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Proving the set where probability density function becomes infinite is bounded
For a continuous random variable $X$, with probability density function $p_X(x)$, it is known that there exists a $p_{min} > 0$ such that $p_X(x) \geq p_{min} \forall x \in X$. Also, I know that $X$...
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Show that $\mathbb{E}\left|\hat{f_n}-f \right| \leq \frac{2}{n^{1/3}}$ where $\hat{f_n}$ is a density estimator for $f$
Question
Suppose we have a continuous probability density $f : \mathbb{R} \to [0,\infty)$ such that $\text{sup}_{x \in \mathbb{R}}(\left|f(x)\right| + \left|f'(x)\right|) \leq 1. \;$ Define the ...
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