Sequential estimation of a location parameter and powers of a scale parameter from delayed observations

Baran, Jerzy; Stępień-Baran, Agnieszka

doi:10.1111/stan.12006

Cited by 4 publications

(3 citation statements)

References 11 publications

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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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“…The Bayesian and variational sequential hypotheses testing problems on the drift of an observable Wiener process under randomly delayed observations were studied by Nobelis (1999, 2000) (see also Miroshnitchenko 1979). Other optimal sequential estimation procedures for parameters and continuous distribution functions from sequences of random variables under delayed observations were considered by Magiera (1998), Jokiel-Rokita and Stȩpień (2009), Stȩpień- Baran (2011), and Baran and Stȩpień-Baran (2013) among others. More recently, Shiryaev (2019, Chap.…”

Section: Introductionmentioning

confidence: 99%

On the problems of sequential statistical inference for Wiener processes with delayed observations

Gapeev

2020

Stat Papers

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We study the sequential hypothesis testing and quickest change-point (or disorder) detection problems with linear delay penalty costs for observable Wiener processes under (constantly) delayed detection times. The method of proof consists of the reduction of the associated delayed optimal stopping problems for one-dimensional diffusion processes to the equivalent free-boundary problems and solution of the latter problems by means of the smooth-fit conditions. We derive closed-form expressions for the Bayesian risk functions and optimal stopping boundaries for the associated weighted likelihood ratio processes in the original problems of sequential analysis. KeywordsSequential testing problem • Quickest change-point (disorder) detection problem • Weighted likelihood ratio • (Time-homogeneous) diffusion process • Delayed optimal stopping problem • Free-boundary problem • Change-of-variable formula with local time on curves

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Sequential estimation of a location parameter and powers of a scale parameter from delayed observations

Cited by 4 publications

References 11 publications

On shrinkage estimation for balanced loss functions

On shrinkage estimation for balanced loss functions

A Multilevel Modeling Approach Towards Wind Farm Aggregated Power Curve

On the problems of sequential statistical inference for Wiener processes with delayed observations

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