varIatIon Deviation from linear regression (X 10) Deviation from quadratic

Given two sources of forecasts of the same quantity, it is possible to compare prediction records. In particular, it can be useful to test the hypothesis of equal accuracy in forecast performance. We analyse the behaviour of two possible tests, and of modifications of these tests designed to circumvent shortcomings in the original formulations. As a result of this analysis, a recommendation forone particular testing approach is made for practical applications.

this article a formula for the mean square L

average of its neighbors ’ values, and each new value is corrupted by an additive noise with zero mean. The quality of consensus can be measured by the total mean-square deviation of the individual variables from their average, which converges to a steady-state value. We consider the problem of finding

This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given

We study the convolution function x C[f(x)]:= 1 f(y)f ( x dy y y when f(x) is a suitable number-theoretic error term. Asymptotics and upper bounds for C[f(x)] are derived from mean square bounds for f(x). Some applications are given, in particular to |ζ ( 1 2 + ix)|2k and the classical Rankin

Abstract. A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional differential equation. In this work the asymptotic behavior in mean

This paper studies the effect of parametric mismatch in minimum mean square error (MMSE) estimation. In particular, we consider the problem of estimating the input signal from the output of an additive white Gaussian channel whose gain is fixed, but unknown. The input distribution is known

probability, when θ is the true value of the parameter. Let X = (X1,..., Xn) be a vector of i.i.d. observations with distribution Pθ. Suppose g = g(θ) is a real-valued function of the parameter θ. One criterion for choosing an estimator T = T(X) of g(θ) is to minimize the mean-squared error (MSE) Eθ((T(X) − g

for timeseries x in below. The mean describes the central location of the data, and the standard deviation describes the spread. The standard deviation remains the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. In mathematics, the root mean square