Denis Chetverikov

The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, the authors show that restricting the problem to models with monotone regression functions and monotone instruments significantly weakens the ill-posedness of the problem.

Slepian and Sudakov–Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories.

In this work we consider series estimators for the conditional mean in light of four new ingredients: (i) sharp LLNs for matrices derived from the non-commutative Khinchin inequalities, (ii) bounds on the Lebesgue factor that controls the ratio between the L∞ and L2-norms of approximation errors, (iii) maximal inequalities for processes whose entropy integrals diverge at some rate, and (iv) strong approximations to series-type processes.

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n.

In this paper, we derive central limit and bootstrap theorems for probabilities that centered high-dimensional vector sums hit rectangles and sparsely convex sets. Sparsely convex sets are sets that can be represented as intersections of many convex sets whose indicator functions depend nontrivially only on a small subset of their arguments, with rectangles being a special case.

Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov–Bickel–Rosenblatt (SBR) condition; see, for example, Giné and Nickl [Probab. Theory Related Fields 143 (2009) 569–596].

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm.

We develop a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the supremum norm.

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n.

In this work we consider series estimators for the conditional mean in light of three new ingredients: (i) sharp LLNs for matrices derived from the non-commutative Khinchin inequalities, (ii) bounds on the Lebesgue factor that controls the ratio between the L∞ and L2-norms, and (iii) maximal inequalities for processes whose entropy integrals diverge at some rate.

We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors.

This paper derives a central limit theorem for the maximum of a sum of high dimensional random vectors.

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating empirical processes themselves in the sup-norm.

This paper develops a general nonparametric framework for testing monotonicity of a regression function.

In this paper, the author constructs a new test of conditional moment inequalities based on studentised kernel estimates of moment functions.