Using the fact that the pointwise bias of the histogram is given by, [operatorname{Bias}left[bar{f}_{n}(x)ight]=frac{1}{2} f^{prime}(x)left[h-2left(x-g_{i}ight)ight]+Oleft(h^{2}ight),] as (h
Question:
Using the fact that the pointwise bias of the histogram is given by,
\[\operatorname{Bias}\left[\bar{f}_{n}(x)ight]=\frac{1}{2} f^{\prime}(x)\left[h-2\left(x-g_{i}ight)ight]+O\left(h^{2}ight),\]
as \(h ightarrow 0\), prove that the square bias is given by
\[\operatorname{Bias}^{2}\left[\bar{f}_{n}(x)ight]=\frac{1}{4}\left[f^{\prime}(x)ight]^{2}\left[h-2\left(\left(x-g_{i}ight)ight]^{2}+O\left(h^{3}ight) .ight.\]
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answered By
Kennedy Odhiambo
As a professional writer, I have been in the field for over 5 years having worked as a lecture in different tertiary institutions across the world. With this impeccable experience, I assure provision of a good and supporting environment for students to learn.
2+ Reviews
10+ Question Solved
Related Book For 
Question Posted:
