Related papers: Uniform convergence rates for a class of martingal…

In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the $\ell^1$ norm of the…

We discuss in this paper uniform exponential convergence of sample average approximation (SAA) with adaptive multiple importance sampling (AMIS) and asymptotics of its optimal value. Using a concentration inequality for bounded martingale…

In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…

We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic…

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…

We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…

In this paper, we consider the problem of estimating the marginal density in some nonlinear autoregressive time series models for which the conditional mean and variance have a parametric specification. Under some regularity conditions, we…

In this paper we derive tail bounds on the norms of random submatrices with non-uniformly distributed supports. We apply these results to sparse approximation and conduct an analysis of the average case performance of thresholding,…

In this paper we consider the rate of convergence of solutions of a scalar ordinary differential equation which is a perturbed version of an autonomous equation with a globally stable equilibrium. Under weak assumptions on the nonlinear…

This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro…

We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…

We derive high-probability finite-sample uniform rates of consistency for $k$-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that $k$-NN regression adapts to an unknown lower intrinsic…

Delayed outcomes are ubiquitous in online experimentation. When such a temporal dimension is present, treatment influences not only the outcome value but also the outcome timing, which can move in opposite directions. Motivated by the…

The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…

Confidence sequences, anytime p-values (called p-processes in this paper), and e-processes all enable sequential inference for composite and nonparametric classes of distributions at arbitrary stopping times. Examining the literature, one…

We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…

Under the Neyman causal model, it is well-known that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to…

We prove that a sum of random matrices generated by a $\psi$-mixing Markov chain has similar spectral properties to a Gaussian matrix with the same mean and covariance structure. This nonasymptotic universality principle enables sharp…