Cya stattya maye kilka nedolikiv Bud laska dopomozhit udoskonaliti yiyi abo obgovorit ci problemi na storinci obgovorennya U cij statti vidsutnij vstupnij rozdil sho maye mistiti viznachennya predmeta i stislij oglyad najvazhlivishih aspektiv statti Vi mozhete dopomogti proyektu napisavshi preambulu cherven 2023 Cya stattya ne maye interviki posilan Vi mozhete dopomogti proyektu znajshovshi 1 ta dodavshi yih do vidpovidnogo elementu Vikidanih cherven 2023 Nehaj X 1 X n N 1 E X displaystyle X 1 ldots X n sim mathrm N 1 mathbb E X i Y 1 Y n N 2 E Y displaystyle Y 1 ldots Y n sim mathrm N 2 mathbb E Y nezalezhni vibirki z normalnih rozpodiliv de E X displaystyle mathbb E X i E Y displaystyle mathbb E Y vidomi seredni Oznachemo dovilne a 0 1 displaystyle alpha in 0 1 i pobuduyemo a displaystyle alpha dovirchij interval dlya nevidomoyi kovariaciyi C o v X Y displaystyle mathrm Cov mathbf X mathbf Y Tverdzhennya Vipadkova velichina H E X E X Y E Y C o v X Y C o v X Y C o v X Y 1 displaystyle H frac mathbb E left X mathbb E X Y mathbb E Y right mathrm Cov mathbf X mathbf Y frac mathrm Cov mathbf X mathbf Y mathrm Cov mathbf X mathbf Y 1 maye rozpodil x 2 n displaystyle chi 2 n Nehaj x a n 2 displaystyle chi alpha n 2 a displaystyle alpha procentil cogo rozpodilu Todi mayemo P x 1 a 2 n 2 H x 1 a 2 n 2 a displaystyle mathbb P left chi frac 1 alpha 2 n 2 leq H leq chi frac 1 alpha 2 n 2 right alpha Pislya pidstanovki virazu dlya H displaystyle H i nevazhkih algebrayichnih peretvoren otrimuyemo P E X E X Y E Y x 1 a 2 n 2 C o v X Y E X E X Y E Y x 1 a 2 n 2 a displaystyle mathbb P left frac mathbb E left X mathbb E X Y mathbb E Y right chi frac 1 alpha 2 n 2 leq mathrm Cov mathbf X mathbf Y leq frac mathbb E left X mathbb E X Y mathbb E Y right chi frac 1 alpha 2 n 2 right alpha Div takozh red Dovirchij interval KovariaciyaLiteratura red Jana Jankov a and Sara van de Geer 2015 Confidence intervals for high dimensional inverse covariance estimation Electronic Journal of Statistics Vol 9 2015 1205 1229 DOI 10 1214 15 EJS1031 Sarkar P Bandyopadhyay U amp Bhattacharya R On Fixed Accuracy Confidence Interval in Multivariate Normal Distribution with Order 1 Autoregressive Covariance Structure J Stat Theory Pract 17 13 2023 https doi org 10 1007 s42519 022 00310 7 STATISTIChNE OCINYuVANNYa PARAMETRIV ROZPODILU S 132 139Posilannya red Confidence Interval Covariance and CorrelationCya stattya potrebuye dodatkovih posilan na dzherela dlya polipshennya yiyi perevirnosti Bud laska dopomozhit udoskonaliti cyu stattyu dodavshi posilannya na nadijni avtoritetni dzherela Zvernitsya na storinku obgovorennya za poyasnennyami ta dopomozhit vipraviti nedoliki Material bez dzherel mozhe buti piddano sumnivu ta vilucheno cherven 2023 nbsp Portal Matematika nbsp Ce nezavershena stattya z matematiki Vi mozhete dopomogti proyektu vipravivshi abo dopisavshi yiyi Dovirchij interval dlya kovariaciyi vipadkovih velichin u Google Otrimano z https uk wikipedia org w index php title Dovirchij interval dlya kovariaciyi vipadkovih velichin amp oldid 39624587
