A note on robust and non-robust variogram estimators

Mingoti, Sueli Aparecida; Rosa, Gilmar

doi:10.1590/s0370-44672008000100014

Cited by 5 publications

(5 citation statements)

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“…A estimação da função semivariogram a não se constitui como algo trivial encontrado na literatura, sendo possível justificar estatisticamente diferentes estratégias, embasadas em diferentes princípios e pressupostos, alguns destes de difícil verificação objetiva (MINGOTI & ROSA, 2008). Em função dessa diversidade metodológica, para tal estimação, neste estudo, foram feitas conjugações de alternativas em duas etapas de estimação: (i) Na primeira etapa, escolheu-se qual ou quais estimadores seriam usados na estimação das semivariâncias (consideraram-se dois estimadores possíveis: o estimador clássico de Matheron (MA) e o estimador robusto de CressieHawkins (CH)); (ii) Na segunda etapa, o ajuste dos modelos para a função semivariograma foi feito utilizando diferentes métodos de estimação (consideraram-se quatro métodos possíveis: o método dos quadrados mínimos ordinários (OLS); o método dos quadrados mínimos ponderados (WLS); o método da máxima verossimilhança (ML), e o método da máxima verossimilhança restrita (REML).…”

Section: Methodsunclassified

Variabilidade espacial da força de desprendimento de frutos do cafeeiro

et al. 2014

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RESUMO:O objetivo deste trabalho foi utilizar técnicas de georreferenciamento e de geoestatística para analisar a variabilidade espacial da força de desprendimento de frutos de cafeeiros por meio de semivariogramas e pela interpolação por krigagem. O trabalho foi conduzido no município de Três Pontas -MG, Brasil. A força de desprendimento dos frutos verdes e de cerejas dos cafeeiros foi obtida por meio de um protótipo de dinamômetro em pontos georreferenciados. A dependência espacial dos dados foi analisada por meio de ajustes de semivariogramas, clássico e robusto, para o método dos mínimos quadrados ordinários e ponderados, e apenas o ajuste clássico, para os métodos da máxima verossimilhança e máxima verossimilhança restrita. Testaram-se, para cada um dos métodos, os modelos esférico, exponencial e gaussiano. Os mapas de isolinhas obtidos por krigagem foram produzidos, baseados no melhor método e modelo de ajuste da função semivariograma, que foram obtidos pelas estatísticas de validação. As variáveis em estudo apresentaram estruturas de dependência espacial, as quais foram modeladas pelos semivariogramas, o que possibilitou a confecção dos mapas de isolinhas de distribuição espacial, obtidos por krigagem. Foi possível identificar os locais mais propícios para se iniciar a colheita seletiva e mecanizada dos frutos do cafeeiro. PALAVRAS-CHAVE:Face de exposição solar, agricultura de precisão, geoestatística, colheita mecanizada e seletiva, café. SPATIAL VARIABILITY OF THE DETACHMENT FORCE OF COFFEE FRUITABSTRACT: The aim of this study was to use the georeferencing and geostatistics techniques to evaluate the spatial variability of coffee fruit detachment force by semivariograms adjustments and kriging interpolation. The study was conducted in Três Pontas, MG, Brazil. The detachment force of green and mature coffee fruit was obtained throughout a prototype dynamometer on georeferenced locations. The spatial dependence data was evaluated by classical and robust semivariogram adjustments, using ordinary least square and weighted least squares methods. Maximum likelihood and restricted maximum likelihood methods were also evaluated, but only for the classical semivariogram. Spherical, exponential and Gaussian models were compared for all the evaluated methods of semivariogram estimation. The isoline maps obtained by kriging were generated based on the best adjustment method and model of the semivariogram function obtained by the statistical validation. The studied variables showed spatial dependence, which were modeled by semivariograms that allowed plot isoline maps of the spatial distribution obtained by kriging. It was possible to identify the best places to start the mechanical and selective coffee fruit harvest.

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Section: Methodsunclassified

Variabilidade espacial da força de desprendimento de frutos do cafeeiro

et al. 2014

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“…On the other hand, the semivariograms for the examined soil variables with outliers were obtained using a robust variogram estimator (Cressie & Hawkins 1980), as recommended by Oliver & Webster (2014): where the denominator is a correction factor based on the assumption that the underlying process to be estimated has normally distributed differences over all lag distances (Webster & Oliver 2007). This estimator, known as one of the robust estimators against outliers (Mingoti & Rosa 2008), was selected from among the recommended robust variogram estimators by Oliver & Webster (2014) because of its better accuracy compared to the others (i.e., Dowd 1984, Genton 1998) (data are not shown here). We also confirmed that the standardized semivariograms constructed by the classical (Matheron 1965) and robust variogram estimators (Cressie & Hawkins 1980) earned similar shapes in terms of nugget, sill, and range when applied to the data sets with normal distribution but without outliers (i.e., pH, EC, OC, TN, and Ex-K) (data are not shown here).…”

