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How to use derivatives of a function to better estimate its variance over the domain?

How to use derivatives of a function to better estimate its variance over the domain? I have a scalar smooth function $f(x)$ and a multivariate random variable $x$ with known distribution (e.g. ...
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linearization of an estiamtor

Suppose we have two variables $x$ and $y$ defined in some population, with all values of $x$ known. A Poisson sample is drawn, with corresponding inclusion probabilities $\pi_k$ that are proportional ...