Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
statistician_ja_lt5.pdf
Search
Takayuki Uchiba
November 15, 2020
Science
0
680
statistician_ja_lt5.pdf
一様最小分散不偏推定量が存在しない例を紹介しました。
Takayuki Uchiba
November 15, 2020
Tweet
Share
More Decks by Takayuki Uchiba
See All by Takayuki Uchiba
縮小推定のはなし.pdf
utaka233
1
2.5k
高次元データに対するL1正則化の有効性
utaka233
1
3.1k
Other Decks in Science
See All in Science
Quelles valorisations des logiciels vers le monde socio-économique dans un contexte de Science Ouverte ?
bluehats
1
530
baseballrによるMLBデータの抽出と階層ベイズモデルによる打率の推定 / TokyoR118
dropout009
2
580
データから見る勝敗の法則 / The principle of victory discovered by science (open lecture in NSSU)
konakalab
1
180
06_浅井雄一郎_株式会社浅井農園代表取締役社長_紹介資料.pdf
sip3ristex
0
650
データベース04: SQL (1/3) 単純質問 & 集約演算
trycycle
PRO
0
1k
データベース05: SQL(2/3) 結合質問
trycycle
PRO
0
810
02_西村訓弘_プログラムディレクター_人口減少を機にひらく未来社会.pdf
sip3ristex
0
630
ド文系だった私が、 KaggleのNCAAコンペでソロ金取れるまで
wakamatsu_takumu
2
1.4k
論文紹介 音源分離:SCNET SPARSE COMPRESSION NETWORK FOR MUSIC SOURCE SEPARATION
kenmatsu4
0
330
知能とはなにかーヒトとAIのあいだー
tagtag
0
140
データベース10: 拡張実体関連モデル
trycycle
PRO
0
990
Celebrate UTIG: Staff and Student Awards 2025
utig
0
240
Featured
See All Featured
Fireside Chat
paigeccino
40
3.7k
Cheating the UX When There Is Nothing More to Optimize - PixelPioneers
stephaniewalter
285
14k
Speed Design
sergeychernyshev
32
1.1k
Practical Orchestrator
shlominoach
190
11k
What's in a price? How to price your products and services
