Functional Estimation of a Density Under a New Weak Dependence Condition

The purpose of this paper is to prove, through the analysis of the behaviour of a standard kernel density estimator, that the notion of weak dependence defined in a previous paper (cf. Doukhan & Louhichi, 1999) has sufficiently sharp properties to be used in various situations. More precisely we investigate the asymptotics of high order losses, asymptotic distributions and uniform almost sure behaviour of kernel density estimates. We prove that they are the same as for independent samples (with some restrictions for a.s. behaviours). Recall finally that this weak dependence condition extends on the previously defined ones such as mixing, association and it allows considerations of new classes such as weak shifts processes based on independent sequences as well as some non-mixing Markov processes.     

High-dimensional VAR with low-rank transition

Statistics and Computing - We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This model is well suited to predict high-dimensional series that are...     

Statistical inference for DNA sequences of promoters: a non-stationary qualitative model

ABSTRACT

Gene promoters have variable repartition of AGCT nucleotides according to some probabilistic behaviours essentially depending on their position in a string. The paper aims to provide a model for this configuration. With this model we derive non-uniform confidence bounds for those probability distributions in the strings. A uniform bound deriving from previous works in Wu and Zhao [Inference of trends in time series. J R Stat Soc B. 2007;69:391–410] is more demanding for the model. A data-based study allows to clarify our suggestions and open the way for applications in molecular biology.