This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive IN-CAR model and the input nonlinear controlled autoregressive autoregressive moving average IN-CARARMA model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algori...

This paper deals with the Gaussian and bootstrap approximations to distribution of max statistic in high dimensions. takes form maximum over components sum independent random vectors its plays a key role many high-dimensional estimation testing problems. Using novel iterative randomized Lindeberg method, derives new bounds for distributional approximation errors. These substantially improve upo...

The feedback capacity of the stationary Gaussian additive noise channel has been open, except for the case where the noise is white. Here we obtain the closed-form feedback capacity of the first-order moving average additive Gaussian noise channel. Specifically, the channel is given by Yi = Xi +Zi, i = 1, 2, . . . , where the input {Xi} satisfies a power constraint and the noise {Zi} is a first...

A renormalization group analysis is applied to autoregressive processes with an infinite series of coefficients. A simple fixed point is given by a random walk, and a second class is found that is proportional to the high order coefficients of fractional autoregressive integrated moving average (ARIMA) processes. The approach might be useful to detect nonstationarity in autoregressive processes.

We combine Malliavin calculus with Stein’s method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-Itô integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nuala...

We have previously developed a Fishervoice framework that maps the JFA-mean supervectors into a compressed discriminant subspace using nonparametric Fishers discriminant analysis. It was shown that performing cosine distance scoring (CDS) on these Fishervoice projected vectors (denoted as f-vectors) can outperform the classical joint factor analysis. Unlike the ivector approach in which the cha...

In this chapter, we examine the use of special forms of correlated random e ects in the generalized linear mixed model (GLMM) setting. A special feature of our GLMM is the inclusion of random residual e ects to account for lack of t due to extra variation, outliers and other unexplained sources of variation. For random e ects, we consider, in particular, the correlation structure and improper p...