In this paper we consider a wide class of truncated stochastic approximation procedures. These procedures have three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We establish...

The generalized gamma distribution (GGD) is a very popular distribution since it includes many well known distributions. Estimation of the parameters of the GGD is quite problematic because of the complicated structure of its density function. We introduce two new estimation methods called...

A test for the serial independence of errors in panel data models is proposed. The test is based on the difference between the joint empirical characteristic function of residuals at different lags and the product of their marginal empirical characteristic functions. The test is...

Markovian binary trees form a class of continuous-time branching processes where the lifetime and reproduction epochs of individuals are controlled by an underlying Markov process. An Expectation–Maximization (EM) algorithm is developed to estimate the parameters of the Markov process from the...

We propose a mean-reverting interest rate model whose mean-reverting level, speed of mean-reversion and volatility are all modulated by a weak Markov chain (WMC). This model features a simple way to capture the regime-switching evolution of the parameters as well as the memory property of the...

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H1/2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>H</mi> <mo></mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation>. The estimator is based on discrete time observations of the stochastic differential...</equationsource></equationsource></inlineequation>

We present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity. It turns out that this function has a maximum at its fixed point. Fixed-point equation is used to estimate the parameter...