Heteroskedasticity

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Panneau travaux.png Artikel ieu keur dikeureuyeuh, ditarjamahkeun tina basa Inggris.
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Dina statistik, sekuen atawa vektor tina variabel acak disebut heteroskedastic lamun variabel acak dina sekuen atawa vektor beda jeung varian. Lawanna disebut homoscedasticity. (Di Amerika, umumna dieja homoscedastic. Hiji hal nu husus dina aturan ejaan Amerika nu leuwih ilahar tinimbang ejaan Inggris).

Waktu make teknik variasi dina statistik, saperti kuadrat leutik biasa (Ordinary Least Square - en), jumlah ieu dianggap tipikal. Salah sahijina nyaeta watesan nu dijieun konstan nyaeta 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 deals with data exhibiting it. It comes in two forms, pure and impure. Because there are so many types of each, most textbooks limit themselves to dealing with heteroskedasticity in general, or one or two examples.

Consequences[édit | sunting sumber]

The consequences are similar to serial correlation.

  1. When OLS to is applied heteroskedastic models it is no longer a minimum variance estimator. The variances and standard errors are understated.
  2. The variance of the sample betas increases.

Conto[édit | sunting sumber]

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

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

Sumber sejen[édit | sunting sumber]

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

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