RUTILEA社内で定期的に行っている勉強会の第3回です． 第三回のテーマは”意外な統計”です.

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# l Z s c o r e v i a robust s t a t i s t i c s
# 2 Bayesian perspective

3. # l Z s c o r e v i a robust s t a t i s t i c s
Z
z=¥¥Y#
He,I f z > 3 , w e regard
×
i t a s a n outlier.
But, this method could be unstable.
|CA# t r u e observation i 6,27, 6.34, 6,25, 6,31, 6.28
mistake observation: 6,27, 6,34, 6.25, 63, I , 6.28
-

4. ( l
Non robust s t a t i s t i c s c a n n o t detect outliers'
i n the c a s e of s m a l l samples."
Actuall, m e a n ( x ) =
T I L X = 17.65
Std ( X ) =
2 5 . 4 1
Z = -
0 . 4 5 , - 0 . 4 5 , - 0 . 4 5 , # - 0 , 4 5
W e w i l l modify this conventional s t a t i s t i c s
with robust s t a t i s t i c s .
m e a n → median
S td → median absolute deviation (MAD)

5. median (X)
6. 2 5 I 6.27 E # E b. 3 4 E 63,10
stable e s t i m a t o r
M A D (X) =
1.48 med: ahl X i - m e d i a n 1411
=
0 , 0 4 4 (true Std i s
0.035)
stable e s t i m a t o r
Robust z s c o r e
-
0 . 2 2 E 1,35 E - O . 6 7 E / 2 7 7, 5 E O, O

6. Discussion a n d Conclusion
* I n the c a s e of small dataset, normal s t a t i s t i c s
i s affected by outliers to o heavily.
* The influence could be asseseid by the
influence analysis.
Ref, M i a hubert, et.cl. 2017.

7. # 2 Bayesian perspective
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