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I have this kind of problem:

The market share $Z$ of a company is estimated in two independent survey polls. The sample sizes are $n_1=500$ and $n_2=2000$ with corresponding observed shares $p_1$ and $p_2$, respectively. These two results are to be combined. Two alternative estimators of $Z$ are presented as follows:

$Z_a=\frac{p_1+p_2}{2}$

$Z_b=\frac{p_1+4p_1}{5}$

  1. Are these estimators unbiased?
  2. Which one of these estimators is more efficient?

I know that

$E(Z)=0.2p_1+0.8p_2=E(Z_b)\rightarrow Z_b$

is unbiased and

$E(Z_a)=0.5p_1+0.5p_2$

so $Z_b$ is biased. Still I can't calculate MSE of these estimator so I don't know which one of these estimators is more efficient

aiao
  • 291
Dennis
  • 21
  • Hi Dennis welcome to Mathstackexchange! From which course is this question? are $p_1$ and $p_2$ efficient estimators of the given data? what is the distribution of the data in $n_1$ and $n_2$? Please use $here you write your equations$. – Seyhmus Güngören Feb 12 '13 at 13:55

0 Answers0