Trimmed Linear moments (TL-moments) are natural generalization of Lmoments that do not require the mean of the underlying distribution to exist. It is known that the sample TL-moments is unbiased estimators to corresponding population TL-moment. Since different choices for the amount of trimming give different variances for the estimators it is important to choose the estimator that has less va...

Many stochastic optimization algorithms work by estimating the gradient of the cost function on the fly by sampling datapoints uniformly at random from a training set. However, the estimator might have a large variance, which inadvertantly slows down the convergence rate of the algorithms. One way to reduce this variance is to sample the datapoints from a carefully selected non-uniform distribu...

We consider the problem of estimating vector-valued variables from noisy “relative” measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables. This type of measurement model appears in several sensor network problems, such as sensor localization...

We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in the sparsity of the system and not in its size, and allows to provide error estimates for any solution method. At the heart of our approach is the so-called reg...

We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in the sparsity of the system and not in its size, and allows to provide error estimates for any solution method. At the heart of our approach is the so-called reg...

A. Proof of Theorem 1 In Appendix A, we give the full derivation of our primary theoretical contribution — the importance-sampling (IS) variance gradient. We also present the variance gradient for the doubly-robust (DR) estimator. We first derive an analytic expression for the gradient of the variance of an arbitrary, unbiased off-policy policy evaluation estimator, OPE(H,θ). Importance-samplin...

We derive the minimum variance quadratic unbiased estimator (MIVQUE) of the variance of the components of a random vector having a compound normal distribution (CND). We show that the MIVQUE converges in probability to a random variable whose distribution is essentially the mixing distribution characterising the CND. This fact is very important, because the MIVQUE allows us to make out the sign...

Based on progressively Type-II censored samples, the uniformly minimum variance unbiased (UMVU), Bayes and empirical Bayes estimates for the unknown parameter and the reliability function of the Burr model are derived. The Bayes and empirical Bayes estimates are obtained based on absolute error and logarithmic loss functions. We also present a numerical example and a Monte Carlo simulation stud...

This material is designed to introduces basic concepts and fundamental theory of mathematical statistics. A review of basic concepts will include likelihood functions, sufficient statistics, and exponential family of distributions. Then point estimation will be discussed, including minimum variance unbiased estimates, Cramér-Rao inequality, maximum likelihood estimates and asymptotic theory. To...