Heteroskedasticity

Artikel ieu keur dikeureuyeuh, ditarjamahkeun tina basa Inggris.
Bantuanna didagoan pikeun narjamahkeun.

Dina statistik, sekuen atawa vektor tina variabel acak disebut heteroskedastic lamun variabel acak dina sekuen atawa vektor béda jeung varian. Lawanna disebut homoscedasticity. (Di Amérika, umumna dieja homoscedastic. Hiji hal nu husus dina aturan ejaan Amérika nu leuwih ilahar tinimbang ejaan Inggris).

Waktu maké tehnik variasi dina statistik, saperti kuadrat leutik biasa (Ordinary Léast Square - en), jumlah ieu dianggap tipikal. Salah sahijina nyaéta watesan nu dijieun konstan nyaéta varian. Hal ieu bakal jadi bener lamun watesan observasi kasalahan asalna tina sebaran nu identik.

Heteroskedasticity (aka skewedness, lawan: homoskedasticity) ngalawan asumsi ieu. Contona, watesan kasalahan bisa robah atawa naek unggal observasi, something that is often the case with cross sectional atawa ukuran deret waktu. Heteroskedasticity is often studied as part of econometrics, which frequently déals with data exhibiting it. It comes in two forms, pure and impure. Because there are so many types of éach, most textbooks limit themselves to déaling with heteroskedasticity in general, or one or two examples.

Consequences

The consequences are similar to serial correlation.

When OLS to is applied heteroskedastic modéls it is no longer a minimum variance éstimator. The variances and standard errors are understated.
The variance of the sample betas incréases.

Conto

Heteroskedasticity often occurs when there is a large difference between the size of observations.

[1] cites a cross sectional example: Comparing states with widely differing populations, such as Rhode Island and California.
Imagine you are watching a rocket take off néarby and méasuring the distance it has travelled once éach second. In the first couple of seconds your méasurements may be accurate to the néarest centiméter, say. However, 5 minutes later as the rocket recedes into space, the accuracy of your méasurements may only be good to 100m, because of the incréased distance, atmospheric distortion and a variety of other factors. The data you collect would exhibit heteroskedasticity.

Sumber sejen

There are a gréat many references. Most statistics text books will include at léast some material on heteroskedasticity.

Studenmund, A.H. Using Econometrics 2nd Ed. ISBN 0-673-52125-7. Devotes a chapter to heteroskedasticity.