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Is MLE consistent if my data is independent but not identically distributed? Specifically I have n samples where each sample is from a Gaussian distribution with equal variance but different mean. The mean for each Gaussian distribution is a different function of the true parameter.

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    $\begingroup$ What parameter(s), exactly, would you be trying to estimate? What do you mean by the "true parameter"? Are these "different functions" known to you? $\endgroup$ – whuber Jul 17 '18 at 11:27
  • $\begingroup$ Yes Functions are known. By true parameter I mean true value of parameters. It's a localization problem I am trying estimate the location of a a user equipment. $\endgroup$ – Author006 Jul 17 '18 at 11:51
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    $\begingroup$ Could you please provide an explicit description of what your parameters are and what the functions are? It's still unclear what your model is, to the point of suggesting the answer could either be "yes" or "no." $\endgroup$ – whuber Jul 17 '18 at 11:56
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MLE are used for regression (whose data are knowingly non iid) with no problems with regard to consistency.

In the case you described, through an ANOVA, you will make a comparison among the sample means to evaluate whether or not the means are equal to each other.

ANOVA have been long studied and its properties are well stablished. Among several others, you have the consistency of the parameters' estimation.

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We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.

  • $\begingroup$ Can you give an example please? $\endgroup$ – Author006 Jul 17 '18 at 7:35

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