This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the chapter builds up to the construction (and use) of robust alternatives for some methods for multivariate analysis frequently used in chemometrics, such as prin...

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very lar...

Two methods for the estimation of harmonic parameters of periodic arbitrary signals were compared: a method based on least squares and a Bayesian method using approximations based on the normal distribution and the posterior mode. The methods are reviewed and comparison results are presented and analyzed in this paper.

Lemma A.3 Under Assumption 4 (iii), we have (i) P i P 2 ii = o(K), P i 6=j PiiPjj = K 2 + o(K), P i 6=j PijPij = P i 6=j PijPji = K + o(K); (ii) P iMiiPii = o(K), P i 6=jMiiPjj = Ktr(M) + o(K) = O(K), P i 6=jMijPij = P i 6=jMijPji = tr(M) + o(K) = O(K); (iii) P iM 2 ii = O(K), P i 6=jMiiMjj = tr (M) P iM 2 ii = O(K ), P i 6=jMijMij = tr(MM 0) P iM 2 ii = O(K), P i 6=jMijMji = tr(M) P iM 2 ii = ...

Least squares problems and solution techniques to solve them have a long history briefly addressed by Björck (2001, [4]). In this article we focus on two classes of complex least squares problems. The first one is established by models involving differential equations. The other class is made by least squares problems involving difficult models which need to be solved for many independent obser...

where m = f f is a unimodal function with mode m . In this paper, we establish almost sure convergence of (1.2) with optimal convergence rates up to a logarithmic factor, under the assumption of the exponential tail for the error distributions. Suppose throughout the sequel that Xi are iid random variables from a continuous distribution GX such that the density G ′ X exists in a neighborhood of...

Short duration design rainfall intensity data is a basic input to many water related projects, particularly in urban drainage design. The main problem in deriving short duration design rainfall data is the lack of continuous pluviograph rainfall data. The use of regionalisation techniques is common in design rainfall estimation, which pools data from a large region. This paper presents a region...

This note discusses some problems that should be taken into account in the implementation of the proposed use of fundamental constants in the definition of measurement units: use of CODATA adjusted values of the constants for this specific purpose; how the CODATA Task Group could continue performing meaningful least squares adjustments of the fundamental constants taking into account future data.

This paper assesses the effect of political institutions on stock market performance in 14 African countries for which stock market data is available for the period 1990-2010. The estimation technique used is a Two-Stage-Least Squares Instrumental Variable methodology. Political regime channels of democracy, polity and autocracy are instrumented with legal-origins, religious-legacies, income-le...