ROBUST INFERENCE IN PARAMETRIC MODELS USING THE FAMILY OF GENERALIZED NEGATIVE EXPONENTIAL DISPARITIES

We examine robust estimators and tests using the family of generalized negative exponential disparities, which contains the Pearson's chi‐square and the ordinary negative exponential disparity as special cases. The influence function and α‐influence function of the proposed estimators are discussed and their breakdown points derived. Under the model, the estimators are asymptotically efficient, and are shown to have an asymptotic breakdown point of 50%. The proposed tests are shown to be equivalent to the likelihood ratio test under the null hypothesis, and their breakdown points are obtained. The competitive performance of the proposed estimators and tests relative to those based on the Hellinger distance is illustrated through examples and simulation results. Unlike the Hellinger distance, several members of this family of generalized negative exponential disparities generate estimators which also possess excellent inlier‐controlling capability. The corresponding tests of hypothesis are shown to have better power breakdown than the Hellinger deviance test in the cases examined.     

Generalized Wald-type tests based on minimum density power divergence estimators

In testing of hypothesis, the robustness of the tests is an important concern. Generally, the maximum likelihood-based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations from the assumed conditions. In this paper, we have proposed generalized Wald-type tests based on minimum density power divergence estimators for parametric hypotheses. This method avoids the use of nonparametric density estimation and the bandwidth selection. The trade-off between efficiency and robustness is controlled by a tuning parameter β. The asymptotic distributions of the test statistics are chi-square with appropriate degrees of freedom. The performance of the proposed tests is explored through simulations and real data analysis.     

INTERMARRIAGE AND THE LABOR MARKET OUTCOMES OF ASIAN WOMEN

The impact of intermarriage with natives, on labor market outcomes of immigrants, is not homogeneous across ethnic groups. Wages of Asian women are compared with non‐Asians. Both ordinary least squares and instrumental variables estimates of the effects of intermarriage on the wages of Asian women are negative and significant. Non‐Asian women earn a wage premium that becomes insignificant when controls for selection into marriage are introduced. One possible explanation for the intermarriage penalty for Asians is an income effect of having a high‐earning native husband. Intermarriage penalties rise with husband's education. Assimilation patterns of intermarried Asians indicate that they have lower initial wages, market hours, and employment, but exhibit faster rates of growth over their years of stay. The results are robust across Asian subgroups and husband's ethnicity. (JEL J16, J12, J31, J61)     

Tests for statistical significance of a treatment effect in the presence of hidden sub-populations

For testing the statistical significance of a treatment effect, we often compare between two parts of a population; one is exposed to the treatment, and the other is not exposed to it. Standard parametric or nonparametric two-sample tests are commonly used for this comparison. But direct applications of these tests can yield misleading results, especially when the population has some hidden sub-populations, and the effect of this sub-population difference on the response dominates the treatment effect. This problem becomes more evident if these sub-populations have widely different proportions of representatives in the samples obtained from these two parts. In this article, we propose some simple methods to overcome these limitations. These proposed methods first use a suitable clustering algorithm to find the hidden sub-populations, and then they eliminate the sub-population effect by using a suitable transformation of the data. Standard two-sample tests, when they are applied on the transformed data, usually yield better results. We analyze some simulated and real data sets to demonstrate the utility of these proposed methods.     

Robust and efficient parameter estimation based on censored data with stochastic covariates

Analysis of random censored life-time data along with some related stochastic covariables is of great importance in many applied sciences. The parametric estimation technique commonly used under this set-up is based on the efficient but non-robust likelihood approach. In this paper, we propose a robust parametric estimator for censored data with stochastic covariates based on the minimum density power divergence approach. The resulting estimator also has competitive efficiency with respect to the maximum likelihood estimator under pure data. The strong robustness property of the proposed estimator with respect to the presence of outliers is examined and illustrated through an appropriate real data example and simulation studies. Further, the theoretical asymptotic properties of the proposed estimator are also derived in terms of a general class of M-estimators based on the estimating equation.     

Aggregating Infinite Utility Streams with InterGenerational Equity: The Impossibility of Being Paretian

It has been known that, in aggregating infinite utility streams, there does not exist any social welfare function, which satisfies the axioms of Pareto, intergenerational equity, and continuity. We show that the impossibility result persists even without imposing the continuity axiom, and in frameworks allowing for more general domains of utilities than those used in the existing literature.     

Minimum disparity estimation based on combined disparities: Asymptotic results

The maximum likelihood estimator (MLE) is asymptotically efficient for most parametric models under standard regularity conditions, but it has very poor robustness properties. On the other hand some of the minimum disparity estimators like the minimum Hellinger distance estimator (MHDE) have strong robustness features but their small sample efficiency at the model turns out to be very poor compared to the MLE. Methods based on the minimization of some combined disparities can substantially improve their small sample performances without affecting their robustness properties (Park et al., 1995). All studies involving the combined disparity have so far been empirical, and there are no results on the asymptotic properties of these estimators. In view of the usefulness of these procedures this is a major gap in theory, which we try to fill through the present work. Some illustrations of the performance of the estimators and the corresponding tests are also provided.     

An investigation of Kendall's τ modified for censored data with applications

To accommodate testing for independence in bivariate data subject to censoring, several modifications of Kendall's τ are discussed. An extensive computer simulation is done to investigate power properties of these modifications under alternatives of the bivariate normal or bivariate exponential types. The statistics are then applied to available heart pacemaker patient survival data.