Near-Optimal A-B Testing

We consider the problem of A-B testing when the impact of the treatment is marred by a large number of covariates. Randomization can be highly inefficient in such settings, and thus we consider the problem of optimally allocating test subjects to either treatment with a view to maximizing the precision of our estimate of the treatment effect. Our main contribution is a tractable algorithm for this problem in the online setting, where subjects arrive, and must be assigned, sequentially, with covariates drawn from an elliptical distribution with finite second moment. We further characterize the gain in precision afforded by optimized allocations relative to randomized allocations, and show that this gain grows large as the number of covariates grows. Our dynamic optimization framework admits several generalizations that incorporate important operational constraints such as the consideration of selection bias, budgets on allocations, and endogenous stopping times. In a set of numerical experiments, we demonstrate that our method simultaneously offers better statistical efficiency and less selection bias than state-of-the-art competing biased coin designs. This paper was accepted by Noah Gans, stochastic models and simulation.

PENGUKURAN RISIKO GLUE-VALUE-AT-RISK PADA DATA DISTRIBUSI ELLIPTICAL (Studi Kasus: Data Saham PT Indocement Tunggal Prakarsa Tbk, PT Unilever Indonesia Tbk, PT United Tractors Tbk, Periode 1 Juni 2018 – 29 November 2019)

Risk measurement is carried out to determine the risk. Popular methods that can be used to measure risk at a confidence level are Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR). A Risk measurement should satisfy: translation invariance, positive homogenicity, monocity and subadditivity. VaR does not satisfy one of coherent axioms, namely subadditivity. TVaR is considered capable of overcoming VaR problems, but it’s too large for a risk measure. Glue-Value-at-Risk (GlueVaR) is a method that can overcome these problems because it can be valued between VaR and TVaR and fulfills four coherent axioms. In this paper GlueVaR used in the elliptical distribution for normal distribution to measure the risk of the stock of PT Indocement Tunggal Prakarsa Tbk (INTP), PT Unilever Indonesia Tbk (UNVR), and PT United Tractors Tbk (UNTR) for the period June 1st 2018 – 29th November 2019. After knowing the stock return is normally distributed and used confidence levels of α = 95% and β = 98%, a high selection of distortion ℎ1=0,3≤1−𝛽1−𝛼 and ℎ2=0,4≥ℎ1. The high distortion selected makes GlueVaR worth between VaR and TVaR. GlueVaR for INTP, UNVR, and UNTR respectively are 4.886%; 2.999%; and 4.083%. Thus the lowest risk level is PT Unilever Indonesia Tbk.Keywords : Value-at-Risk, Tail-Value-at-Risk, Glue-Value-at-Risk

Wavelet shrinkage generalized Bayes estimation for elliptical distribution parameter’s under LINEX loss

In this paper, the generalized Bayes estimator of elliptical distribution parameter’s under asymmetric Linex error loss function is considered. The new shrinkage generalized Bayes estimator by applying wavelet transformation is investigated. We develop admissibility and minimaxity of shrinkage estimator on multivariate normal distribution.We present the simulation in order to test validity of purpose estimator.