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In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme depends on...
This paper presents a new algorithm to perform regression estimation, in both the inductive and transductive setting. The estimator is defined as a linear combination of functions in a given dictionary. Coefficients of the combinations are computed sequentially using projection on some simple sets. These sets are defined as confidence regions provided by a deviation (PAC) inequality on an estimator in one-dimensional models. We prove that every projection the algorithm actually improves the performance...
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