On the grouped selection and model complexity of the adaptive elastic net

Lasso proved to be an extremely successful technique for simultaneous estimation and variable selection. However lasso has two major drawbacks. First, it does not enforce any grouping effect and secondly in some situation lasso solutions are inconsistent for variable selection. To overcome this inconsistency adaptive lasso is proposed where adaptive weights are used for penalizing different coefficients. Recently a doubly regularized technique namely elastic net is proposed which encourages grouping effect i.e. either selection or omission of the correlated variables together. However elastic net is also inconsistent. In this paper we study adaptive elastic net which does not have this drawback. In this article we specially focus on the grouped selection property of adaptive elastic net along with its model selection complexity. We also shed some light on the bias-variance tradeoff of different regularization methods including adaptive elastic net. An efficient algorithm was proposed in the line of LARS-EN, which is then illustrated with simulated as well as real life data examples.     

An Examination of the Effect of Continuous Quality Improvements on Optimal Pricing for Durable Goods*

This paper investigates the nature of optimal prices for a durable good in the presence of continuous quality improvements. The analysis of optimal prices is based on a nonlinear dynamic model of sales response that relates price, quality, average life of a product and the persistence of quality perceptions. Numerical solutions to the model are derived by employing the generalized reduced gradient algorithm. The results show that optimal price depends on the persistence of quality perceptions and the average life of a product (an aspect of quality). The analysis of optimal results affirms results based on other models and provides insights on the influence that quality has on optimal pricing. The implications of the results and suggestions for future research are discussed.     

On the mixtures of Weibull and Pareto (IV) distribution: An alternative to Pareto distribution

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.     

Impact of Mid-Life Symptoms of Alcoholism on the Health and Wellbeing of Aging Parents of Adults with Disabilities

The study examined the effect of adult children’s disability on parents’ physical health in later life and the extent to which parents’ symptoms of alcoholism in mid-life moderates the link between children’s disability and later life parental health. Analyses are based on data from the Wisconsin Longitudinal Study. The analytic sample included parents of children with developmental disabilities (n = 145) or mental health problems (n = 200) and 2,432 parents of unaffected children. The results showed that the negative health consequences in later life of having a child with a developmental disability were greater for those who showed more symptoms of alcoholism in mid-life. However, symptoms of alcoholism in mid-life did not significantly moderate the impact of an adult child’s mental health problems on parents’ later life physical health. The findings suggest a potential area where gerontological social workers could intervene, given the negative impact of symptoms of alcoholism on the health of aging parents of children with a disability who may be significantly more susceptible to the negative health impacts of alcohol compared to their younger counterparts.     

Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators

Statistical Methods & Applications - We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum...     

A note on the residual median process

We study the residual median process, defined as the median of those observations which are greater than a number t. Using appropriate limit theorems, it is shown that the stochastic process converges in law to a Gaussian process defined in terms of a Brownian bridge.