# Questions tagged [robust-statistics]

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normally distributed. Robust statistical methods have been developed for many common problems, such as estimating location, scale and regression parameters.

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### Infinitesimal Robustness, influence function of $T$ at $F$.

This text is taken from Introduction to robust estimation and hypothesis testing. Wilcox R. First I will write down the description that leads to definition of relative influence on $T(F)$ and then I ...
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1 vote
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### Minimiser of risk for linear-exponential error loss

Question: Solve the following optimisation problem: $$\arg\min_{f} \mathbb{E} \left( \exp (-(Y- f(X))) + (Y - f(X)) - 1 \right)$$ Context: The linear-exponential loss function (LINEX loss for short) ...
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### Sample mean of contaminated normal distributions

Consider the statistical structure $(\mathbb R, \mathcal{B}, \{N(\mu,1): \mu\in \mathbb{R}\}$ and suppose the problem of estimating $\mu$ with quadratic loss function. Consider the estimate $\bar x$ (...
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