Evaluation of forecast optimality in economics and Þnance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors should be serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results, we show in this paper that ...

This paper considers parameter estimations in Lomax distribution under progressive type-II censoring with random removals, assuming that the number of units removed at each failure time has a binomial distribution. The maximum likelihood estimators (MLEs) are derived using the expectation-maximization (EM) algorithm. The Bayes estimates of the parameters are obtained using both the squared erro...

Consider a parametric statistical model P (dx|θ) and an improper prior distribution ν(dθ) that together yield a (proper) formal posterior distribution Q(dθ|x). The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of θ is admissible under squared error loss. Eaton [Ann. Statist. 20 (1992) 1147–1179] has shown that a sufficient condition for strong ...

Allometric relationships are commonly used to estimate average biomass of trees of a particular size and to predict biomass of individual trees based on an easily measured covariate variable such as stem diameter. They are typically power relationships which, for the purpose of data fitting, are transformed using natural logarithms to convert the model to its linear equivalent. Implementation o...

The problem of asymptotic (i.e., low-distortion) behavior of the rate-distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. For example, for an input-weighted squared error distortion measure d(x; y) = kW (x)(y x)k2...

In recent papers, Miller, Goodman & Smyth (1991, 1993) provided conditions on the cost function used for the training of a neural network in order to ensure that the output of the network approximates the conditional expectation of the desired output, given the input. However, they only considered the single-output case. In this paper, we provide another, rather straightforward, proof of the sa...

This paper aims to study the empirical Bayes estimation of the parameter of ЭРланга distribution under a weighted squared error loss function. Bayes estimator is firstly to derive based on pivot method. Then empirical Bayes estimator of unknown parameter is constructed in a priori unknown circumstances. The asymptotically optimal property of this empirical Bayes estimator is also discussed. It ...

Support Vector Machines Regression (SVMR) is a learning technique where the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called the -Insensitive Loss Function (ILF), which is similar to loss functions used in the field of robust statistics. The quadratic loss function is well justified under the assumption of Gaus...