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Uniform Convergence Results for the Local Linear Regression Estimation of the Conditional Distribution

Haitian Xie

arXiv 16 Dec 2021 · Econometrics · publishedStatistics & Probability Letters (2023) · 3 citations (OpenAlex)

arXiv:2112.08546 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper examines the local linear regression (LLR) estimate of the conditional distribution function $F(y|x)$. We derive three uniform convergence results: the uniform bias expansion, the uniform convergence rate, and the uniform asymptotic linear representation. The uniformity in the above results is with respect to both $x$ and $y$ and therefore has not previously been addressed in the literature on local polynomial regression. Such uniform convergence results are especially useful when the conditional distribution estimator is the first stage of a semiparametric estimator. We demonstrate the usefulness of these uniform results with two examples: the stochastic equicontinuity condition in $y$, and the estimation of the integrated conditional distribution function.

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Fan, Y. and Guerre, E (2016) Multivariate Local Polynomial Estimators: Uniform Boundary Properties and Asymptotic Linear Representation, volume 36, pages 489…0.8435460%
2Hansen, B. E (2004) Nonparametric estimation of smooth conditional distributions0.84333100%
3Giné, E. and Guillou, A (2001) On consistency of kernel density estimators for randomly censored data: rates holding uniformly over adaptive intervals0.7373367%
4Kong, E., Linton, O., and Xia, Y (2010) Uniform bahadur representation for local polynomial estimates of m-regression and its application to the additive model0.73732100%
5Masry, E (1996) Multivariate local polynomial regression for time series: uniform strong consistency and rates0.73732100%
6Nolan, D. and Pollard, D (1987) U-processes: Rates of convergence0.6443267%
7Giné, E. and Guillou, A (2002) Rates of strong uniform consistency for multivariate kernel density estimators0.64422100%
8Yu, K (1997) Smooth regression quantile estimation0.64422100%
9Yu, K. and Jones, M. C (1998) Local linear quantile regression0.64422100%
10Giné, E. and Guillou, A (1999) Laws of the Iterated Logarithm for Censored Data0.51121100%

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1Sharp Bounds and Inference in Sample Selection Models with Treatment Endogeneity0.40511