# the MLE question. what is the MLE if the variance is heteroskedasticity

#### wawataiji

##### New Member
The normal distribution of MLE is start {x1,,,,,xn} random sample from N(u,σ^2)

This family of distributions has two parameters: θ = (μ, σ), so we maximize the likelihood, , over both parameters simultaneously using logarithm...

I know this. but what if the normal distribution's {x1,,,,,xn} random sample from N(u,σi^2)

I mean the variance is not homoscedasticity. now the variance is heteroskedasticity...

I atteched the image. My questions is that What is the MLE if variance change σ^2 to σi^2.
σ^2 - homoscedasticity,
σi^2- variance is heteroskedasticity.
So

f(x/u, σi^2) = 1/sqrt(2pi)σi exp((x-u)^2/2σi^2
I don't know.... How can I solved...

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#### Dason

Your notation and phrasing make it difficult to understand what you're asking. Are you saying each observation has a different unknown variance?

#### wawataiji

##### New Member
I atteched the image. My questions that What is the MLE if the variance is change σ^2 to σi^2.
σ^2 - homoscedasticity,
σi^2- variance is heteroskedasticity.
So f(x/u, σi^2) = 1/sqrt(2pi)σi exp((x-u)^2/2σi^2

#### Dason

Your terminology doesn't make sense. Once again I am asking are you saying that every observation [/math]x_i[/math] has their own variance term $\sigma_i^2$? Heteroskedasticity means that the variance isn't constant but typically if we model that we either have repeated observations (multiple x's take on the same value) or we model the variance as a function of the mean or something...
Your terminology doesn't make sense. Once again I am asking are you saying that every observation [/math]x_i[/math] has their own variance term $\sigma_i^2$? Heteroskedasticity means that the variance isn't constant but typically if we model that we either have repeated observations (multiple x's take on the same value) or we model the variance as a function of the mean or something...