Sampling and empirical risk minimization

ABSTRACT

In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full samples is hardly feasible, if not unfeasible. A natural approach in this context consists in using survey schemes and substituting the ‘full data’ statistics with their counterparts based on the resulting random samples, of manageable size. It is the main purpose of this paper to investigate the impact of survey sampling on statistical learning methods based on empirical risk minimization through the standard binary classification problem, considered here as a ‘case in point’. Precisely, we prove that, in presence of auxiliary information, appropriate use of optimally coupled Poisson survey plans may not affect much the learning rates, while possibly reducing significantly the number of terms that must be averaged to compute the empirical risk functional with overwhelming probability. These striking results are next shown to extend to more general sampling schemes by means of a coupling technique, originally introduced by Hajek [Asymptotic theory of rejective sampling with varying probabilities from a finite population. Ann Math Stat. 1964;35(4):1491–1523].     

Parameter estimation of the flexible Weibull distribution for type I censored samples

Often in practice one is interested in the situation where the lifetime data are censored. Censorship is a common phenomenon frequently encountered when analyzing lifetime data due to time constraints. In this paper, the flexible Weibull distribution proposed in Bebbington et al. [A flexible Weibull extension, Reliab. Eng. Syst. Safety 92 (2007), pp. 719–726] is studied using maximum likelihood technics based on three different algorithms: Newton Raphson, Levenberg Marquardt and Trust Region reflective. The proposed parameter estimation method is introduced and proved to work from theoretical and practical point of view. On one hand, we apply a maximum likelihood estimation method using complete simulated and real data. On the other hand, we study for the first time the model using simulated and real data for type I censored samples. The estimation results are approved by a statistical test.     

Non linear parametric mode regression

In this article, we propose a semi-parametric mode regression for a non linear model. We use an expectation-maximization algorithm in order to estimate the regression coefficients of modal non linear regression. We also establish asymptotic properties for the proposed estimator under assumptions of the error density. We investigate the performance through a simulation study.     

How leader humility helps teams to be humbler,psychologically stronger,and more effective: A moderated mediation model

We hypothesize that (a) the level of humility expressed by leaders predicts team performance through, serially, team humility and team PsyCap, and (b) the strength (i.e., consensus within the team) of the leader humility, team humility and team PsyCap moderates the paths of that hypothesized model. A sample comprising 82 teams (82 leaders; 332 team members) was collected. Team members reported leader humility, team humility and team PsyCap. Leaders reported team performance. To handle the risks of common method bias, each mediating path of the hypothesized model is based on data from two different subsamples within each team. Our model's most novel theoretical contribution is the (moderated mediated) connection between leader humility, collective humility, and team PsyCap, and this was consistently supported in our data. Our inconsistent findings dealing with the relationship between team PsyCap and performance is well established in the literature and our results in both sub-samples were in the theorized direction. The study contributes to understand why, how and when humble leaders are more effective.     

An optimal k of kth MA-ARIMA models under a class of ARIMA model

In this article, we discuss finding the optimal k of (i) kth simple moving average, (ii) kth weighted moving average, and (iii) kth exponential weighted moving average based on simulated ARIMA(p, d, q) model. We run a simulation using the three above examining methods under specific conditions. The main finding is that 5th exponential weighted moving average (5th EWMA) ARIMA model is the best forecasting model among others, which means the optimal k = 5. For Turkish Telecommunications (TTKOM) stock market, real data reveal the similar results of simulation study.     

Some contributions on the multivariate Poisson–Skellam probability distribution

In this article, we introduce a new form of distribution whose components have the Poisson or Skellam marginal distributions. This new specification allows the incorporation of relevant information on the nature of the correlations between every component. In addition, we present some properties of this distribution. Unlike the multivariate Poisson distribution, it can handle variables with positive and negative correlations. It should be noted that we are only interested in modeling covariances of order 2, which means between all pairs of variables. Some simulations are presented to illustrate the estimation methods. Finally, an application of soccer teams data will highlight the relationship between number of points per season and the goal differential by some covariates.     

The Touchard distribution

We present a novel model, which is a two-parameter extension of the Poisson distribution. Its normalizing constant is related to the Touchard polynomials, hence the name of this model. It is a flexible distribution that can account for both under- or overdispersion and concentration of zeros that are frequently found in non-Poisson count data. In contrast to some other generalizations, the Hessian matrix for maximum likelihood estimation of the Touchard parameters has a simple form. We exemplify with three data sets, showing that our suggested model is a competitive candidate for fitting non-Poisson counts.     

The nexus between extreme weather events,sexual violence,and early marriage: a study of vulnerable populations in Bangladesh

Population and Environment - This study aims to explore whether a relationship exists between extreme weather events, sexual violence, and early marriage. We selected two districts in Bangladesh...     

Fair Production and Allocation of an Excludable Nonrival Good

We study fairness in economies with one private good and one partially excludable nonrival good. A social ordering function determines for each profile of preferences an ordering of all conceivable allocations. We propose the following Free Lunch Aversion condition: if the private good contributions of two agents consuming the same quantity of the nonrival good have opposite signs, reducing that gap improves social welfare. This condition, combined with the more standard requirements of Unanimous Indifference and Responsiveness, delivers a form of welfare egalitarianism in which an agent's welfare is measured by the quantity of the nonrival good that, consumed at no cost, would leave her indifferent to the bundle she is assigned.