Robust Regression Estimators-The Choice of Tuning Constants

Kelly, Gabrielle

doi:10.2307/2348552

Cited by 9 publications

(9 citation statements)

References 22 publications

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“…(Fan et al 1994;Welsh 1994). It has been shown that this type of robustification approach is suitable for a large range of contaminated distributions (Kelly 1992). The M-type estimator described here directly follows from that developed by Pinson et al (2007) for local polynomial regression with time-varying coefficients.…”

Section: Robustification Of the Estimation Methodsmentioning

confidence: 98%

Local linear regression with adaptive orthogonal fitting for the wind power application

et al. 2007

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Short-term forecasting of wind generation requires a model of the function for the conversion of meteorological variables (mainly wind speed) to power production. Such a power curve is nonlinear and bounded, in addition to being nonstationary. Local linear regression is an appealing nonparametric approach for power curve estimation, for which the model coefficients can be tracked with recursive Least Squares (LS) methods. This may lead to an inaccurate estimate of the true power curve, owing to the assumption that a noise component is present on the response variable axis only. Therefore, this assumption is relaxed here, by describing a local linear regression with orthogonal fit. Local linear coefficients are defined as those which minimize a weighted Total Least Squares (TLS) criterion. An adaptive estimation method is introduced in order to accommodate nonstationarity. This has the additional benefit of lowering the computational costs of updating local coefficients every time new observations become available. The estimation method is based on tracking the left-most eigenvector of the augmented covariance matrix. A robustification of the estimation method is also proposed. Simulations on semi-P. Pinson ( ) · artificial datasets (for which the true power curve is available) underline the properties of the proposed regression and related estimation methods. An important result is the significantly higher ability of local polynomial regression with orthogonal fit to accurately approximate the target regression, even though it may hardly be visible when calculating error criteria against corrupted data.

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Section: Robustification Of the Estimation Methodsmentioning

confidence: 98%

Local linear regression with adaptive orthogonal fitting for the wind power application

et al. 2007

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“…To address the small sample size and high variances, a robust linear regression based on maximum likelihood type estimators (M-estimators) (e.g., Huber & Ronchetti, 2009;Stuart, 2011) was preferred. Following common usage and a couple of successful simulation studies, Huber's M-estimator was selected (Kelly, 1992;Lambert-Lacroix & Zwald, 2011;Stuart, 2011), with Huber's tuning constant set to its default value of 1.345 (Mathworks, 2016). Given the high variances and potential breakpoints in the data, the statistical significances of the breakpoints needed to be estimated without any assumptions of normally, identically, and independently distributed residuals.…”

Section: Statistical Tests For Breakpointsmentioning

confidence: 99%

Nonlinear dynamics in agricultural systems in Chad

Nilsson

Uvo

2018

African Geographical Review

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Changes to agricultural systems in Sub-Saharan Africa are subject to a wide range of drivers, often resulting in rapid and nonlinear dynamics. Such dynamics are however rarely recognized in studies of trends and drivers, which usually rely on assumptions of gradual progressions, and often using highly aggregated data. This paper addresses this lack of recognition and understanding of nonlinear processes in agricultural systems in Sub-Saharan Africa by statistically identifying breakpoints and trends in regional crop production data in Chad for 1983-2016, which also makes it the most extensive and detailed study of the agricultural sector in Chad to date. By summarizing and visualizing the identified breakpoints and trends of a large group of variables in a concise and informative way, the roles of both abrupt and gradual processes are made clear. Results show that the progressions in the data predominantly have been driven by abrupt changes with lasting effects rather than gradual changes, contrary to what analyses on higher levels of aggregation would conclude. The potency of the developed methodology lies in its capacity to identify and summarize nonlinear progressions in agricultural systems constituted by a large set of variables, by separating the influence of abrupt and gradual processes.

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“…Krasker & Welsch (1982), Kelly (1992), Kelly (1996), Warwick (2005), and Warwick & Jones (2005). Krasker, Kuh & Welsch (1983) point out that a bound value o f around two is a good choice for the Krasker-Welsch estimator for diagnostic purposes.…”

Section: Lad Estimation With Bounded Influencementioning

confidence: 99%

“…Krasker, Kuh & Welsch (1983) point out that a bound value o f around two is a good choice for the Krasker-Welsch estimator for diagnostic purposes. However as Kelly (1992) shows, the choice o f the tuning constant is extremely important in the trade off between estimator variance and estimator bias. Kelly (1992) also demonstrates that the optimal tuning constant can be significantly different from two.…”

Section: Lad Estimation With Bounded Influencementioning

confidence: 99%

“…However as Kelly (1992) shows, the choice o f the tuning constant is extremely important in the trade off between estimator variance and estimator bias. Kelly (1992) also demonstrates that the optimal tuning constant can be significantly different from two. Kelly (1996) presents an adaptive method based on minimizing the jack-knife-estimated asymptotic mean squared error.…”

Section: Lad Estimation With Bounded Influencementioning

confidence: 99%

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Robust daily exchange rate forecasting Mark Blanchette.

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Robust Regression Estimators-The Choice of Tuning Constants

Cited by 9 publications

References 22 publications

Local linear regression with adaptive orthogonal fitting for the wind power application

Local linear regression with adaptive orthogonal fitting for the wind power application

Nonlinear dynamics in agricultural systems in Chad

Robust daily exchange rate forecasting Mark Blanchette.

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