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The standard way to solve this is to just consider each of your data points as unit vectors, then take the average of those unit vectors. The direction of this averaged vector is the estimated direct …

This is just weighted least squares and here is how I would approach it. To keep my notation simple I'll just have polynomials of order 1. It's trivial to extend the approach to polynomials of any ord …

This question is perhaps more suited to stats exchange. Darsh suggested using the Cholesky decomposition, but this only works if the distribution of the random variables you want to generate is Gauss …

I see now that Andrei would like to know what to do when the distribution has 2 modes and is symmetric about these modes. It seems better to just give a second (more detailed) answer rather than compl …

Ok, so now I will describe why Niels's estimator works so well. Take a bimodal and symmetric circular density function $f$ with modes $p$ and $-p$ (we will assume that $p$ is positive) such as the one …

Let $H$ be a set of $(d-1)$-dimensional hyperplanes in $\mathbb{R}^d$. For each hyperplane $h \in H$ let $D(h)$ and $\bar{D}(h)$ be the corresponding half spaces of $\mathbb{R}^d$. For a point $x \i …