Miary nieefektywności estymacji metodą najmniejszych kwadratów

• Autorzy: Barbara Bogacka , Joanna Pomianowska

Warianty tytułu

Measures of Inefficiency of the Least Squares Estimators

• Języki publikacji: PL

Abstrakty

Problem związku pomiędzy OLSE i BLUE liczy już niemal 40 lat. Po raz pierwszy poruszył ten temat Tukey w swej pracy z 1948 r. [17]. Od tego czasu wielu autorów próbowało odpowiedzieć na pytanie, kiedy BLUE może być zastąpiony przez OLSE i jakiej "straty" można się wtedy spodziewać. Celem tej pracy jest zebranie różnych miar, które dają ocenę, na ile "zły" jest estymator otrzymany metodą najmniejszych kwadratów w porównaniu z najlepszym, nieobciążonym estymatorem liniowym. (fragment tekstu)

EN

In the paper the linear model (y, Xβ, <σ²V) is considered, where y stands for a vector of observable random variables, X - for a known matrix not necessery of a full column rank, V - for a known non-negative definite matrix, σ² - for a positive scalar and β - for a vector of unknown parameters. There are presented relationships between two estimators of E(y)=Xβ: the Ordinary Least Squares Estimator (OLSE) and the Best Linear Unbiased Estimator (BLUE). In section 2 the conditions for equality between OLSE and BLUE are gathered. In section 3 there are shown different measures of inefficiency of least squares estimators. (original abstract)

Słowa kluczowe

PL

Metoda najmniejszych kwadratów; Estymacja; Macierze

EN

Least squares method; Estimation; Matrix

• Czasopismo: Przegląd Statystyczny
• Rocznik: 1989
• Tom: 36
• Numer: z. 3-4
• Strony: 225--233

Twórcy

autor

Barbara Bogacka

• Akademia Rolnicza w Poznaniu

autor

Joanna Pomianowska

• Akademia Rolnicza w Poznaniu

Bibliografia

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