This paper presents a data-driven adaptive steady state-integral-derivative (SS-ID) control algorithm that uses gradient descent and recursive least squares (RLS) with forgetting factor. A simplified first-order differential equation of the system was designed its parameters were estimated in real-time using RLS algorithm. The steady-state input for target-state tracking derived based on perfor...

The scope of application of iteratively reweighted least squares to statistical estimation problems is considerably wider than is generally appreciated. It extends beyond the exponential-family-type generalized linear models to other distributions, to non-linear parameterizations, and to dependent observations. Various criteria for estimation other than maximum likelihood, including resistant a...

In this paper, we will discuss a parametric approach to risk-neutral density extraction from option prices based on the knowledge of the estimated historical density. A flexible distribution is needed in order to find an equivalent change of measure and, at the same time, take into account the historical estimates. To this end, we introduce a new tempered stable distribution we refer to as the ...

Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponential family multi-view learning methods of the partial least squares and canonic...

The development of accurate material models and computational methods are two fundamental components in building a real-time realistic surgery simulator. In this paper, we use a least-squares method to calibrate an exponential model of pig liver based on the assumption of incompressible material under a uniaxial testing mode. With the obtained parameters, the stress-strain curves generated from...

Contrary to popular belief, the method of least squares (LS) does not require that the data have normally distributed (Gaussian) error for its validity. One practically important application of LS fitting that does not involve normal data is the estimation of data variance functions (VFE) from replicate statistics. If the raw data are normal, sampling estimates s(2) of the variance sigma(2) are...

In this paper, we study the theoretical properties of a class of iteratively re-weighted least squares (IRLS) algorithms for sparse signal recovery in the presence of noise. We demonstrate a one-to-one correspondence between this class of algorithms and a class of Expectation-Maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribu...

This paper investigates the use of individual cross section data to describe macro functions. Necessary and sufficient conditions (denoted AS) are found for OLS slope coefficients from a cross section to consistently estimate the first derivatives of the macro function. AS embodies both sets of aggregation assumptions known; linear aggregation and sufficient statistics , and thus represents gen...