Credibility estimators with dependence structure over risks and time under balanced loss function

Zhang, Qiang; Chen, Ping

doi:10.1111/stan.12125

Cited by 5 publications

(2 citation statements)

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“…They relate conceptually to methods for combining estimators (e.g., Judge & Mittlehammer, 2004), as well as penalized leastsquares estimation. The study of balanced loss functions has frequently been cast in a regression framework (e.g., Hu & Peng, 2011, and the references therein), but it also has arisen or related to credibility theory, finance, sequential estimation, etc (Baran & Stepień- Baran, 2013;Zhang & Chen, 2018). In Zellner's framework, the target estimator was least-squares, but such a target can be viewed more broadly (e.g., Jafari Jozani et al, 2006Jozani et al, , 2014.…”

Section: Introductionmentioning

confidence: 99%

On shrinkage estimation for balanced loss functions

Marchand

Strawderman

2020

Journal of Multivariate Analysis

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The estimation of a multivariate mean θ is considered under natural modifications of balanced loss function of the form:, where δ 0 is a target estimator of γ(θ). After briefly reviewing known results for original balanced loss with identity ρ or ℓ, we provide, for increasing and concave ρ and ℓ which also satisfy a completely monotone property, Baranchik-type estimators of θ which dominate the benchmark δ 0 (X) = X for X either distributed as multivariate normal or as a scale mixture of normals. Implications are given with respect to model robustness and simultaneous dominance with respect to either ρ or ℓ.AMS 2010 subject classifications: 62F10, 62J07 (primary); 62C15, 62C20 (secondary).

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Section: Introductionmentioning

confidence: 99%

On shrinkage estimation for balanced loss functions

Marchand

Strawderman

2020

Journal of Multivariate Analysis

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“…Balanced loss functions are appealing as they combine the proximity of a given estimator to a target value as well as the unknown parameter of interest (Marchand and Strawderman, 2020). These loss functions have captured the interest of some researchers for regression problems (Hu and Peng, 2011), estimation and prediction problems (Jafari Jozani et al, 2012Jozani et al, , 2006, as well as credibility theory, finance, sequential estimation (Baran and Stepien-Baran, 2013;Zhang and Chen, 2018).…”

Section: Introductionmentioning

confidence: 99%

A Multilevel Modeling Approach Towards Wind Farm Aggregated Power Curve

Mehrjoo

Jozani

Pawlak

et al. 2021

IEEE Trans. Sustain. Energy

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Wind turbine power curve modeling plays an important role in wind energy management. Accurate estimation of power curves can help reducing power systems maintenance costs. In this thesis, we use machine learning techniques such as clustering, spline regression as well as statistical learning approaches such as multilevel modeling and isotonic regression to reduce bias and/or variance of fitted power curves to improve their performance. First, we focus on reducing the effect of outliers in the wind speed-power data. To this end, we propose to enforce the inherent property of manufacturer power curve on fitted power curves to reduce outliers' impact. Manufacturer power curve is a worthy source of information about turbines' performance which has been ignored in the literature. So, we propose two nonparametric techniques based on the tilting method and monotonic spline regression methodology to preserve monotonicity on fitted power curves according to manufacturer power curve. Another challenging issue in fitting empirical power curve which was investigated seldom in the literature is heteroscedasticity of the wind speed-power data set. Age of turbine, location, air density, wind direction, and measurement errors are some of the reasons which may cause heteroscedasticity or non-homogeneity among observed data. To overcome this problem, we propose a novel methodology to use a hybrid estimation approach based on weighted balanced loss functions that account for both estimation error and goodness of fit by shrinking estimates toward standardized target models. Our proposed approach is very general and can be used with any desirable weighting scheme as an effective tool to improve the performance of existing power curve modeling approaches. Finally, we investigate improving wind farm aggregated power curve modeling instead of fitting power curves for individual turbines to reduce the complexity of wind farm management analyses. To solve this issue, we propose a novel clustering feature set based on turbines' overall performance and utilize K-Means clustering to classify turbines into homogeneous groups accordingly. We then apply multilevel modeling methods, including random intercept and random slope models on turbine clusters, to consider the hidden correlation among different clusters. We show that the proposed method is a solution for handling the complexity-accuracy trade-off issue since its accuracy is significantly higher than the single aggregated method alongside an equal complexity.

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