The classical binary classification problem is investigated when it is known in advance that the posterior probability function (or regression function) belongs to some class of functions. We introduce and analyze a method which effectively exploits this knowledge. The method is based on...

We obtain minimax lower and upper bounds for the expected distortion redundancy of empirically designed vector quantizers. We show that the mean squared distortion of a vector quantizer designed from $n$ i.i.d. data points using any design algorithm is at least $\Omega (n^{-1/2})$ away from the...

Minimax lower bounds for concept learning state, for example, that for each sample size $n$ and learning rule $g_n$, there exists a distribution of the observation $X$ and a concept $C$ to be learnt such that the expected error of $g_n$ is at least a constant times $V/n$, where $V$ is the VC...

I study the impact of a universal child benefit on fertility and family well-being. I exploit the unanticipated introduction of a new, sizeable, unconditional child benefit in Spain in 2007, granted to all mothers giving birth on or after July 1, 2007. The regression discontinuity-type design...

In recent years, Spain has received unprecedented immigration flows. Between 2001 and 2006 the fraction of the population born abroad more than doubled, increasing from 4.8% to 10.8%. For Spanish provinces with above-median inflows (relative to population), immigration increased the high school...