michaelherold
246
12k
Improving Core Web Vitals using Speculation Rules API
sergeychernyshev
19
1.2k
The Language of Interfaces
destraynor
162
25k
Practical Tips for Bootstrapping Information Extraction Pipelines
honnibal
PRO
23
1.5k
Bootstrapping a Software Product
garrettdimon
PRO
307
110k
Measuring & Analyzing Core Web Vitals
bluesmoon
9
610
Why You Should Never Use an ORM
jnunemaker
PRO
59
9.6k
Art, The Web, and Tiny UX
lynnandtonic
303
21k
Transcript
Ұ༷࠷খࢄෆภਪఆྔඞͣଘࡏ͢Δ͔ʁ !VUBLB
Ұ༷࠷খࢄෆภਪఆྔ ͷҰ༷࠷খࢄෆภਪఆྔʢ6.76&ʣɹ ෆภੑ ͕ͲΜͳͰ͋ͬͯɺ ͕Γཱͭɻ Ұ༷࠷খࢄੑ ͕ͲΜͳͰ͋ͬͯɺଞͷෆภਪఆྔ
ʹൺͯ ͷࢄ͕খ͍͞ɻཁ͢Δʹɺ ͕Γཱͭɻ ྫαΠζ ͷಠཱඪຊΛظ ࢄ ͷਖ਼ن͔Βಘͨ߹ ɾظ ͷ6.76&ඪຊฏۉ ɾࢄ ͷ6.76&ෆภࢄ T θ θ [T] = θ θ S T [T] ≤ [S] n μ σ2 μ σ2
6.76&ͷѻ͍͢͞ʢͦͷʣ $SBNFS3BPͷఆཧ͋Δෆภਪఆྔ͕6.76&͔ఆ͢Δํ๏ͷͻͱͭ ɾෆภਪఆྔͷࢄͷେ͖͞ͷԼݶܭࢉͰ͖Δɻ ɹɾ$SBNFS3BPԼݶ'JTIFSใྔ ɾෆภਪఆྔ ͷࢄ͕͜ͷԼݶʹҰக͢Ε6.76& ʢʣ6.76&ͷࢄ͕ඞͣ͜ͷԼݶʹͳΔΘ͚Ͱͳ͍ɻ T
6.76&ͷѻ͍͢͞ʢͦͷʣ -FINBOO4DIF⒎Fͷఆཧ6.76&ಛఆͷ݅ͷͱͰ࡞ΕΔɻ ɾಛఆͷ݅උे౷ܭྔͷଘࡏ ɾඋे౷ܭྔͰද͞ΕΔ౷ܭྔ͕ෆภͳΒ6.76& ɾ$SBNFS3BPͷఆཧ͕༗ޮͰͳ͍έʔεͰಛʹศར ɹɾ'JTIFSใྔ͕ఆٛͰ͖ͳ͍ͱ͖ʢҰ༷ͷ࠷େύϥϝʔλʣ ɹɾ6.76&ͷࢄ㱠$SBNFS3BPԼݶͷͱ͖
6.76&ඞͣଘࡏ͢Δ͔ʁ ύϥϝʔλ ͷ6.76&ඞͣଘࡏ͢Δ͔ʁ ɾ-FINBOO4DIF⒎Fͷఆཧඋे౷ܭྔ͕ଘࡏ͢Ε6.76&࡞ΕΔɻ ɾඋे౷ܭྔ͕ଘࡏ͠ͳ͚ΕͲ͏͔ʁ ɾ)JOUҰ༷࠷খࢄੑʹݱΕΔʮ ͕ͲΜͳͰ͋ͬͯʯڧ͍݅ ˠɹ ͷ͝ͱʹ࠷খࢄͷෆภਪఆྔ͕ҟͳΕɺ6.76&ଘࡏ͠ͳ͍ɻ θ
θ θ
۩ମྫͷߏ ֬ม ͕࣍ͷ࣭֬ྔؔ ʹै͍ͬͯΔͷͱ͠·͢ɻύϥϝʔλ ͷҰ༷࠷খࢄෆภਪఆྔଘࡏ͢Δ͔ʁ ٕज़తͳ3FNBSL Ͱද͞ΕΔͲΜͳ౷ܭྔɺ ͷܗͰද͢͜ͱ͕Ͱ͖Δɻ X
f(x) = { p JGx = − 1 (1 − p)2px JGx = 0,1,2,⋯ p X T(X) = ∞ ∑ x=−1 tx [X = x]
ෆภਪఆྔʹͳΔͨΊͷ݅ Λ༻͍ͯɺ౷ܭྔ ͷظΛܭࢉ͢Δɻ ౷ܭྔ ͕ෆภਪఆྔͳΒɺظඞͣ ʹ͘͠ͳΔɻ ˠɹԽࣜ GPS
