We study the problem of aggregation of M arbitrary estimators of a regression function with respect to the mean squared risk. Three main types of aggregation are considered: model selection, convex and linear aggregation. We define the notion of optimal rate of aggregation in an abstract context and prove lower bounds valid for any method of aggregation. We then construct procedures that attain...

Assessment of a DEM’s quality is usually undertaken by deriving a measure of DEM accuracy – how close the DEM’s elevation values are to the true elevation. Measures such as Root Mean Squared Error and standard deviation of the error are frequently used. These measures summarise elevation errors in a DEM as a single value. A more detailed description of DEM accuracy would allow better understand...

Abstract This paper considers a supply chain with the first order autoregressive and the first order moving average (ARMA (1,1)) demand. The lead time demand is estimated using the minimum mean-square error (MMSE) forecasting technique. The expression of the bullwhip effect for a two stage supply chain consisting of one supplier and one retailer is derived, and the existence condition of the bu...

The classical unbiasedness condition utilized e.g. by the best linear unbiased estimator (BLUE) is very stringent. By softening the ”global” unbiasedness condition and introducing component-wise conditional unbiasedness conditions instead, the number of constraints limiting the estimator’s performance can in many cases significantly be reduced. In this paper we extend the findings on the compon...

For all $a,b>0$, the following two optimal inequalities are presented: $H^{alpha}(a,b)L^{1-alpha}(a,b)geq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ H^{alpha}(a,b)L^{1-alpha}(a,b)leq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. Here, $H(a,b)$, $L(a,b)$, and $M_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

An enormous amount of publications deals with smoothing in the sense of nonparametric regression. However, nearly all of the literature treats the case where predictors and response are related in the form of a function y = m(x) + noise. In many situations this simple functional model does not capture adequately the essential relation between predictor and response. We show by means of speed-fl...