• Publications
  • Influence
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum isExpand
  • 266
  • 75
  • PDF
Central limit theorems and bootstrap in high dimensions
In this paper, we derive central limit and bootstrap theorems for probabilities that centered high-dimensional vector sums hit rectangles and sparsely convex sets. Specifically, we derive GaussianExpand
  • 173
  • 46
  • PDF
Some new asymptotic theory for least squares series: Pointwise and uniform results
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) boundsExpand
  • 133
  • 32
  • PDF
Gaussian approximation of suprema of empirical processes
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 empirical processesExpand
  • 87
  • 21
Testing Many Moment Inequalities
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. There are a variety ofExpand
  • 67
  • 19
  • PDF
Gaussian approximation of suprema of empirical processes
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 wholeExpand
  • 83
  • 15
  • PDF
Comparison and anti-concentration bounds for maxima of Gaussian random vectors
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 theExpand
  • 103
  • 15
  • PDF
Comparison and anti-concentration bounds for maxima of Gaussian random vectors
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 inExpand
  • 57
  • 15
Asymptotics for argmin processes: Convexity arguments
  • K. Kato
  • Mathematics, Computer Science
  • J. Multivar. Anal.
  • 1 September 2009
TLDR
We extend the scope of so-called ‘convexity arguments’ to the case where estimators are obtained as stochastic processes. Expand
  • 48
  • 13
  • PDF
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
We derive a Gaussian approximation result for the maximum of a sum of high dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum isExpand
  • 77
  • 12