We consider a sequence space model of statistical linear inverse problems where we need to estimate a function f from indirect noisy observations. Let a nite set of linear estimators be given. Our aim is to mimic the estimator in that has the smallest risk on the true f. Under general conditions, we show that this can be achieved by simple minimization of unbiased risk estimator, provided the s...

We handle two major issues in applying extreme value analysis to nancial time series, bias and serial dependence, jointly. This is achieved by studying bias correction method when observations exhibit weakly serial dependence, namely the β−mixing series. For estimating the extreme value index, we propose an asymptotically unbiased estimator and prove its asymptotic normality under the β−mixing ...

The Rao-Blackwell theorem offers a procedure for converting a crude unbiased estimator of a parameter θ into a "better" one, in fact unique and optimal if the improvement is based on a minimal sufficient statistic that is complete. In contrast, behind every minimal sufficient statistic that is not complete, there is an improvable Rao-Blackwell improvement. This is illustrated via a simple examp...

Consider the small area estimation when positive area-level data like income, revenue, harvests or production are available. Although a conventional method is the logtransformed Fay-Herriot model, the log-transformation is not necessarily appropriate. Another popular method is the Box-Cox transformation, but it has drawbacks that the maximum likelihood estimator (ML) of the transformation param...

Several methods (independent subsamples, leave-one-out, cross-validation, and bootstrapping) have been proposed for estimating the error rates of classiers. The rationale behind the various estimators and the causes of the sometimes con BLOCKINicting claims regarding their bias and precision are explored in this paper. The biases and variances of each of the estimators are examined empirically....

This paper studies an optimal state estimation (Kalman filtering) problem under the assumption that output measurements are subject to random time delays caused by network transmissions without time stamping. We first propose a random time delay model which mimics many practical digital network systems. We then study the so-called unbiased, uniformly bounded linear state estimators and show tha...

From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, empirical risks on training data will go negative, and we will suffer from serious overfitting. In this paper, we propose a non-negative risk estimator for PU learning: when getting minimized, it is m...

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...

In this paper we consider estimating heterogeneity variance with the DerSimonian-Laird (DSL) estimator as typically used in meta-analysis. In its general form the DSL estimator requires inverse population-averaged study-specific variances as weights, in which case the estimator is unbiased. It has become common practice, however, to use estimates of the study-specific variances instead of their...

The maximum likelihood estimators are uniquely obtained in a multivariate normal distribution with AR(1) covariance structure for monotone data. The maximum likelihood estimator of mean is unbiased.