# How to find an minimum variance unbiased estimator for an integer parameter?

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 $$A$$?

• 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? – whuber Nov 26 '19 at 18:42
• @whuber Kindly excuse the mistake in the question. Now it has been corrected. Kindly give your comments on the updated question. – Thiruppathirajan Nov 27 '19 at 15:38
• 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. – whuber Nov 27 '19 at 16:57
• Also: your title and your text don't agree: are you looking for a minimum variance estimator or an unbiased estimator? – whuber Nov 27 '19 at 17:16
• 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. – whuber Nov 27 '19 at 19:42