This article discusses large sample inference problems for a first-order ARCH(1) process where threshold appears not only in the mean but also in the variance function. Geometric ergodicity of the process is discussed. Least-squares estimators of parameters are derived and relevant limit results...

Controlled branching processes (CBP) with a random control function provide a useful way to model generation sizes in population dynamics studies, where control on the growth of the population size is necessary at each generation. An important special case of this process is the well known...

For count data, robust estimation of the number of mixture components in finite mixtures is revisited using L2 distance. An information criterion based on L2 distance is shown to yield an estimator, which is also shown to be strongly consistent. Monte Carlo simulations show that our estimator is...

Choice of an appropriate kernel density estimator is a difficult one in minimum distance estimation based on density functions. Particularly, for mixture models, the choice of bandwidth is very crucial because the component densities may have different scale parameters, which in turn necessitate...

Kernel smoothing methods are widely used in many areas of statistics with great success. In particular, minimum distance procedures heavily depend on kernel density estimators. It has been argued that when estimating mixture parameters in finite mixture models, adaptive kernel density estimators...

This paper is concerned with a general approach for sequential estimation for dependent observations, and an application to a non-standard first order autoregressive process having Weibull errors. The natural estimator of the autoregressive parameter when the errors are non negative turns out to...