The main object of this paper is to consider maximum likelihood estimators for models used in detection of analytical bias. We consider the regression model proposed in Ripley and Thompson (Analyst, 112, 1987, p. 377) with an EM-type algorithm for computing maximum likelihood estimators and obtain consistent estimators for the asymptotic variance of the maximum likelihood estimators, which seems not to be available in the literature. Wald type statistics are proposed for testing hypothesis related to the bias of the analytical methods with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. The main conclusion is that proposed approaches in the literature underestimate the covariance matrix of the maximum likelihood estimators. Results of simulation studies and applications to real data sets are reported to illustrate comparisons with other approaches. This journal is

SummaryThe problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of individuals is considered by using the EM algorithm. As shown, the EM algorithm provides a general solution for this problem.Its implementation is simple and in its most general form requires no extra iterative procedures within the M step. One important feature of the algorithm in this set up is that the error variance estimates are always positive. Thus, it can be seen as a kind of restricted maximization procedure. The expected information matrix for the maximum likelihood estimators is derived, upon which the large sample estimated covariance matrix for the maximum likelihood estimators can be computed. The problem of testing hypothesis about the calibration lines can be approached by using the Wald statistics. The approach is illustrated by re-analysing two data sets in the literature.

SUMMARYThe structural modeling of spatial dependence, using a geostatistical approach, is an indispensable tool to determine parameters that define this structure, applied on interpolation of values at unsampled points by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations in sampled data. The purpose of this study was to use diagnostic techniques in Gaussian spatial linear models in geostatistics to evaluate the sensitivity of maximum likelihood and restrict maximum likelihood estimators to small perturbations in these data. For this purpose, studies with simulated and experimental data were conducted. Results with simulated data showed that the diagnostic techniques were efficient to identify the perturbation in data. The results with real data indicated that atypical values among the sampled data may have a strong influence on thematic maps, thus changing the spatial dependence structure. The application of diagnostic techniques should be part of any geostatistical analysis, to ensure a better quality of the information from thematic maps.Index terms: local influence, maximum likelihood, restricted maximum likelihood.(