Consider multiple observations $x[n]$ for an integer parameter $A$ under White Gaussian Noise $w[n]$:

$x[n]=A+w[n]; \quad$ $n=0,1,...,N−1$ with $w[n] \sim N(0,σ^2)$.

Is it possible to have an minimum variance unbiased estimator for the integer parameter $A$?

  • $\begingroup$ There is no such thing as "the" estimator of anything: part of doing statistics is choosing a suitable estimation procedure for your problem. Could you tell us whether you have a particular estimation procedure in mind? $\endgroup$ – whuber Nov 26 '19 at 18:42
  • $\begingroup$ @whuber Kindly excuse the mistake in the question. Now it has been corrected. Kindly give your comments on the updated question. $\endgroup$ – Thiruppathirajan Nov 27 '19 at 15:38
  • $\begingroup$ I have reopened it, but suspect most readers--like me--won't have a clue what "DC level A in WGN" means. It doesn't seem like it adds any useful information to the question, though. $\endgroup$ – whuber Nov 27 '19 at 16:57
  • $\begingroup$ Also: your title and your text don't agree: are you looking for a minimum variance estimator or an unbiased estimator? $\endgroup$ – whuber Nov 27 '19 at 17:16
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    $\begingroup$ I can't clarify a statement that is exactly the opposite of what I stated! It's still unclear what you're even trying to ask. $\endgroup$ – whuber Nov 27 '19 at 19:42

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