ˠɹ ͷܗͰද͞ΕΔ౷ܭྔ ͕ෆภਪఆྔʹͳΔɻ f(x) = { p JGx = − 1 (1 − p)2px JGx = 0,1,2,⋯ T(X) [T] = t−1 p + ∞ ∑ x=0 tx (1 − p)2px = t0 + ∞ ∑ x=1 (tx−2 − 2tx−1 + tx )px T(X) p tx − 2tx−1 + tx−2 = 0 x ≥ 2 t1 = 1 − t−1 t0 = 0 tx = x(1 − t−1 ) T(X)
ෆภਪఆྔͷࢄΛܭࢉ͢Δʢͦͷʣ Λ༻͍ͯɺෆภਪఆྔ ͷࢄΛܭࢉ͢Δɻ ͜͏͍͏ͱ͖ʹཱͭͷࢄͷެࣜʂ ͳͷͰɺ Λܭࢉ͠Α͏ɻ f(x) = {
p JGx = − 1 (1 − p)2px JGx = 0,1,2,⋯ T(X) [T] = [T2] − [T]2 = [T2] − p2, ෆภੑ [T2]
ෆภਪఆྔͷࢄΛܭࢉ͢Δʢͦͷʣ Ώ͑ʹɺ ͷࢄ ͱΘ͔Γ·͢ɻ [T2] = t2 −1 p
+ ∞ ∑ x=1 x2(1 − t−1 )2(1 − p)2px = t−1 + (1 − t−1 )2(1 − p)2 ∞ ∑ x=1 x2px = t2 −1 p + (1 − t−1 )2(1 − p)2 p(1 + p) (1 − p)3 = t2 −1 p + (1 − t−1 )2 p(1 + p) 1 − p T(X) [T] = t2 −1 p + (1 − t−1 )2 p(1 + p) 1 − p − p2
ࢄ͕࠷খΛͱΔͨΊͷ݅ʢͦͷʣ ࠷খࢄΛ༩͑Δ ʢΛ༩͑Δ ʣΛٻΊɺ ʹґଘͳΒ6.76&ଘࡏ͠ͳ͍ɻ Λ Ͱཧ͢Δͱɺ͕࣍ؔݱΕΔɻ ฏํͯ͠ɺ࠷খΛ༩͑Δ ΛٻΊͯΈΑ͏ʂ
T(X) t−1 p [T] = t2 −1 p + (1 − t−1 )2 p(1 + p) 1 − p − p2 t−1 [T] = (p + p(1 + p) 1 − p ) t2 −1 − 2 p(1 + p) 1 − p t−1 + ( p(1 + p) 1 − p − p2 ) t−1
ࢄ͕࠷খΛͱΔͨΊͷ݅ʢͦͷʣ ฏํ͢Δͱɺ࣍ͷΑ͏ʹͳΓ·͢ɻ ࣍ؔͷͷ࠲ඪΛಡΉ͜ͱͰɺ ͷͱ͖ࢄ࠷খͱΘ͔Γ·͢ɻ [T] = (p + p(1
+ p) 1 − p ) t−1 − 1 1 + 1 − p 1 + p 2 + const . = (p + p(1 + p) 1 − p ) {t−1 − p + 1 2 } 2 + const . t−1 = p + 1 2
݁ ࢄ͕࠷খʹͳΔෆภਪఆྔ͕ύϥϝʔλ ͷʹґଘ͍ͯ͠Δɻ ˠɹ ͷ6.76&ଘࡏ͠ͳ͍ʂʂʂʂʂ ͜ͷྫ͕ڭ͑ͯ͘Ε͍ͯΔͱࢥ͏͜ͱʢࢲײʣ ɾඞͣ͠ʮ͍ͭͰ҆ఆͯ͠ਫ਼͕ྑ͍ਪఆྔʯ͕ଘࡏ͢ΔͱݶΒͳ͍ɻ ɾԾઆ͕͋ΔͳΒਪఆྔʹөͤͯ͞ΈΔͷେࣄɻ ɹɾࠓճͷྫͰɺ ͷʹԠͨ͡ਪఆྔͷબͷ༨͞Ε͍ͯΔɻ
ɹɾDMJDLখ͘͞ͳΓ͕͔ͪͩΒɺͪΐͬͱॖখͨ͠ͷΛ͓͏ͱ͔ɻ p p p
͝ਗ਼ௌ͋Γ͕ͱ͏͍͟͝·ͨ͠ʂ ࣗݾհͰͬͱ͖·͢ɻɻɻ ɾ!VUBLB ɾגࣜձࣾ͢͏͕͘ͿΜ͔ ڭ෦ ෦ ɾڵຯཧ౷ܭֶͷσʔλϚΠχϯάͷԠ༻ زԿֶ ɾจ ɹओஶ(MVJOH4UBCJMJUZ$POEJUJPOTPO3VMFE4VSGBDFXJUI1PTJUJWF(FOVT
ɹɹɹɹ0TBLB+PVSOBMPG.BUIFNBUJDT BDDFQUFE ɹڞஶࠓຊɺ͍ͣΕػցֶशͷจɻ