For the Gaussian channel with intersymbolinterference (ISI), it is known that there is no loss in channel capacity if the receiver is an ideal minimum mean-squared error (MMSE) decision-feedback equalizer (DFE) with error-free feedback. However, combining the DFE with channel coding is problematic. Transmitter precoding and reduced-state sequence estimation are two common approaches (cf. [1] an...

We develop and test robust methods for design construction, for estimation and for prediction in spatial studies. The designs are robust against misspecified variance/covariance structures, and against misspecified regression responses. Robustness against contaminated error distributions is provided by the use of generalized M-estimators in the estimation and prediction procedures. The loss fun...

This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated by a simple steepest-descent recursion to minimize the error signal of the glo...

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...

Minimization of the Euclidean distance between output distribution and Dirac delta functions as a performance criterion is known to match the distribution of system output with delta functions. In the analysis of the algorithm developed based on that criterion and recursive gradient estimation, it is revealed in this paper that the minimization process of the cost function has two gradients wit...

Vapnik described the “three main learning problems” of pattern recognition, regression estimation and density estimation. These are defined in terms of the loss functions used to evaluate performance (0-1 loss, squared loss and log loss respectively). But there are many other loss functions one could use. In this chapter I will summarise some recent work by myself and colleagues studying the th...

Maximum likelihood and Bayes estimators of the parameters, survival function (SF) and hazard rate function (HRF) are obtained for the three-parameter exponentiated Burr type XII distribution when sample is available from type II censored scheme. Bayes estimators have been developed using the standard Bayes and MCMC methods under square error and LINEX loss functions, using informative type of p...

We consider the task of evaluating a policy for a Markov decision process (MDP). The standard unbiased technique for evaluating a policy is to deploy the policy and observe its performance. We show that the data collected from deploying a different policy, commonly called the behavior policy, can be used to produce unbiased estimates with lower mean squared error than this standard technique. W...