Hi all Ch.6, page 4 Please anyone explain what does it mean- 'neither m(∅) nor s²(∅) depends on j'?? And also on page 13- Here 1/n×E[s²(∅)] is subtracted from var[m(∅)] to get an unbiased estimator. I am not getting it completely. How it(variance between risks) becomes an unbiased estimator by subtracting a term(variance within the risks) from it? And why we divide E(s²∅) by n here while subtracting? Please anyone clarify asap. Thanks
They have the same values for different years. On average the \(\sum {(\bar X_i - \bar X)^2 }\) gives an estimate that is too big, hence we subtract a bit from it so on average it gives the correct value (ie it is unbiased).
I am not getting how they have same values for different years? What I am getting is m(∅i) and s²(∅i) are the means and variances of particular risk respectively. Then how can we have same value of mean for different years, i.e. if we have data for 3 years or data for 4 years.. how can the means are same for 3 years and 4 years? Please clarify.
It's an assumption. If they weren't the same each year we wouldn't be able to estimate them without knowing how they increased.
