On the consistency between model-and design-based estimators in survey sampling

In finite population sampling, often a distinction is made between model-and design-based estimators of the parameters of interest (like the population total, population variance, etc.). The model-based estimators depend on the (known) parameters of the model, while the design-based estimators depend on the (known) selection probabilities of the different units in the population. It is shown in this paper that the two approaches are not necessarily incompatible, and indeed can often lead to the same estimator. Our ideas are illustrated with the Horvitz-Thompson, and the generalized Horvitz-Thompson estimator. These estimators are identified as hierarchical Bays estimators. Also, certain “stepwise-Bayes” estimators of Vardeman and Meeden (J. Stat. Inf. (1983), V7, pp 329-341) are unified from a hierarchical Bayes point of view.     

OPTIMAL ENFORCEMENT OF NONCOMPETE COVENANTS

Noncompete covenants or covenant not to compete (CNC) are clauses in employment contracts in which the employee agrees not to gain employment with a competitor firm. In this article, we study the efficiency aspects of such contracts by incorporating the effect of labor mobility restrictions on knowledge transfer across firms, investment decisions by firms, and investment by workers. Following research that shows state‐wise variations in the degree of CNC enforcement, we allow the strength of CNC enforcement to vary as a matter of regulatory policy and derive the optimal strength of enforcement. We also look at how regulations around CNCs should be optimally designed when employers can use collusive agreements, such as “no poaching” agreements, as an alternative to noncompete clauses. Given recent allegations of employer collusion among large Silicon Valley firms, we argue for a cautious approach in designing policies on CNC enforcement. (JEL J24, J41, J63, K31)     

A Stochastic Model for Assessing Chlamydia trachomatis Transmission Risk Using Longitudinal Observational Data

Bacterium Chlamydia trachomatis causes genital chlamydia infection. Yet little is known about the transmission efficiency of this organism. Ethical constraint against exposing healthy subjects to infected partners precludes the possibility of quantifying transmission risk through controlled experiments. This research proposes an alternative strategy that relies on observational data. Specifically, we present a stochastic model that treats longitudinally observed infection states in a group of young women as a Markov process. The proposed model explicitly accommodates the parameters of C. trachomatis transmission, including per-encounter sexually transmitted infection (STI) acquisition risks, with and without condom protection, and the probability of antibiotic treatment failure. The male-to-female transmission probability of C. trachomatis is then estimated by combining the per-encounter disease acquisition risk and the organism's prevalence in the male partner population. The proposed model is fitted in a Bayesian computational framework.     

Maximum likelihood estimation for directional conditionally autoregressive models

A spatial process observed over a lattice or a set of irregular regions is usually modeled using a conditionally autoregressive (CAR) model. The neighborhoods within a CAR model are generally formed using only the inter-distances or boundaries between the regions. To accommodate directional spatial variation, a new class of spatial models is proposed using different weights given to neighbors in different directions. The proposed model generalizes the usual CAR model by accounting for spatial anisotropy. Maximum likelihood estimators are derived and shown to be consistent under some regularity conditions. Simulation studies are presented to evaluate the finite sample performance of the new model as compared to the CAR model. Finally, the method is illustrated using a data set on the crime rates of Columbus, OH and on the elevated blood lead levels of children under the age of 72 months observed in Virginia in the year of 2000.     

A geometric optimally of Cox's partial likelihood

The paper proves geometric optimality of Cox's partial likelihood score functions via estimating functions. As an illustration, Cox's proportional-hazards model is considered. Les auteurs démontrent l'optimalité g?ométrique des fonctions scores de vraisemblance partielle de Cox au moyen des fonctions d'estimation. Le modéle des risques proportionnels de Cox permet d'illustrer leur résultat.     

Data mining driven DMAIC framework for improving foundry quality – a case study

Six Sigma Define-Measure-Analyze-Improve-Control (DMAIC) methodology has been widely used across industries as the best systematic and data driven problem solving approach for quality improvement. Statistical Design of Experiment (DOE) is used in the ‘Improve’ stage for obtaining optimal process settings for significant variables contributing towards quality improvement. But, DOE is an offline activity requiring time and other resources for conducting experiments and analyses. Further, there are many small and medium scale enterprises that cannot afford to conduct DOE. Under such practical constraints, it is desirable to apply DMAIC using online process data under day-to-day production situations or with little changes in process settings without compromising production. In this article, we propose a DMAIC framework, driven by data mining techniques for defect diagnosis and quality improvement where historical and online process data can be effectively utilised. We have used two decision tree algorithms namely, Classification and Regression Tree and Chi-squared Automatic Interaction Detection in developing the proposed framework. The proposed approach is applied in an Indian grey iron foundry where conducting DOE is not a feasible option for the management. The result demonstrates a significant reduction in casting defect and validates the practical viability of this approach.     

Improvements in the small sample efficiency of the minimum S-divergence estimators under discrete models

This paper considers the problem of inliers and empty cells and the resulting issue of relative inefficiency in estimation under pure samples from a discrete population when the sample size is small. Many minimum divergence estimators in the S-divergence family, although possessing very strong outlier stability properties, often have very poor small sample efficiency in the presence of inliers and some are not even defined in the presence of a single empty cell; this limits the practical applicability of these estimators, in spite of their otherwise sound robustness properties and high asymptotic efficiency. Here, we study a penalized version of the S-divergences such that the resulting minimum divergence estimators are free from these issues, without altering their robustness properties and asymptotic efficiencies. We present a general proof for the asymptotic properties of these minimum penalized S-divergence estimators. This provides a significant addition to the literature, as the asymptotics of penalized divergences which are not finitely defined are currently unavailable in the literature. The small sample advantages of the minimum penalized S-divergence estimators are examined through an extensive simulation study and some empirical suggestions regarding the choice of the relevant underlying tuning parameters are also provided.     

Optimality in presence of damaged observations

In this paper we study a situation where, instead of observing $\text{y}\text{(N×1)}$, we observe $\text{y}\text{+}\text{d}$; where the random variables in the vector d are called damage components. It is shown that A- and E-optimum designs minimize the effect of d in the mean square error (m.s.e.) of estimable linear functions of parameters under the ordinary linear model.