Section: Variogram Analysismentioning

confidence: 99%

“…On the other hand, the robust variogram estimator (see Eq. (3) above) was applied to the transformed data sets of Av-P, Ex-Ca, Ex-Mg, and ECEC, which still had outliers after the transformation, in order to downplay the effects of the existing outliers on the shape of the semivariogram (Mingoti & Rosa 2008). However, the data sets which did not approximate the normal distribution (Av-P and Ex-Ac) and those which still had outliers even after the transformation need careful interpretation in the geostatistical analysis because the skewed distribution and the existing outliers distort and/or inflate the semivariance and affect the shape of the semivariogram (Mingoti & Rosa 2008, Oliver & Webster 2014.…”

Section: Exploratory Data Analysismentioning

confidence: 99%

Spatial Variability and Geostatistical Mapping of Selected Soil Properties in Mt. Wakakusa Grassland of Japan

Kamarudin

Tomita

Kondo

et al. 2019

JARQ

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Mt. Wakakusa in Central Japan is a semi-natural grassland which has been maintained by repeated application of prescribed burnings of vegetation for more than 500 years. We assessed the spatial variability of selected soil properties and constructed their distribution maps using a geostatistical method to provide spatial information on soil resource for sustainable land management in this grassland. All the examined soil properties showed intermediate (coefficient of variation [CV] = 10%-90%) or high (CV > 90%) variability, except for the soil pH (CV < 10%), suggesting that the precision soil management approach is recommendable in the study site. The variogram analysis revealed that all of the soil properties, except for the electrical conductivity with a very weak spatial dependency (nugget-to-sill [N/S] ratio > 0.75), showed a very strong or moderately strong spatial dependency (N/S ratio ≤ 0.50), which might occur under the strong influence of intrinsic factors such as the inherent soil quality. The soil maps constructed by the ordinary kriging method helped in understanding the distribution patterns of the examined soil properties and identifying specific locations with signs of degradation and pollution. These spatial distribution patterns should be considered when developing a sustainable soil management strategy in Mt. Wakakusa grassland. Discipline: Agricultural EnvironmentAdditional key words: ordinary kriging, prescribed burning, semivariogram, spatial dependency

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“…Boxplots of the scale (a), position (b) and shape (c) parameters of the GEV distribution, with their outlier because the analyses of the boxplots enabled the detection of possible outliers, it was determined that the presence of outliers was detrimental to semivariogram modeling, as observed inFeld et al (2016),Duggimpudi et al (2017),St. Luce et al (2014),Mingoti & Rosa (2008),Tobin et al (2011) andTeixeira & Scalon (2014). These authors indicate that discrepant outliers can destabilize the computation of the parameters of the theoretical semivariogram, making the data spatialization unfeasible.…”

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confidence: 99%

Spatialization of the Annual Maximum Daily Rainfall in Southeastern Brazil

et al. 2019

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Extreme rainfall can lead to heavy damage and losses, such as landslides, floods and agricultural productivity as well as the loss of human and animal lives. To mitigate these losses, water resources management policies are needed, among other goals, to study and predict the frequency of such events in a given region to minimize their harmful effects. The present study investigated the Generalized Extreme Value (GEV) probability distribution applied to the annual maximum daily precipitation data from rainfall stations in the southeastern Brazil. A total of 1,921 rainfall stations were considered, among which the stations with at least 15 years of uninterrupted observations were selected. Subsequently, the stationarity and adherence were tested. GEV probability distribution parameters were then estimated. The results enabled satisfactory spatial interpolation by ordinary kriging and the generation of maps of the distribution parameters. The semivariogram model with the best fit to the three GEV distribution parameters was the exponential model.

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A note on robust and non-robust variogram estimators

Abstract: In 1998 Genton proposed a variogram estimator claimed to be robust against outliers and compared it to Matheron's and Cressie-Hawkins' variogram estimators. Lark (2000)

Cited by 5 publications

References 9 publications

Variabilidade espacial da força de desprendimento de frutos do cafeeiro

Variabilidade espacial da força de desprendimento de frutos do cafeeiro

Spatial Variability and Geostatistical Mapping of Selected Soil Properties in Mt. Wakakusa Grassland of Japan

Spatialization of the Annual Maximum Daily Rainfall in Southeastern Brazil

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