Goodness of Fit and Related Inference Processes for Quantile Regression

Koenker, Roger; Machado, José A. F.

doi:10.1080/01621459.1999.10473882

Cited by 1,152 publications

(857 citation statements)

References 25 publications

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“…that a certain threshold will be exceeded) and the latter is given by a quantile for a particular probability level of interest (Bouallègue et al, 2015). Since the outputs of the QRNN model are quantiles, it is reasonable to evaluate the performance with a skill score which has been developed for predictive quantiles (Koenker and Machado, 1999;Friederichs and Hense, 2007), known as the quantile score (QS). It is based on an asymmetric piecewise linear function, the so-called check function, ρ τ y i − q τ,i , which is a function of the probability level τ (0 < τ < 1) and the error between the observation y i and the quantile forecast q τ,i for i = 1, .…”

Section: Verificationmentioning

confidence: 99%

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Bogner¹,

Liechti²,

Zappa³

2017

Hydrol. Earth Syst. Sci.

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Abstract. The enhanced availability of many different hydro-meteorological modelling and forecasting systems raises the issue of how to optimally combine this great deal of information. Especially the usage of deterministic and probabilistic forecasts with sometimes widely divergent predicted future streamflow values makes it even more complicated for decision makers to sift out the relevant information. In this study multiple streamflow forecast information will be aggregated based on several different predictive distributions, and quantile forecasts. For this combination the Bayesian model averaging (BMA) approach, the nonhomogeneous Gaussian regression (NGR), also known as the ensemble model output statistic (EMOS) techniques, and a novel method called Beta-transformed linear pooling (BLP) will be applied. By the help of the quantile score (QS) and the continuous ranked probability score (CRPS), the combination results for the Sihl River in Switzerland with about 5 years of forecast data will be compared and the differences between the raw and optimally combined forecasts will be highlighted. The results demonstrate the importance of applying proper forecast combination methods for decision makers in the field of flood and water resource management.

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Section: Verificationmentioning

confidence: 99%

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Bogner¹,

Liechti²,

Zappa³

2017

Hydrol. Earth Syst. Sci.

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“…Para avaliar o potencial da RQ na geração de um feixe de curvas de índice de local, sem a presença de dados discrepantes e sem utilizar o método da curva-guia, foram ajustadas equações referentes ao modelo 1, tendo-se considerado diferentes percentis dos dados observados. Para avaliar a qualidade do ajuste da regressão quantílica em cada percentil da distribuição dos dados, utilizouse a estatística R 1 , conforme descrita por Koenker & Machado (1999), dada por…”

Section: Methodsunclassified

Curvas de índices de local em povoamentos de eucalipto obtidas por regressão quantílica

Júnior

Soares

Leite

2016

Pesq. agropec. bras.

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Resumo -O objetivo deste trabalho foi obter curvas de índice de local, em povoamentos de eucalipto, por meio de regressão quantílica, e compará-las às obtidas com o uso de regressões ajustadas pelo método de mínimos quadrados ordinários. A regressão quantílica pode ser utilizada para a geração de curvas de índice de local, especialmente em presença de dados discrepantes. O método gera um feixe de curvas mais bem ajustadas aos dados observados, em comparação ao feixe gerado com as estimativas de mínimos quadrados ordinários, seja pelo método da curva-guia (curvas anamórficas), seja pela geração de curvas polimórficas (com o uso de diferentes percentis).Termos para indexação: Eucalyptus, dados discrepantes, método da curva-guia, mínimos quadrados ordinários, percentis. Site index curves in eucalyptus plantation obtained by quantile regressionAbstract -The objective of this work was to obtain site index curves in eucalyptus plantations by quantile regression, and to compare them to the obtained ones with the use of fitted regressions by the method of ordinary least squares. Quantile regression can be used to generate site index curves, especially in the presence of outliers. The method generates a bundle of curves better adjusted to the observed data, compared to the one generated with the estimates of ordinary least squares, either by the guide curve method (anamorphic curves) or by polymorphic curves (using different percentiles).

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“…Instead of focusing on the mean, quantile regression gives the relationship between at least one covariate and the conditional median or other quantiles of the distribution of the response variable, which is usually between zero and one [39][40][41][42]. Because this method fits the regression line to a portion of the distribution [43], it can be used to retrieve boundary lines in two-dimensional spectral space [44,45].…”

Section: Quantile Regression Methodsmentioning

confidence: 99%

A New Concept of Soil Line Retrieval from Landsat 8 Images for Estimating Plant Biophysical Parameters

Ahmadian

Demattê

et al. 2016

Remote Sensing

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Extraction of vegetation information from remotely sensed images has remained a long-term challenge due to the influence of soil background. To reduce this effect, the slope and intercept of the soil line (SL) should be known to calculate SL-related vegetation indices (VIs). These VIs can be used to estimate the biophysical parameters of agricultural crops. However, it is a difficult task to retrieve the SL parameters under the vegetation canopy. A feasible method for retrieving these parameters involves extracting the bottom boundary line in two-dimensional spectral spaces (i.e., red and near-infrared bands). In this study, the slope and intercept of the SL was extracted from Landsat 8 OLI images of a test site in northeastern Germany. Different statistical methods, including the Red-NIR min method, quantile regression method (using a floating tau with the smallest p-value), and a new approach proposed in this paper using a fixed quantile tau known as the diffuse non-interceptance (DIFN) value, were applied to retrieve the SL parameters. The DIFN value describes the amount of light visible below the canopy that reaches the soil surface. Therefore, this value can be used as a threshold for retrieving the bottom soil line. The simulated SLs were compared with actual ones extracted from ground truth data, as recorded by a handheld spectrometer, and were also compared with the SL retrieved from bare soil pixels of the Landsat 8 image collected after harvest. Subsequently, the SL parameters were used to separately estimate the dry biomasses of winter wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), and canola (Brassica napus L.) at the local and field scales using different SL-related vegetation indices. The SL can be retrieved more accurately at the local scale compared with the field scale, and its simulation can be critical in the field due to significant differences from the actual SL. Moreover, the slope and intercept of the simulated SLs found using the floating and fixed quantile tau (slope ≈ 1.1 and intercept ≈ 0.05) show better agreement with the actual SL parameters (slope ≈ 1.2 and intercept ≈ 0.03) in the late growing stages (i.e., end of ripening and senescence stages) of crops. The slope and intercept of the soil line extracted from bare soil pixels of the Landsat 8 OLI data after harvest (slope = 1.3, intercept = 0.03, and R 2 = 0.94) are similar to those of the simulated SL. The correlation coefficient (R 2 ) of the simulated SLs are greater than 0.97 during different growing stage and all of the SL parameters are statistically significant (p < 0.05) at the local scale. The results also imply the need for different vegetation indices to best retrieve the crop biomass depending on the growing stage, but relatively small differences in performances were observed in this study.

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Goodness of Fit and Related Inference Processes for Quantile Regression

Cited by 1,152 publications

References 25 publications

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Technical note: Combining quantile forecasts and predictive distributions of streamflows

Curvas de índices de local em povoamentos de eucalipto obtidas por regressão quantílica

A New Concept of Soil Line Retrieval from Landsat 8 Images for Estimating Plant Biophysical Parameters

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