Mixing
Simplifying a summation by removing a data point
$begingroup$
I have below 2 functions:
${g}(x) = frac{sum_{i=1}^n K(x, x_i) * y_i }{sum_{i=1}^n K(x, x_i)}$
and $g_i(x_i)$ is for i = 1, · · · , i − 1, i + 1, · · · , n. Basically it's just omitting data point i.
How can we write $g_i(x_i)$ in term of ${g}(x)$ as simply as possible.
So far I am thinking to expand the first equation with another index j = 1 to n and remove the ith observation from there but I am stuck.
sequences-and-series summation
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
$endgroup$
add a comment |
$begingroup$
I have below 2 functions:
${g}(x) = frac{sum_{i=1}^n K(x, x_i) * y_i }{sum_{i=1}^n K(x, x_i)}$
and $g_i(x_i)$ is for i = 1, · · · , i − 1, i + 1, · · · , n. Basically it's just omitting data point i.
How can we write $g_i(x_i)$ in term of ${g}(x)$ as simply as possible.
So far I am thinking to expand the first equation with another index j = 1 to n and remove the ith observation from there but I am stuck.
sequences-and-series summation
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
$endgroup$
add a comment |
$begingroup$
I have below 2 functions:
${g}(x) = frac{sum_{i=1}^n K(x, x_i) * y_i }{sum_{i=1}^n K(x, x_i)}$
and $g_i(x_i)$ is for i = 1, · · · , i − 1, i + 1, · · · , n. Basically it's just omitting data point i.
How can we write $g_i(x_i)$ in term of ${g}(x)$ as simply as possible.
So far I am thinking to expand the first equation with another index j = 1 to n and remove the ith observation from there but I am stuck.
sequences-and-series summation
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
$endgroup$
I have below 2 functions:
${g}(x) = frac{sum_{i=1}^n K(x, x_i) * y_i }{sum_{i=1}^n K(x, x_i)}$
and $g_i(x_i)$ is for i = 1, · · · , i − 1, i + 1, · · · , n. Basically it's just omitting data point i.
How can we write $g_i(x_i)$ in term of ${g}(x)$ as simply as possible.
So far I am thinking to expand the first equation with another index j = 1 to n and remove the ith observation from there but I am stuck.
sequences-and-series summation
sequences-and-series summation
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
asked Jan 19 at 19:19
Jadu SenJadu Sen
12
12
add a comment |
add a comment |
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