Nzira yeBootstrap muStatistics
Pendauluan
Statistics isayenzi inovavarira kuunganidza, kuongorora, kududzira, uye kupa data. Kuongorora statistics kunowanzo vimba nepfungwa dzakati kana dzidziso dzezvingangoitika dzinoda saizi huru dzesamples kuti pave nefungidziro dzakarurama. Zvisinei, mune dzakawanda mamiriro ezvinhu, kuwana samples hombe hazvishandi uye hazvigoneki. Apa ndipo panobatsira zvikuru nzira yebootstrap, nzira yekuenzanisa data patsva.
Nzira yebootstrap yakatanga kuunzwa naBradley Efron muna 1979 uye yave imwe yenzira dzakakurumbira muhuwandu hwevanhu nekuda kwekuchinjika kwayo uye kugona kwayo kugadzira fungidziro dzakarurama dzehuwandu hwevanhu pasina kuita fungidziro chaiyo yekugovera. Chinyorwa chino chichatsanangura misimboti yekutanga yenzira yebootstrap, matanho ayo ekushandisa, uye mienzaniso yakati wandei yekushandiswa kwayo muhuwandu hwevanhu.
Nheyo dzekutanga dzeBootstrap Method
Nzira yebootstrap inzira isiri yeparametric inotibvumira kufungidzira kugoverwa kwenhamba (semuenzaniso, mean, median, variance) nekudzokorora sampuli yedata redu rekutanga. Nheyo huru yenzira iyi ndeyekushandisa data riripo (muenzaniso wekutanga) kutevedzera akawanda ma data matsva nekudzokorora sampuli.
Anotevera matanho ekutanga anotorwa nenzira yebootstrap:
1. Muenzaniso: Kubva padata rekutanga rehukuru N, dzokorora nguva dzeN uchitsiva. Izvi zvinoreva kuti zvinhu zvakasarudzwa kuti zviongororwe zvinogona kusarudzwa kanopfuura kamwe chete.
2. Verenga Nhamba: Verenga nhamba dzinodiwa (semuenzaniso, pakati, pakati) dzemuenzaniso wega wega.
3. Dzokorora Maitiro: Dzokorora matanho 1 ne2 kakawanda (semuenzaniso B=1000 kana kupfuura) kuti uwane kugoverwa kwenhamba yaunofarira kubva pakutanga kusvika padanho rekutanga.
4. Kufungidzira uye Mhedziso: Shandisa iyi bootstrap distribution kugadzira confidence intervals, edza hypotheses, kana kugadzira dzimwe inferential statistics.
Matanho Ekushandisa Bootstrap
Nzira ye bootstrap inogona kutsanangurwa zvakadzama mumatanho anotevera:
1. Kutorazve sampuro
Kudzokorora sampuli nekuchinjana ndiyo pfungwa huru yenzira yebootstrap. Tichishandisa data rekutanga, tinogadzira seti itsva dzakawanda dzedata, dzinonzi bootstrap samples. Sampuro yega yega yebootstrap imhedzisiro yekutora sampuli N times kubva kudata rekutanga rehukuru N, asi nekutsiva, kuitira kuti zvinhu zviri musampuli yekutanga zvioneke kanopfuura kamwe musampuli yebootstrap.
Muenzaniso:
Kana tine data rekutanga \[3, 5, 7, 9\], saka imwe sampuro yebootstrap inogona kuva \[3, 9, 9, 5\].
2. Kuverenga Nhamba dzeBootstrap
Pamuenzaniso wega wega webootstrap, verenga nhamba yaunoda. Ngatitii tine hanya neavhareji, taizoverenga avhareji yemuenzaniso wega wega webootstrap. Kana tikadzokorora maitiro aya kaB, tichava neB inofungidzirwa yeavhareji.
3. Kugadzira Kugoverwa kweBootstrap
Nekubatanidza nhamba dzese dzakaverengwa kubva kuB bootstrap samples, tinogadzira bootstrap distribution yenhamba inodiwa. Kugoverwa uku kunoshandiswa kufungidzira kugoverwa kwesampuli yenhamba.
4. Kufungidzira kweStatistical
Kubva mukugoverwa uku kwe bootstrap, tinogona kuita fungidziro dzakasiyana dzemasvomhu. Semuenzaniso, tinogona kuona nguva dzekuvimba nekutora ma percentiles kubva mukugoverwa kwe bootstrap kana kuyedza fungidziro nekutarisa p-value yakawanikwa kubva mukugoverwa uku.
