Weighted local linear composite quantile estimation for the case of general error distributions

Sun, Jing; Gai, Yujie; Li, Lin

doi:10.1016/j.jspi.2013.01.002

Cited by 41 publications

(27 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The MCQRNN model architecture is extremely flexible and many of its features are also not explored in this study. For example, the use of different weights for each s in the composite QR error function (Jiang et al 2012;Sun et al 2013), multiple hidden layers, and the ability to estimate non-crossing, nonlinear expectile regression functions ) are left for future research. Finally, code implementing the MCQRNN model is freely available from the Comprehensive R Archive Network as part of the qrnn package.…”

Section: Resultsmentioning

confidence: 99%

Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes

Cannon

2018

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

The goal of quantile regression is to estimate conditional quantiles for specified values of quantile probability using linear or nonlinear regression equations. These estimates are prone to ''quantile crossing'', where regression predictions for different quantile probabilities do not increase as probability increases. In the context of the environmental sciences, this could, for example, lead to estimates of the magnitude of a 10-year return period rainstorm that exceed the 20-year storm, or similar nonphysical results. This problem, as well as the potential for overfitting, is exacerbated for small to moderate sample sizes and for nonlinear quantile regression models. As a remedy, this study introduces a novel nonlinear quantile regression model, the monotone composite quantile regression neural network (MCQRNN), that (1) simultaneously estimates multiple non-crossing, nonlinear conditional quantile functions; (2) allows for optional monotonicity, positivity/ non-negativity, and generalized additive model constraints; and (3) can be adapted to estimate standard least-squares regression and non-crossing expectile regression functions. First, the MCQRNN model is evaluated on synthetic data from multiple functions and error distributions using Monte Carlo simulations. MCQRNN outperforms the benchmark models, especially for non-normal error distributions. Next, the MCQRNN model is applied to real-world climate data by estimating rainfall Intensity-Duration-Frequency (IDF) curves at locations in Canada. IDF curves summarize the relationship between the intensity and occurrence frequency of extreme rainfall over storm durations ranging from minutes to a day. Because annual maximum rainfall intensity is a non-negative quantity that should increase monotonically as the occurrence frequency and storm duration decrease, monotonicity and non-negativity constraints are key constraints in IDF curve estimation. In comparison to standard QRNN models, the ability of the MCQRNN model to incorporate these constraints, in addition to non-crossing, leads to more robust and realistic estimates of extreme rainfall.

show abstract

Section: Resultsmentioning

confidence: 99%

Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes

Cannon

2018

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

show abstract

“…But when the biases of initial estimators are of the same magnitude, this methodology often fails to reduce bias unless the weights are chosen to be negative (see Rigollet and Tsybabov 2007) or some strong constraints are assumed on initial estimators (see Sun, Gai and Lin, 2013).…”

Section: Motivation and Existing Methodologiesmentioning

confidence: 99%

“…Although the nonparametric regression function r(x) is what we want to estimate, it is not easy to separate r(x) and α k (see Kai, Li and Zou, 2010). Sun, Gai and Lin (2013) showed that the weights in the above composition asymptotically play no role in estimation efficiency enhancement, and the bias cannot be reduced to have a faster convergence rate to zero.…”

Section: Motivation and Existing Methodologiesmentioning

confidence: 99%

See 1 more Smart Citation

Composite Estimation: An Asymptotically Weighted Least Squares Approach

et al. 2019

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is three-fold. First, based on the asymptotic presentation of initial estimators, and model-independent parameters either hidden in the model or combined with the initial estimators, a pro forma linear regression between the initial estimators and the parameters is defined in an asymptotic sense. Then a weighted least squares estimation is constructed within this framework. Second, systematic studies are conducted to examine when both variance and bias reductions can be achieved simultaneously and when only variance can be reduced. Third, a generic rule of constructing composite estimation and unified theoretical properties are introduced. Some important examples such as quantile regression, nonparametric kernel estimation, blockwise empirical likelihood estimation are investigated in detail to explain the methodology and theory. Simulations are conducted to examine its performance in finite sample situations and a real dataset is analysed for illustration. The comparison with existing competitors is also made.

show abstract

“…If

({}, {\overset{false^}{a}}_{1}, \dots, {\overset{false^}{a}}_{q}, {\overset{false^}{b}}_{1}, \dots, {\overset{false^}{b}}_{p})

denotes the minimizer of (12), the LCQR estimator is defined as the average

\overset{m}{true} ((), x) = ((), 1 / q) \sum_{k = 1}^{q} {\overset{false^}{a}}_{k}

. Sun, Gai, and Lin () and Zheng, Gallagher, and Kulasekera () extended the weighted LCQR method to relax the symmetric error distribution assumption and to improve its efficiency. Reasonable robustness properties of these method can however be guaranteed only if no extreme quantiles are used in estimation, for example, if 1/4 ≤

\underset{k}{true}

q and

\overset{k}{true} / q \leq 3 / 4

, as even the breakdown point of the τ‐ th unconditional quantile estimator is bounded by min{⌈ τn ⌉, ⌈ n − τn ⌉}/ n .…”

Section: Robust Nonparametric Estimatorsmentioning

confidence: 99%

Robust nonparametric regression: A review

Čı́žek

Sadikoglu

2019

WIREs Computational Stats

View full text Add to dashboard Cite

Nonparametric regression methods provide an alternative approach to parametric estimation that requires only weak identification assumptions and thus minimizes the risk of model misspecification. In this article, we survey some nonparametric regression techniques, with an emphasis on kernel-based estimation, that are additionally robust to atypical and outlying observations. While the main focus lies on robust regression estimation, robust bandwidth selection and conditional scale estimation are discussed as well. Robust estimation in popular nonparametric models such as additive and varying-coefficient models is summarized too. The performance of the main methods is demonstrated on a real dataset. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical and Graphical Methods of Data Analysis > Nonparametric Methods K E Y W O R D S nonparametric regression, outliers, robust estimation 1 | INTRODUCTIONNonparametric regression models have received substantial attention in the theoretical and applied statistics literature over the last few decades. The underlying reason for their growing popularity and importance is that they do not rely on any particular form of the regression function characterizing the relationship between the dependent and explanatory variables and that they are thus robust to model misspecification. On the other hand, many classical nonparametric estimators are not robust in the sense that they are sensitive to atypical and outlying observations in the data. To address this, many authors have explored robust nonparametric regression estimation. As many nonparametric estimators of the regression function are local versions of the estimators of the location-scale model or the linear regression model, many initially proposed robust nonparametric regression estimators were inspired by the developments and construction of robust estimators in those two simple models, which we briefly recall in Section 1.1. Later, we introduce the main concepts of nonparametric regression in Section 1.2 and discuss the robust nonparametric methods from Section 2 on. | Robust estimation of the location and regression modelsConsider the simple univariate location-scale model Y = μ + σε, where Y is a continuously distributed univariate random variable, μ and σ are the location and scale parameters, respectively, and ϵ is an error term. For a random sample

show abstract

Weighted local linear composite quantile estimation for the case of general error distributions

Cited by 41 publications

References 11 publications

Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes

Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes

Composite Estimation: An Asymptotically Weighted Least Squares Approach

Robust nonparametric regression: A review

Contact Info

Product

Resources

About