Suppose you have N items with values xi from which we want to sample n items...

Suppose you have N items with values x_i from which we want to sample n items with replacement. Each item has its own probability p_i of being selected across all times we pick items.

Let T = > 1, 1=1

What's the bias for the following estimator of T: $\hat{T} = \sum_{i \in S} \frac{x_i}{p_i}$

Let T = > 1, 1=1

Expert Solution

The bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated.

Given that

So, the bias is given by:

orchestra answered 3 years ago

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Suppose you have N items with values xi from which we want to sample n items...

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