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Kernel Density Estimator : Let K(u) be a probability density function symmetric about zero.

Let K(u) be a probability density function symmetric about zero.

Please show; integral f(x) dx =1.

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Kernel density estimator

Let K(u) be a probability density function symmetric about zero.

I need to show; integral f(x) dx =1.

Kernel Density Estimators
Kernel density estimators belong to a class of estimators called non-parametric density estimators. In comparison to parametric estimators where the estimator has a fixed functional form (structure) and the parameters of this function are the only information we need to store, Non-parametric estimators have no fixed structure and depend upon all the data points to reach an estimate.
To understand kernel estimators we first need to understand histograms whose disadvantages provides the motivation for kernel estimators. When we construct a histogram, we need to consider the width of the bins ( equal sub-intervals in which ...

Solution Summary

A pdf is investigated. The solution shows the integral function as a detailed and well presented answer.

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