Muenzaniso wekushandisa Bootstrap Method
Kuti tipe mufananidzo wakajeka, ngatitarisei mimwe mienzaniso yekuti nzira ye bootstrap inoshandiswa sei mumamiriro ezvinhu anoshanda.
Muenzaniso 1: Nguva Yekuvimba Yakaenzana
Ngatitii tine ruzivo rwemimwe mienzaniso yehuremu hwemuviri hwevanhu gumi seizvi: \[60, 62, 67, 70, 65, 68, 64, 60, 66, 63].
1. Kubva pane data iri, tinotora samples dzebootstrap dzinosvika chiuru dzine saizi imwe chete, semuenzaniso:
– Muenzaniso wechipiri: \[62, 67, 70, 67, 64, 62, 63, 65, 68, 60\]
– Muenzaniso wechipiri: \[60, 62, 70, 70, 63, 64, 63, 65, 68, 62\]
- nezvimwewo…
2. Kubva pamuenzaniso wega wega webootstrap, tinoverenga avhareji:
– Avhareji yemuenzaniso 1: (62+67+70+67+64+62+63+65+68+60) / 10
– Avhareji yemuenzaniso 2: (60+62+70+70+63+64+63+65+68+62) / 10
- nezvimwewo…
3. Nekudzokorora danho iri ka1000, tichawana huremu hweavhareji hunosvika chiuru.
4. Neavhareji iyi yedata 1000, tinogadzira bootstrap distribution totora 2.5th ne97.5th percentiles kuti tigadzire 95% confidence interval.
Muenzaniso 2: Bvunzo yeMultiple Median Hypothesis
Ngatitii tinoda kuyedza kana ma median emaseti maviri edata akaenzana. Tinogona kushandisa bootstrapping kugadzira kugoverwa kwemusiyano muma median.
1. Tora sampuli dzebootstrap kubva kune imwe neimwe yedata rekutanga.
2. Verenga musiyano wepakati wemuenzaniso wega wega webootstrap.
3. Gadzira kugoverwa kwemusiyano wepakati we bootstrap.
4. Ona kana zero iri mukati menguva yekuvimba yekugoverwa.
Zvakanakira uye Zvisina Kukwana zveBootstrap Method
Kelebihan
- Hazvina kuenzanisa: Hazvidi fungidziro pamusoro pekugoverwa kwedata.
- Kushanda Kwemasampuli Madiki: Kunoshanda kunyangwe kumasampuli madiki.
- Inochinjika: Inogona kushandiswa kuhuwandu hwehuwandu hunosanganisira huwandu hwepakati, hwepakati, hwekudzoka, nezvimwewo.
– Zviri Nyore Kushandiswa: Nekufambira mberi kwetekinoroji yemakombiyuta, nzira yebootstrap iri nyore kushandisa nerubatsiro rwesoftware yehuwandu hwakadai seR kana Python.
Miganhu
- Mutengo weKushandisa Komputa: Inogona kuda zvinhu zvakawanda zvekushandisa pakombuta kunyanya nehukuru hwedata kana huwandu hwakawanda hwesamples dzebootstrap (B).
– Mhando dzakasiyana-siyana dzemuenzaniso: Dzakakodzera chete mienzaniso inomiririra zvakakwana huwandu hwepakutanga.
- Hazvidziviriri Kubva Kurusaruro: Kana data rekutanga rakarerekera, saka sampuro dzese dzebootstrap dzine rusaruro rwakafanana.
Mhedziso
Nzira yebootstrap inopa mhinduro ine simba uye inochinjika kumatambudziko mazhinji ekufungidzira kwenhamba. Nekukwanisa kwayo kufungidzira zvinobudirira kugoverwa kwenhamba dzakasiyana pasina kufunga nezvekugoverwa kwacho, nzira yebootstrap yave chishandiso chakakosha mukuongorora data. Pasinei nemiganhu yayo, mabhenefiti ayo anowanzo pfuura mari yekuverenga. Kana ikashandiswa nemazvo, nzira yebootstrap inogona kupa ruzivo rwakadzama uye rwakarurama mukuongorora nhamba.
