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Estimating the mixing density of a mixture distribution remains an interesting problem in statistics literature. Using a stochastic approximation method, Newton and Zhang (1999) introduced a fast recursive algorithm for estimating the mixing density of a mixture. Under suitably chosen weights the stochastic approximation estimator converges to the true solution. In Tokdar et. al. (2009) the consistency of this recursive estimation method was established. However, the proof of consistency of the resulting estimator used independence among observations as an assumption. Here, we extend the investigation of performance of Newtons algorithm to several dependent scenarios. We first prove that the original algorithm under certain conditions remains consistent when the observations are arising form a weakly dependent process with fixed marginal with the target mixture as the marginal density. For some of the common dependent structures where the original algorithm is no longer consistent, we provide a modification of the algorithm that generates a consistent estimator.
Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We focus her
We study the problem of the non-parametric estimation for the density $pi$ of the stationary distribution of a stochastic two-dimensional damping Hamiltonian system $(Z_t)_{tin[0,T]}=(X_t,Y_t)_{t in [0,T]}$. From the continuous observation of the sam
In this article we study the existence and strong consistency of GEE estimators, when the generalized estimating functions are martingales with random coefficients. Furthermore, we characterize estimating functions which are asymptotically optimal.
A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of asymptotic no
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data, with distribu