This paper is concerned with estimating the regression function fρ in supervised learning by utilizing piecewise polynomial approximations on adaptively generated partitions. The main point of interest is algorithms that with high probability are optimal in terms of the least square error achieved for a given number m of observed data. In a previous paper [1], we have developed for each β > 0 a...

It is well known that the class of strong (Generalized) AutoRegressive Conditional Heteroskedasticity (or GARCH) processes is not closed under contemporaneous aggregation. This paper provides the dynamics followed by the aggregate process when the individual persistence parameters are drawn from the same (unknown) distribution. Assuming heterogeneity across individual parameters, the dynamics o...

A type of parameter estimation technique based on the linear integral filter (LIF) method, the least-absolute error with variable forgetting factor (LAE+VFF) estimation method, is proposed in this paper to estimate the railway wheelset parameters modelled as a time-varying continuous-time (C-T) system. The inputs to the parameter estimator are the control signal and the railway wheelset system ...

An empirical correlation is established for relating Raman stretching frequencies of niobium-oxygen (Nb-O) bonds to their respective bond distances in niobium oxide compounds. The correlation is an exponential least-squares fit between measured Raman frequencies and reported crystallographic bond lengths. Niobium-oxygen bond strengths (in valence units) are also related to Raman stretching freq...