Robust estimators for additive models using backfitting

Additive models provide an attractive setup to estimate regression functions in a nonparametric context. They provide a flexible and interpretable model, where each regression function depends only on a single explanatory variable and can be estimated at an optimal univariate rate. Most estimation procedures for these models are highly sensitive to the presence of even a small proportion of outliers in the data. In this paper, we show that a relatively simple robust version of the backfitting algorithm (consisting of using robust local polynomial smoothers) corresponds to the solution of a well-defined optimisation problem. This formulation allows us to find mild conditions to show Fisher consistency and to study the convergence of the algorithm. Our numerical experiments show that the resulting estimators have good robustness and efficiency properties. We illustrate the use of these estimators on a real data set where the robust fit reveals the presence of influential outliers.     

Social choice with infinite populations: construction of a rule and impossibility results

 We provide a simple construction of social choice rules for economies with infinite populations. The rules are continuous, Pareto and non-dictatorial; they are constructed as limits of individual preferences when the limit exists, and otherwise as adequate generalizations. This contrasts with the impossibility results of Arrow (1951) and Chichilnisky (1980), which are valid on economies with finitely many individuals. Our social choice rules are, however, limits of dictatorial rules. This paper was written in 1979. Received: 30 October 1994/Accepted: 22 April 1996     

SYSTEMIC AND IDIOSYNCRATIC SOVEREIGN DEBT CRISES

The theoretical literature on sovereign defaults has focused on adverse shocks to debtors' economies, suggesting that defaults are of an idiosyncratic nature. Still, sovereign debt crises are also of a systemic nature, clustered around panics in the financial center, such as the European Sovereign Debt Crisis in the aftermath of the US Subprime Crisis in 2008. Crises in the financial centers are rare disasters and, thus, their effects on the periphery can only be captured by examining long episodes. In this paper, we examine sovereign defaults from 1820 to the Great Depression, with a focus on Latin America. We find that 63% of the crises are of a systemic nature. These crises are different. Both the international collapse of liquidity and the growth slowdown in the financial centers are at their core. These global shocks trigger longer default spells and larger losses for investors.     

Une analyse en termes d'équilibre de l'écart salarial entre hommes et femmes

Partant de l'hypothèse selon laquelle les apports en travail domestique des hommes et des femmes sont complémentaires, les auteures vérifient l'existence d'équilibres multiples. Dans certains cas, le travail est réparti àégalité et les salaires sont identiques. Dans d'autres, la répartition est différente, de même que les salaires. Dans ce contexte, les stéréotypes relatifs à l'infériorité de la productivité des femmes se révèlent autoréalisateurs. Partant d'exemples numériques, les auteures montrent que le bien‐être est supérieur lorsque le couple répartit le travail à part égale, puis elles énoncent des recommandations politiques.     

Wages, employment and economic shocks: Evidence from Indonesia

After over a quarter century of sustained economic growth, Indonesia was struck by a large and unanticipated crisis at the end of the 20th Century. Real GDP declined by about 12% in 1998. Using 13 years of annual labor force data in conjunction with two waves of a household panel, the Indonesia Family Life Survey (IFLS), this paper examines the impact of the crisis on labor market outcomes. Received: 31 December 1999/Accepted: 3 August 2000     

Estimating additive models with missing responses

ABSTRACT

For multivariate regressors, the Nadaraya–Watson regression estimator suffers from the well-known curse of dimensionality. Additive models overcome this drawback. To estimate the additive components, it is usually assumed that we observe all the data. However, in many applied statistical analysis missing data occur. In this paper, we study the effect of missing responses on the additive components estimation. The estimators are based on marginal integration adapted to the missing situation. The proposed estimators turn out to be consistent under mild assumptions. A simulation study allows to compare the behavior of our procedures, under different scenarios.     

Patterns of Sexual Behaviors in Young Men Who Have Sex With Men in Mexico

Recent research has documented the importance of understanding the multidimensional nature of sexual risk behavior. However, little is known about patterns of sexual behavior among men who have sex with men (MSM) in Mexico, men who are at greatest risk for HIV and sexually transmitted infections compared to other subpopulations in the country. This study applied latent class analysis to data from a large, HIV-negative sample of 18- to 25-year-old Mexican MSM recruited from a social and sexual networking website (N = 3,722) to uncover multidimensional patterns of sexual behaviors, partner factors, and protective behaviors, and examine how these were associated with health and well-being correlates. We selected a model with seven classes. The most common class included those who reported both insertive and receptive behaviors with more than one partner, but smaller groups of individuals were in classes marked by only insertive or receptive anal sex, romantic relationships, or sexual inactivity. Class membership differed by sexual orientation, age, depressive symptoms, alcohol problems, and self-acceptance, with individuals in a class marked by same-sex relationships generally reporting more positive outcomes. Findings suggest heterogeneity of behaviors among Mexican MSM and the possible efficacy of prevention messages tailored to individuals’ specific patterns of sexual behavior.     

Sexual Behaviors and Attitudes and Ethnic Identity During College

This study examined ethnic differences in sexual behaviors and attitudes, and associations between ethnic identity commitment and sexual behaviors and attitudes. African American (32%), Latino American (29%), and European American (39%) first-year college students (N = 434; 52% female) completed surveys about their sexual behaviors (number of partners, condom use, and alcohol use before intercourse) and attitudes (conservative attitudes, condom-related beliefs, and fear of AIDS) and ethnic identity commitment. Analyses of covariance and hierarchical linear regressions were performed. Among the three groups, Latino Americans reported riskier condom-related behaviors and attitudes, whereas European Americans were less fearful of AIDS. Ethnic identity commitment was a protective factor against risky attitudes regardless of ethnicity. For sexual behaviors, however, ethnic identity served as a protective factor only for European Americans. This study contributes to the understanding of adolescents' sexuality during college and the role of ethnic identity in their sexual experiences.     

Actions of symmetry groups

This paper studies maps which are invariant under the action of the symmetry group S _k . The problem originates in social choice theory: there are k individuals each with a space of preferences X, and a social choice map :X ^k X which is anonymous i.e. invariant under the action of a group of symmetries. Theorem 1 proves that a full range map :X ^k X exists which is invariant under the action of S _k only if, for all i1, the elements of the homotopy group _i (X) have orders relatively prime with k. Theorem 2 derives a similar results for actions of subgroups of the group S _k . Theorem 3 proves necessary and sufficient condition for a parafinite CW complex X to admit full range invariant maps for any prime number k:X must be contractible.Hospitality and research support from the Standard Institute for Theoretical Economics during the summer of 1991 is gratefully acknowledged. This paper was presented at a Colloquium in the Department of Mathematics, Columbia University, February 6, 1991. I thank the participants of the Colloquium and Jerry Kelly for helpful comments.