AbstructA fixed-rate universal lossy coding scheme is introduced for independent and identically distributed (i.i.d.) sources. It is shown for finite alphabet sources and arbitrary single letter distortion measures that as the sample size T I grows the expected distortion obtained using this universal scheme converges to Shannon’s distortion rate function D ( R ) at a rate 0 (log , I / , , ) . ...

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...

It has long been customary to measure the adequacy of an estimator by the smallness of its mean squared error. The least squares estimators were studied by Gauss and by other authors later in the nineteenth century. A proof that the best unbiased estimator of a linear function of the means of a set of observed random variables is the least squares estimator was given by Markov [12], a modified ...

Beamforming methods are used extensively in a variety of different areas, where one of their main goals is to estimate the source signal amplitude s(t) from the array observations y(t) = s(t)a + i(t) + e(t), t = 1,2,..., where a is the steering vector, i(t) is the interference, and e(t) is a Gaussian noise vector [1, 2]. To estimate s(t), we may use a beamformer with weights w so that s(t) = w*...

For calculating non-life insurance premiums, actuaries traditionally rely on separate severity and frequency models using covariates to explain the claims loss exposure. In this paper, we focus claim severity. First, build two reference models, a generalized linear model additive model, relying log-normal distribution of including most significant factors. Thereby, relate continuous variables r...

The maximum $${\log }_q$$ likelihood estimation method is a generalization of the known $$\log $$ to overcome problem for modeling non-identical observations (inliers and outliers). parameter q tuning constant manage capability. Weibull flexible popular distribution problems in engineering. In this study, used estimate parameters when exist. Since main idea based on capability objective functio...

In this paper, by considering an $$M|M|1|\infty$$ queueing model, Bayes estimators of traffic intensity and system performance measures are discussed under (i) squared error loss function (SELF) (ii) entropy (ELF) (iii) LINEX with Beta prior. Further, minimum posterior risk associated obtained SELF. The the model compared Uniformly Minimum Variance Unbiased Estimators (UMVUEs) through simulation.

A popular approach for estimating an unknown signal x0 ∈ R from noisy, linear measurements y = Ax0 +z ∈ R is via solving a so called regularized M-estimator: x̂ := arg minx L(y−Ax)+λf(x). Here, L is a convex loss function, f is a convex (typically, non-smooth) regularizer, and, λ > 0 is a regularizer parameter. We analyze the squared error performance ‖x̂ − x0‖2 of such estimators in the high-dim...