This paper presents new uniform Gaussian strong approximations for empirical processes
indexed by classes of functions based on $ d $-variate random vectors ($ d\geq1 $). First, a …

This paper presents uniform estimation and inference theory for a large class of
nonparametric partitioning-based M-estimators. The main theoretical results include:(i) …

We derive sharp upper and lower bounds for the pointwise concentration function of the
maximum statistic of $ d $ identically distributed real-valued random variables. Our first main …

In this article, we consider the multiplicative chaos measure associated to the log-correlated
random Fourier series, or random wave model, with iid coefficients taken from a general …

This paper proposes a semiparametric sieve approach to estimate impulse response
functions of nonlinear time series within a general class of structural autoregressive models …

Nonparametric methods are central to modern statistics, enabling data analysis with minimal
assumptions in a wide range of scenarios. While contemporary procedures such as random …

We introduce a maximal inequality for a local empirical process under strongly mixing data.
Local empirical processes are defined as the (local) averages $\frac {1}{nh}\sum_ {i= 1} …

We consider estimation and inference using data collected from reinforcement learning
algorithms. These algorithms, characterized by their adaptive experimentation, interact with …

This dissertation consists of three papers contributing to the theory of estimation and
inference of high-frequency financial data. In the second chapter, a general framework is …

The availability of timely and accurate forecasts of key macroeconomic variables is of crucial
importance to economic policymakers, businesses, and the banking sector alike …