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...

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from distribution D and subsequently corrupted on some fraction of points, our algorithm outputs a linear function whose squared error is close to the squared error of t...

Distance measures between a reference signal and the autoregressive estimate are used as an objective reference for comparing autoregressive order-determining criteria. The distance measures discussed are the rms log spectral deviation, its normalized cepstral distance approximation, the normalized autoregressive transfer function error, the equivalent Itakura distance, and the average squared ...

This paper describes the Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data. First we consider the Bayesian inference of the unknown parameter under a squared error loss function. Although we have discussed mainly the squared error loss function, any other loss function can easily be considered. Gibbs sampling procedure is used to draw Markov Chain M...

Bayes and classical estimators have been obtained for two-parameter exponentiated-Weibull distribution when sample is available from type-II censoring scheme. Bayes estimators have been developed under squared error loss function as well as under LINEX loss function using non-informative type of priors for the parameters. Besides, the generalized maximum likelihood estimators and the usual maxi...

The nonparametric problem of estimating a variance based on a sample of size n from a univariate distribution which has a known bounded range but is otherwise arbitrary is treated. For squared error loss, a certain linear function of the sample variance is seen to be minimax for each n from 2 through 13, except n = 4. For squared error loss weighted by the reciprocal of the variance, a constant...

The estimation of a log-concave density on Rd represents a central problem in the area of nonparametric inference under shape constraints. In this paper, we study the performance of log-concave density estimators with respect to global loss functions, and adopt a minimax approach. We first show that no statistical procedure based on a sample of size n can estimate a log-concave density with res...