y=1 φ(y) = 0, θ ∈ {1, 2, . . .}, i.e., φ(y) = 0, y ∈ {1, 2 . . .}. Consequently, if g : IR → IR is an unbiased estimator of θ on the basis of Y , it is “essentially unique”: if g̃ : IR → IR is another unbiased estimator, then it must hold by the completeness of {U(1, . . . , θ), θ ∈ {1, 2 . . .}} that g̃(Y ) = g(Y ) Pθ-a.s. θ ∈ {1, 2, . . .}, whence g̃(y) = g(y), y ∈ {1, 2, . . .}. Next, Eθ[g(Y )]...

Minimum mean squared error linear unbiased estimation of the total of a nite population is investigated utilizing a characterization of such estimators involving unbiased estimators of zero. Several criteria emerging from taking either or both of the design and a model into account are discussed. For each criterion, necessary and su cient conditions for existence of a best estimator and the opt...

In the design of randomized algorithms, we sometimes wish to estimate some quantity using an unbiased estimator. (Say we wish to estimate some quantity A, X ∼ μ is an unbiased estimator if E[X] = A.) We would like those estimations to be close to its mean w.h.p. Given some distribution μ, let Y1, · · · , Yn be i.i.d samples from μ and Y = 1 n ∑ i Yi be the empirical mean. Recall that in Problem...

Univariate studies of the hypothesis of unit roots in real exchange rates have yielded consensus point estimates of the half-life of deviations from purchasing power parity (PPP) of between three to five years (Rogoff, 1996). However, conventional least-squares-based estimates of half-lives are biased downward. Accordingly, as a preferred measure of the persistence of real exchange rate shocks ...

A well-known result by Stein (1956) shows that in particular situations, biased estimators can yield better parameter estimates than their generally preferred unbiased counterparts. This letter follows the same spirit, as we will stabilize the unbiased generalization error estimates by regularization and finally obtain more robust model selection criteria for learning. We trade a small bias aga...

<p style='text-indent:20px;'>Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory sublinear expectations. In this paper, we proved that maximum estimator largest unbiased upper mean and minimum smallest lower mean.</p>

We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Therefore, several standard theorems on properties of U-statistics apply. In particular, it has minimal variance among all unbiased estimators and is asymptotically normal...

BACKGROUND The ratio of two measured fluorescence signals (called x and y) is used in different applications in fluorescence microscopy. Multiple instances of both signals can be combined in different ways to construct different ratio estimators. METHODS The mean and variance of three estimators for the ratio between two random variables, x and y, are discussed. Given n samples of x and y, we...

The effect of multiplicative noise on a signal when compared with that of additive noise is very large. In this paper, we address the problem of suppressing multiplicative noise in one-dimensional signals. To deal with signals that are corrupted with multiplicative noise, we propose a denoising algorithm based on minimization of an unbiased estimator (MURE) of meansquare error (MSE). We derive ...