (1.5) (2.5) (2.4) (0.4) (0.6) (1.3) (1.8) (2.6) (2.1) (0.4) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 69

76 5 #2.30d D. N K ,045 (1.1) (1.6) (1.8) (0.9) (0.2) (0.4) (1.6) (2.3) (2.6) (1.3) (0.4) (0.7) (1.5) (2.2) (2.5) (1.2) ( ) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 70

77 5.2. #2.30e D. N K ,045 (1.0) (1.3) (1.8) (1.7) (0.8) (0.4) (1.5) (2.0) (2.7) (2.5) (1.0) (0.6) (1.2) (1.8) (2.4) (2.1) (1.2) (0.7) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 71

78 5 #2.30g D. N K ,045 (1.3) (1.4) (2.0) (1.6) (0.4) (0.4) (1.9) (2.0) (2.9) (2.4) (0.5) (0.6) (1.7) (2.0) (2.7) (1.9) (0.7) (0.7) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 72

79 5.2. #2.30h D. N K ,045 (1.3) (1.6) (1.8) (1.1) (0.3) (0.3) (1.9) (2.6) (2.7) (1.6) (0.6) (0.5) (1.9) (1.9) (2.2) (1.6) (0.3) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 73

80 D. N K ,045 (1.3) (1.5) (1.8) (1.0) (0.2) (0.3) (1.8) (2.2) (2.7) (1.4) (0.4) (0.5) (1.7) (2.1) (2.5) (1.4) (0.2) (0.4) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 74

81 5.2. #7.30a D. N K ,045 (1.1) (1.7) (1.8) (1.4) (1.2) (0.3) (0.3) (1.8) (2.7) (2.7) (2.1) (1.8) (0.3) (0.3) (1.3) (1.7) (2.4) (1.8) (1.7) (0.4) (0.5) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 75

82 5 #2.3* D. N K ,045 (0.3) (0.6) (0.6) (0.8) (0.5) (1.4) (0.8) (1.1) (1.4) (1.4) (1.1) (0.3) (0.3) (0.8) (0.9) (1.0) (0.6) (1.9) (1.1) (1.7) (2.1) (2.2) (1.7) (0.4) (0.4) (0.8) (0.9) (1.1) (0.8) (1.9) (1.2) (1.4) (2.0) (1.5) (1.2) (0.5) (2012) (2012) (2013) (2013) (2014) ,090 (2013) ,579 76

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