Questions tagged [concavity]

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Median of the sum vs. sum of the median for Gaussian variables

This is a problem I stumbled upon in my research. Consider $n$ Gaussian random variables $x_i \sim \mathcal{N} (\mu_i, \sigma_i^2)$, each with its own mean $\mu_i$ and variance $\sigma_i^2$. Can we ...
• 183
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Stochastic Dominance for convex sum of two random variables with same distribution

This is a very widely used result in finance and economics, and seems fairly intuitive as well (riskier asset is less preferred by risk-averse (concave utility) investors). However, I have not been ...
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Is this objective function convex? [closed]

Given that $F(x)$ is the cumulative distribution function (CDF) of continuous random variable $X$, is $$\frac{\int_0^\infty 1-F(x) dx}{\int_{-\infty}^0 F(x) dx}$$ convex? or is it non-convex/concave? ...
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Convex variant of Bhattacharyya coefficient

For (discrete, finite) probability distributions $P,Q$, the Bhattacharyya coefficient is $B(P,Q) := \sum_x \sqrt{P_x Q_x}$. It can be shown that this is jointly concave in $P$ and $Q$. My question is, ...
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Lower bound on expectation of concave function

Let $X$ be a random variable, and let $f$ be a concave function. Are there any known lower bounds for (or methods of lower bounding) $\mathbb{E}[f(X)]$? Jensen's inequality only gives an upper ...
• 205
1 vote
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Maximizing a non-parametric Probability Density

Assume we have a set of samples and estimate the underlying distribution with a non-parametric density estimator like the Kernel Density Estimator. Lets assume with a gaussian kernel. In my case it ...
• 495
As I understand, the proposal distribution, which I'll call $h(x)$, in adaptive rejection sampling is a linear piece-wise function which converges to the true distribution as the number of iterations ...