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1 vote
1 answer
50 views

How to combine a noisy (but unbiased) estimate with a precise (but possibly biased) estimate in A/B tests?

Suppose I want to estimate some set of unknown quantities $\theta_1$, …, $\theta_N$. For each $i \in \{1, …, N\}$, I have two estimators: $\hat{\theta_i}_A$ and $ \hat{\theta_i}_B$. The goal is to ...
frelk's user avatar
  • 1,447
5 votes
2 answers
258 views

What is the theoretical justification for alternatives to MSE minimisation?

I'm trying to wrap my head around the connection between statistical regression and its probability theoretical justification. In many books on statistics/machine learning, one is introduced to the ...
Othman El Hammouchi's user avatar
2 votes
0 answers
1k views

Most efficient estimator of mean

Let's say we want to estimate a mean $E[F]$ for some unknown distribution $F$. If we only care about the MSE (and don't mind using biased and non-linear estimator), what theory is available to help us ...
max's user avatar
  • 1,684