What are the basics of local polynomial regression?
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Local polynomial regression is a nonparametric method used for smoothing scatterplots and estimating conditional means in various scenarios. Wang et al. developed a general theory for local polynomial regression in spatial data, establishing asymptotic normality of estimators and proposing confidence interval construction methods . They also applied these methods to two-sample testing problems. Additionally, Ma and Braun highlighted that local polynomial regression introduces bias due to smoothing effects . Wang et al. further investigated local polynomial estimators for conditional means with pooled response data, studying their asymptotic properties and conducting simulation studies to compare performance under different pooling designs and model settings . He and Opsomer extended the local polynomial estimator to handle ordered categorical covariates, deriving asymptotic bias and variance under specific assumptions and evaluating the estimator through simulation studies .
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24 Nov 2022 | Local polynomial regression is developed for spatial data on $\mathbb{R}^d$, providing asymptotic theory, confidence intervals, and uniform convergence rates for LP estimators of general order $p \geq 1. |
| Local polynomial regression is a method for smoothing scatterplots, commonly used due to its bias assessment. It involves fitting polynomials locally to data points for effective smoothing. | |
Open access•Posted Content | Local polynomial regression involves estimating the conditional mean of a continuous response using pooled data under various pooling designs, with investigated asymptotic properties and practical applications in real-life scenarios. |
| Local polynomial regression is proposed for estimating conditional mean with pooled response data. It offers asymptotic properties for continuous response variables under various pooling designs. | |
3 Citations | Local polynomial regression extends to ordered categorical covariates, estimating nonparametric models by considering quantiles of an unobserved continuous latent variable, as outlined in the paper. |
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