Parameter estimation of a covariance
function in the study of spatial variability
of calcium content in the soil

Maria Cristina Neves de OLIVEIRA[1]

Décio BARBIN[2]

Enio Fraga da SILVA[3]

José Ronaldo de MACEDO3

Cláudio Lucas CAPECHE3

Helga Restum HISSA3

§    ABSTRACT: Until the 1970s, the problem of spatial variability of many agronomic variables in field experiments was solved by using randomized block designs associated with the randomization and repetition principles. Although this method is efficient to evaluate experimental variability, it does not consider the spatial position among observations. When random and spatial aspects are presented for these variables, an evaluation of spatial dependence is required and geostatistical tools considering unbiased estimators can do it. The purpose of this paper was to evaluate the spatial dependence of calcium content using the exponential covariance function. The parameter estimates were obtained by maximum likelihood and restricted maximum likelihood.

§    KEYWORDS: Geostatistics; spatial dependence; variogram; maximum likelihood; restricted maximum likelihood; exponential covariance function; calcium in the soil.

[1]EMBRAPA - Pesquisa & Desenvolvimento - Embrapa Soja, CEP 86001-970, Londrina, PR, Brasil, E-mail:

[2]Departamento de Ciências Exatas, Universidade de São Paulo, campus de Piracicaba – ESALQ/USP, CEP 13418-900, Piracicaba, SP, Brasil, E-mail:

[3]EMBRAPA – Pesquisa & Desenvolvimento - Embrapa Solos, CEP 22460-000, Rio de Janeiro - RJ, Brasil, E-mail: