Birnbaum-Saunders spatial modelling and diagnostics applied to agricultural engineering data

Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these application assume that the data follow a Gaussian distributions. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders distribution has excelled. This paper proposes a spatial log-linear model based in the Birnbaum-Saunders distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data-set, where the spatial variability of phosphorus concentration in the soil is considered- which is extremely important for agricultural management

Birnbaum-Saunders spatial regression models: Diagnostics and application to chemical data

Geostatistical modelling is widely used to describe data with spatial dependence structure. Such modelling often assumes a Gaussian distribution, an assumption which is frequently violated due to the asymmetric nature of variables in diverse applications. The Birnbaum-Saunders distribution is asymmetrical and has several appealing properties, including theoretical arguments for describing chemical data. This work examines a Birnbaum-Saunders spatial regression model and derives global and local diagnostic methods to assess the influence of atypical observations on the maximum likelihood estimates of its parameters. Modelling and diagnostic methods are then applied to experimental data describing the spatial distribution of magnesium and calcium in the soil in the Parana state of Brazil. This application shows the importance of such a diagnostic analysis in spatial modelling with chemical data

SPECTRAL CHARACTERISTICS OF SOYBEAN DURING THE VEGETATIVE CYCLE WITH LANDSAT 5/TM IMAGES IN THE WESTERN PARANA, BRAZIL

The objective of this study was to analyze changes in the spectral behavior of the soybean crop through spectral profiles of the vegetation indexes NDVI and GVI, expressed by different physical values such as apparent bi-directional reflectance factor (BRF), surface BRF, and normalized BRF derived from images of the Landsat 5/TM. A soybean area located in Cascavel, Parana, was monitored by using five images of Landsat 5/TM during the 2004/2005 harvesting season. The images were submitted to radiometric transformation, atmospheric correction and normalization, determining physical values of apparent BRF, surface BRF and normalized BRF. NDVI and GVI images were generated in order to distinguish the soybean biomass spectral response. The treatments showed different results for apparent, surface and normalized BRF. Through the profiles of average NDVI and GVI, it was possible to monitor the entire soybean cycle, characterizing its development. It was also observed that the data from normalized BRF negatively affected the spectral curve of soybean crop, mainly, during the phase of vegetative growth, in the 12-9-2004 image.29232833

SPATIAL AUTOCORRELATION OF NDVI AND GVI INDICES DERIVED FROM LANDSAT/TM IMAGES FOR SOYBEAN CROPS IN THE WESTERN OF THE STATE OF PARANA IN 2004/2005 CROP SEASON

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This research aims at studying spatial autocorrelation of Landsat/TM based on normalized difference vegetation index (NDVI) and green vegetation index (GVI) of soybean of the western region of the State of Parana. The images were collected during the 2004/2005 crop season. The data were grouped into five vegetation index classes of equal amplitude, to create a temporal map of soybean within the crop cycle. Moran I and Local Indicators of Spatial Autocorrelation (LISA) indices were applied to study the spatial correlation at the global and local levels, respectively. According to these indices, it was possible to understand the municipality-based profiles of tillage as well as to identify different sowing periods, providing important information to producers who use soybean yield data in their planning.333525537Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundacao AraucariaConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

Asymptotic distribution, Bartlett-type correction, Bootstrap, Chi-squared distribution, Heavy-tailed errors, Score statistic, Symmetric model, t distribution,

Comparison of maps of spatial variability of soil resistance to penetration constructed with and without covariables using a spatial linear model Comparação de mapas de variabilidade espacial da resistência do solo à penetração construídos com e sem covariáveis usando um modelo espacial linear

A study about the spatial variability of data of soil resistance to penetration (RSP) was conducted at layers 0.0-0.1 m, 0.1-0.2 m and 0.2-0.3 m depth, using the statistical methods in univariate forms, i.e., using traditional geostatistics, forming thematic maps by ordinary kriging for each layer of the study. It was analyzed the RSP in layer 0.2-0.3 m depth through a spatial linear model (SLM), which considered the layers 0.0-0.1 m and 0.1-0.2 m in depth as covariable, obtaining an estimation model and a thematic map by universal kriging. The thematic maps of the RSP at layer 0.2-0.3 m depth, constructed by both methods, were compared using measures of accuracy obtained from the construction of the matrix of errors and confusion matrix. There are similarities between the thematic maps. All maps showed that the RSP is higher in the north region.<br>Realizou-se um estudo sobre a variabilidade espacial de dados de resistência do solo à penetração (RSP), nas camadas de 0,0-0,1 m, 0,1-0,2 m e 0,2-0,3 m de profundidade, utilizando métodos estatísticos em forma univariada, isto é, utilizando a geoestatística tradicional, construindo os mapas temáticos por krigagem ordinária para cada camada em estudo. Foi analisada a RSP na camada de 0,2-0,3 m de profundidade por meio de um modelo espacial linear (SLM), em que se consideraram as camadas de 0,0-0,1 m e 0,1-0,2 m como covariáveis, obtendo um modelo de estimação e um mapa temático por krigagem universal. Os mapas temáticos da RSP da camada de 0,2-0,3 m de profundidade, construídos por ambos os métodos, foram comparados por meio de medidas de acurácia obtidas a partir da construção da matriz de erros e da matriz de confusão. Verificou-se semelhança entre os mapas temáticos. Todos os mapas mostraram que a RSP é mais alta na região norte