Moment inequalities for U-statistics

We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler norms of the kernel matrix (i.e., norms of some multilinear operators associated with the kernel matrix). As a corollary, we derive tail inequalities for U-statistics with bounded kernels and for some multiple stochastic integrals.Comment: Published at http://dx.doi.org/10.1214/009117906000000476 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses

We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in spirit of Talagrand and Arcones, Gine). We also show that the same proof may be used for chaoses generated by log-concave random variables, recovering results by Lochowski and present an application to exponential integrability of Rademacher chaos.Comment: Slightly enlarged and updated with respect to the previous version. Some misprints correcte

A note on the Hanson-Wright inequality for random vectors with dependencies

We prove that quadratic forms in isotropic random vectors $X$ in $\mathbb{R}^n$, possessing the convex concentration property with constant $K$, satisfy the Hanson-Wright inequality with constant $CK$, where $C$ is an absolute constant, thus eliminating the logarithmic (in the dimension) factors in a recent estimate by Vu and Wang. We also show that the concentration inequality for all Lipschitz functions implies a uniform version of the Hanson-Wright inequality for suprema of quadratic forms (in the spirit of the inequalities by Borell, Arcones-Gin\'e and Ledoux-Talagrand). Previous results of this type relied on stronger isoperimetric properties of $X$ and in some cases provided an upper bound on the deviations rather than a concentration inequality. In the last part of the paper we show that the uniform version of the Hanson-Wright inequality for Gaussian vectors can be used to recover a recent concentration inequality for empirical estimators of the covariance operator of $B$-valued Gaussian variables due to Koltchinskii and Lounici

Open Access

“Would you like to open a subscription to this journal?” “Download this article for $35.00.” “Sign up to receive access to this article.” During my summer research I saw a lot of these windows pop up on my computer screen. One dead end followed by another. I grew weary of not having access to the studies that were highly pertinent to my area of research. Although my frustrations were never abated, I accepted this as my reality. I’ve acquiesced to the idea that my future as a researcher will be filled with endless hours of staring at a computer screen constantly telling me “No you may not read this article.” [excerpt

Freeing Nemo

Floating on the surface of the water, I observe the life teeming below me. The waves were carrying my body further and further into the beautiful reef; but all I was conscious of was the cleaner wrasse below bouncing from fish to fish, the parrotfish scraping algae from the coral, and the anemone protecting the ornate clownfish living within. [excerpt

Rape Culture Ruined My Favorite 80s Movie

I will admit that I wish my best friend was Duckie, I want to attend just one Saturday detention with Emilio Estevez, and I listen to an unhealthy amount of music from the Smiths and the Psychedelic Furs. Yes, I am a child of the nineties, but I spent many high school nights watching John Hughes films and attempting to dye my hair the perfect shade of Molly Ringwald red. [excerpt