arXiv 3 Jul 2023 · Econometrics
arXiv:2307.01328 · PDF · DOI · OpenAlex · Extracted main text
We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}{x - h \leq X_i \leq x+h}f(Z_i)$, where $f$ belongs to a class of functions, $x \in \mathbb{R}$ and $h > 0$ is a bandwidth. Our nonasymptotic bounds control estimation error uniformly over the function class, evaluation point $x$ and bandwidth $h$. They are also general enough to accomodate function classes whose complexity increases with $n$. As an application, we apply our bounds to function classes that exhibit polynomial decay in their uniform covering numbers. When specialized to the problem of kernel density estimation, our bounds reveal that, under weak dependence with exponential decay, these estimators achieve the same (up to a logarithmic factor) sharp uniform-in-bandwidth rates derived in the iid setting by \cite{Einmahl2005}.
appendix boundary found by appendix_command · 48% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Einmahl, U. and D. M. Mason (2005) Uniform in bandwidth consistency of kernel-type function estimators | 1.000 | 5 | 4 | 100% |
| 2 | Rio, E (2017) Asymptotic Theory of Weakly Dependent Random Processes | 0.737 | 5 | 2 | 60% |
| 3 | van der Vaart, A. W. and J. A. Wellner (1996) Weak Convergence and Empirical Processes | 0.737 | 3 | 3 | 67% |
| 4 | Merlevède, F., M. Peligrad, and E. Rio (2009) Bernstein inequality and moderate deviations under strong mixing conditions | 0.644 | 3 | 2 | 67% |
| 5 | Cattaneo, M. D., R. P. Masini, and W. G. Underwood (2022) Yurinskii's coupling for martingales | 0.511 | 2 | 1 | 100% |
| 6 | Escanciano, J. C (2020) Uniform rates for kernel estimators of weakly dependent data | 0.511 | 2 | 1 | 100% |
| 7 | Belloni, A., V. Chernozhukov, I. Fernández-Val, and C. Hansen (2017) Program evaluation and causal inference with high-dimensional data | 0.405 | 1 | 1 | 100% |
| 8 | Merlevède, F., M. Peligrad, and E. Rio (2010, June) (2010) A bernstein type inequality and moderate deviations for weakly dependent sequences | 0.405 | 1 | 1 | 100% |
Showing the top 8 of 8 scored citations.