Problems tagged with "density estimation"

Suppose a density estimate \(f : \mathbb R^3 \to\mathbb R^1\) is made using histogram estimators with bins having a length of 2 units, a width of 3 units, and a height of 1 unit.

What is the largest value that \(f(\vec x)\) can possibly have?

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Suppose data points \(\nvec{x}{1}, \ldots, \nvec{x}{n}\) are drawn from an arbitrary, unknown distribution with density \(f\).

True or False: it is guaranteed that, given enough data (that is, \(n\) large enough), a Gaussian fit to the data using the method of maximum likelihood will approximate the true underlying density \(f\) arbitrarily closely.