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Thu, 11 Oct 2007 12:37:44 +0200Thu, 11 Oct 2007 12:37:44 +0200Some asymptotics for local least-squares regression with regularization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1902
We derive some asymptotics for a new approach to curve estimation proposed by Mr'{a}zek et al. cite{MWB06} which combines localization and regularization. This methodology has been considered as the basis of a unified framework covering various different smoothing methods in the analogous two-dimensional problem of image denoising. As a first step for understanding this approach theoretically, we restrict our discussion here to the least-squares distance where we have explicit formulas for the function estimates and where we can derive a rather complete asymptotic theory from known results for the Priestley-Chao curve estimate. In this paper, we consider only the case where the bias dominates the mean-square error. Other situations are dealt with in subsequent papers.Jürgen Franke; Joseph Tadjuidje; Stefan Didas; Joachim Weickertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1902Thu, 11 Oct 2007 12:37:44 +0200Quantile Sieve Estimates for Time Series
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1834
We consider the problem of estimating the conditional quantile of a time series at time \(t\) given observations of the same and perhaps other time series available at time \(t-1\). We discuss sieve estimates which are a nonparametric versions of the Koenker-Bassett regression quantiles and do not require the specification of the innovation law. We prove consistency of those estimates and illustrate their good performance for light- and heavy-tailed distributions of the innovations with a small simulation study. As an economic application, we use the estimates for calculating the value at risk of some stock price series.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidjepreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1834Mon, 05 Feb 2007 14:01:57 +0100A note on the identifiability of the conditional expectation for the mixtures of neural networks
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1832
We consider a generalized mixture of nonlinear AR models, a hidden Markov model for which the autoregressive functions are single layer feedforward neural networks. The non trivial problem of identifiability, which is usually postulated for hidden Markov models, is addressed here.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidje Kamgaingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1832Fri, 12 Jan 2007 20:16:48 +0100On Geometric Ergodicity of CHARME Models
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1831
In this paper we consider a CHARME Model, a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. We apply the theory of Markov models to derive asymptotic stability of this model. Indeed, the goal is to provide some sets of conditions under which our model is geometric ergodic and therefore satisfies some mixing conditions. This result can be considered as the basis toward an asymptotic theory for our model.Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidje Kamgaingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1831Fri, 12 Jan 2007 20:14:26 +0100