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The article presents information about Samuel S. Wilks, a great contributor to statistics. Wilks' behavior toward applications was peculiarly split, he encouraged his students to work on applications, not always an easy thing to do in a strongly theoretical mathematics department; he often told students about applications that he regarded as "neat" or "cute" or "clever"; the statistical colloquium he guided often had speakers on practical applications of mathematical statistics; he himself wrote some practical papers in statistics, but in the classroom he rarely discussed applications. Repeatedly, however, practical problems explicitly influenced both his own publications and those of his students and Wilks often used applications as motivation for the discussion of distribution theory, usually going well beyond the needs of the original problem. The papers to be discussed exhibit incompletely and fragmentarily a major influence on the work of the man and his students. Wilks watched the development of the statistical theory of order statistics closely. Indeed he wrote a masterful summary of the literature. The general area involves the study of the statistical properties of ordered measurements.

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on population means (totals) of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean (total). Implicitly, calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary information is available for all units in the population, more complex modeling can be handled by means of model calibration; auxiliary variables are used to obtain fitted values of the survey variable for all units in the population, and estimation weights are sought to satisfy calibration constraints on the fitted values population mean, rather than on the auxiliary variables one. In this work we extend model calibration considering more general superpopulation models and use nonparametric methods to obtain the fitted values on which to calibrate. More precisely, we adopt neural network learning and local polynomial smoothing to estimate the functional relationship between the survey variable and the auxiliary variables. Under suitable regularity conditions, the proposed estimators are proven to be design consistent. The moments of the asymptotic distribution are also derived, and a consistent estimator of the variance of each distribution is then proposed. The performance of the proposed estimators for finite-size samples is investigated by means of simulation studies. An application to the assessment of the ecological conditions of streams in the mid-Atlantic highlands in the United States is also carried out. [ABSTRACT FROM AUTHOR]