This paper considers the problem of estimating a high-dimensional vector of parameters θ ∈ R from a noisy observation. The noise vector is i.i.d. Gaussian with known variance. For a squared-error loss function, the James-Stein (JS) estimator is known to dominate the simple maximum-likelihood (ML) estimator when the dimension n exceeds two. The JS-estimator shrinks the observed vector towards th...

For a vast class of discrete model families with cdf’s Fθ, and for estimating θ under squared error loss under a constraint of the type θ ∈ [0,m], we present a general and unified development concerning the minimaxity of a boundary supported prior Bayes estimator. While the sufficient conditions obtained are of the expected form m ≤ m(F ), the approach presented leads, in many instances, to bot...

We consider the problem of the optimal loss functions for predicted clickthrough rates in auctions for online advertising. While standard loss functions such as mean squared error or the log likelihood loss function severely penalize large mispredictions while imposing little penalty on smaller mistakes, we nd that a loss function re ecting the true underlying economic loss resulting from mispr...

Recent advances in the measurement of volatility have utilized high frequency intraday data to produce what are generally known as realised volatility estimates. It has been shown that forecasts generated from such estimates are of positive economic value in the context of portfolio allocation. This paper considers the link between the value of such forecasts and the loss function under which m...

Given a probability space (Ω,F , P ), a F -measurable random variable X , and a sub-σ-algebra G ⊂ F , it is well known that the conditional expectation E[X|G] is the optimal L-predictor (also known as “the least mean square error” predictor) of X among all the G-measurable random variables [8, 11]. In this paper, we provide necessary and sufficient conditions under which the conditional expecta...

In this paper we use Gaussian Process (GP) regression to propose a novel approach for predicting volatility of financial returns by forecasting the envelopes of the time series. We provide a direct comparison of their performance to traditional approaches such as GARCH. We compare the forecasting power of three approaches: GP regression on the absolute and squared returns; regression on the env...

A technique is presented for subband adaptive ltering with nonuniform lter banks. The bandwidth allocations of the subband analysis and synthesis lters are adapted to the spectral characteristics of the input data in such a manner as to minimize an objective function built from the subband error powers. The nonuniform lter bank structure allows for fast convergence times for high order systems ...

One way to define the “randomness” of a fixed individual sequence is to ask how hard it is to predict. When prediction error is measured via squared loss, it has been established that memoryless sequences (which are, in a precise sense, hard to predict) have some of the stochastic attributes of truly random sequences. In this paper, we ask how changing the loss function used changes the set of ...

This paper proposes an average concatenative cost function as the objective measure for naturalness of synthesized speech. All its seven component-costs can be derived directly from the input text and the scripts of speech database. A formal Mean Opinion Score (MOS) experiment shows that the average concatenative cost and its seven components are all highly correlated with MOS obtained subjecti...

The aim of the present paper is to obtain Bayes estimators for the oospring mean of a simple branching process with a power series oospring probability distribution. We study the sensitivity behavior of the obtained estimators with respect to the choice of the loss function. We propose a minimax criterion using the Bayes risk for ranking the eeectiveness (in the sense of robustness) of the loss...