ترغب بنشر مسار تعليمي؟ اضغط هنا

On Estimation and Optimization of Mean Values of Bounded Variables

168   0   0.0 ( 0 )
 نشر من قبل Xinjia Chen
 تاريخ النشر 2012
  مجال البحث
والبحث باللغة English
 تأليف Xinjia Chen




اسأل ChatGPT حول البحث

In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed criterion of absolute and relative errors. By employing the Chernoff-Hoeffding bound and the concept of sampling, the minimization of a probabilistic function is transformed into an optimization problem amenable for gradient descendent algorithms.



قيم البحث

اقرأ أيضاً

181 - Xinjia Chen 2010
In this article, we derive an explicit formula for computing confidence interval for the mean of a bounded random variable. Moreover, we have developed multistage point estimation methods for estimating the mean value with prescribed precision and co nfidence level based on the proposed confidence interval.
115 - Xinjia Chen 2009
In this paper, we develop a multistage approach for estimating the mean of a bounded variable. We first focus on the multistage estimation of a binomial parameter and then generalize the estimation methods to the case of general bounded random variab les. A fundamental connection between a binomial parameter and the mean of a bounded variable is established. Our multistage estimation methods rigorously guarantee prescribed levels of precision and confidence.
129 - Xinjia Chen 2008
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently computable v ia a sample reuse technique, of which the computational complexity is shown to posses a Poisson distribution.
157 - Xinjia Chen 2009
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and relative error s. Second, we consider an inverse sampling scheme such that the sampling is continue until the number of units having a certain attribute reaches a threshold value or the whole population is examined. We have established a simple method to determine the threshold so that a prescribed relative precision is guaranteed. Finally, we develop a multistage sampling scheme for constructing fixed-width confidence interval for the proportion of a finite population. Powerful computational techniques are introduced to make it possible that the fixed-width confidence interval ensures prescribed level of coverage probability.
We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on the Golde nshluger and Lepski approach that jointly selects a kernel and a bandwidth. We derive two estimators that satisfy oracle-type inequalities. They are also proved to be adaptive over a scale of anisotropic or isotropic Sobolev-Slobodetskii classes (which are particular cases of Besov or Sobolev classical classes). The main interest of the isotropic procedure is to obtain adaptive results without any restriction on the smoothness parameter.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا