Martin Gouterman (1931–2020) was one of the foundational figures of modern porphyrin science. After completing his Ph.D. at The University of Chicago in 1958, he joined Harvard, where he developed ...his eponymous four‐orbital model. In 1966, he moved to the University of Washington Seattle (UW). Here he came out as gay and helped set up Seattle's first gay rights group, the Dorian Society. At UW, Gouterman accomplished an “optical taxonomy” of the major classes of porphyrin derivatives and pioneered pressure‐sensitive paints based on phosphorescent platinum porphyrins to map the partial pressure of oxygen on airplane wings. Revered by his students and co‐workers for his brilliant yet gentle advising, Gouterman remains a beacon for a more humane and inclusive scientific enterprise.
Martin Gouterman was an iconic figure of porphyrin science. Using his eponymous four‐orbital model, he accomplished a grand optical taxonomy of porphyrin derivatives. He devoted the latter part of his career to devise pressure‐sensitive paints, which are now widely used by the aerospace industry. A gay man, he helped set up Seattle's first gay rights group. In death, he remains a beacon for a more humane and inclusive scientific enterprise.
Data on rates, percentages, or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology, and several others. In this paper, we develop a robust ...inference procedure for the beta regression model, which is used to describe such response variables taking values in (0, 1) through some related explanatory variables. In relation to the beta regression model, the issue of robustness has been largely ignored in the literature so far. The existing maximum likelihood-based inference has serious lack of robustness against outliers in data and generate drastically different (erroneous) inference in the presence of data contamination. Here, we develop the robust minimum density power divergence estimator and a class of robust Wald-type tests for the beta regression model along with several applications. We derive their asymptotic properties and describe their robustness theoretically through the influence function analyses. Finite sample performances of the proposed estimators and tests are examined through suitable simulation studies and real data applications in the context of health care and psychology. Although we primarily focus on the beta regression models with a fixed dispersion parameter, some indications are also provided for extension to the variable dispersion beta regression models with an application.
We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via minimization of a ...suitable (empirical) version of the popular density power divergence. Based on a long sequence of observations from a first-order stationary Markov chain, we have defined the minimum density power divergence estimator (MDPDE) of the underlying parameter and rigorously derived its asymptotic and robustness properties under appropriate conditions. Performance of the MDPDEs is illustrated theoretically as well as empirically for some common examples of finite Markov chain models. Its applications in robust testing of statistical hypotheses are also discussed along with (parametric) comparison of two Markov chain sequences. Several directions for extending the MDPDE and related inference are also briefly discussed for multiple sequences of Markov chains, higher order Markov chains and non-stationary Markov chains with time-dependent transition probabilities. Finally, our proposal is applied to analyze corporate credit rating migration data of three international markets.
We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. ...Present methods of sparse and robust regression are based on <inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>-penalization, and their theoretical properties are not well-investigated. In contrast, we use a general class of folded concave penalties that ensure sparse recovery and consistent estimation of regression coefficients. We propose an alternating algorithm based on the Concave-Convex procedure to obtain our estimate, and demonstrate its robustness properties using influence function analysis. Under some conditions on the fixed design matrix and penalty function, we prove that this estimator possesses large-sample oracle properties in an ultrahigh-dimensional regime. The performance and effectiveness of our proposed method for parameter estimation and prediction compared to state-of-the-art are demonstrated through simulation studies.
The generalized linear model is a very important tool for analyzing real data in several application domains where the relationship between the response and explanatory variables may not be linear or ...the distributions may not be normal in all the cases. Quite often such real data contain a significant number of outliers in relation to the standard parametric model used in the analysis; in such cases inference based on the maximum likelihood estimator could be unreliable. In this paper, we develop a robust estimation procedure for the generalized linear models that can generate robust estimators with little loss in efficiency. We will also explore two particular special cases in detail—Poisson regression for count data and logistic regression for binary data. We will also illustrate the performance of the proposed estimators through some real-life examples.
DFT calculations on the spin-crossover complex Fe(salen)(NO) provide a striking illustration of the comparative performance of different exchange-correlation functionals vis-à-vis the issue of ...transition metal spin state energetics. Thus, although the "classic" pure functionals PW91 and BLYP favor the S = 1/2 state by about 10 kcal/mol, relative to the S = 3/2 state, the hybrid functional B3LYP favors the latter state by nearly the same margin. In contrast, the newer pure functionals OLYP and OPBE, based on the OPTX exchange functional, as well as the B3LYP* hybrid functional (which has 15% Hartree-Fock exchange, compared with 20% for B3LYP) predict nearly isoenergetic S = 1/2 and 3/2 states, as required for a spin-crossover complex. Intriguingly, the OLYP and B3LYP* spin density profiles for the S = 1/2 state of Fe(salen)(NO) are substantially dissimilar.
Variable selection in ultra-high dimensional regression problems has become an important issue. In such situations, penalized regression models may face computational problems and some pre-screening ...of the variables may be necessary. A number of procedures for such pre-screening has been developed; among them the Sure Independence Screening (SIS) enjoys some popularity. However, SIS is vulnerable to outliers in the data, and in particular in small samples this may lead to faulty inference. In this paper, we develop a new robust screening procedure. We build on the density power divergence (DPD) estimation approach and introduce DPD-SIS and its extension iterative DPD-SIS. We illustrate the behavior of the methods through extensive simulation studies and show that they are superior to both the original SIS and other robust methods when there are outliers in the data. Finally, we illustrate its use in a study on regulation of lipid metabolism.
It is well known that the urban systems, in particular cities, display scaling behaviour regarding socio-economic, infrastructural and individual basic services indicators. However, understanding ...urbanisation and the links between rural and urban areas is fundamental to making the most of the global transformations happening around the world. In this context, it is important to study the scaling laws based on both the urban and rural regions, going beyond cities. This paper explores the extension of the idea of allometric urban scaling law to study the scaling behaviour of Indian districts, with both the urban and rural population. To proceed, we have chosen districts (both rural and urban) of India, a relatively larger local administrative units, which are more or less independently functional within a country. This interdisciplinary work focus on the scaling analysis of various socio-economic indicators (SEIs) corresponding to the size (population) of four distinct urbanisation classes, namely rural, semi-rural, semi-urban and urban districts. The scaling exponents (
β
) were estimated for each classes for the years 2001 and 2011 along with their goodness-of-fit measured by the
R
2
values. Our rigorous statistical analysis indicates that the scaling laws indeed exist even at the district level for most of the SEIs considered, related to education, employment, housing, health, etc.; the
R
2
values obtained for these SEIs are very high (often greater than 0.8 or 0.9) in both the years. Moreover, linearity of the scaling factors have been statistically tested and it has been found, at 95% level of confidence, that not all the SEIs behave linearly (
β
=
1
); some of them are characterised by super-linear (
β
>
1
) behaviour and some behave sub-linearly (
β
<
1
). Statistical hypothesis tests have also been performed to test the equality of two scaling factors corresponding to two distinct classes and two different years to understand the differences in scaling relationships amongst increasing urbanisation classes and their changes over time.
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