Consider a strictly stationary time series Zb =fvalued and Y i real-valued. The nonparametric M-type regression function g 0 () is deened by E(((Y 1 ? g 0 (X 1)) j X 1 = x) = 0. Tensor products of B-splines are adopted to approximate g 0 and a class of M-type regression spline estimators of this function are obtained based on a segment, (X 1 ; Y 1); ; (X n ; Y n), of Z. Suppose that g 0 () is s...

We consider the problem of selecting the number of frequencies, m, in a log-periodogram regression estimator of the memory parameter d of a Gaussian longmemory time series. It is known that under certain conditions the optimal m, minimizing the mean squared error of the corresponding estimator of d, is given by m ˆ Cn, where n is the sample size and C is a constant. In practice, C would be unkn...

We present an O(M logM) method for estimating M -dimensional structured channels that uses techniques from the field of machine learning. Our channel model is typical in communications: the channel vector is normal distributed given an unknown covariance matrix, which depends on random hyperparameters such as the angles of the propagation paths. If the channel model exhibits certain Toeplitz an...

This paper studies the limiting behavior of Tyler’s and Maronna’s Mestimators, in the regime that the number of samples n and the dimension p both go to infinity, and p/n converges to a constant y with 0 < y < 1. We prove that when the data samples are identically and independently generated from the Gaussian distribution N(0, I), the difference between the sample covariance matrix and a scaled...

A smoothing principle for M-estimators is proposed. The smoothing depends on the sample size so that the resulting smoothed M-estimator coincides with the initial M-estimator when n → ∞. The smoothing principle is motivated by an analysis of the requirements in the proof of the Cramér-Rao bound. The principle can be applied to every M-estimator. A simulation study is carried out where smoothed ...

The M-regression estimator has recently been widely used to build spectral estimators in time series models. In this paper, we extend approach when the data follow a periodic autoregressive moving average process. We introduce an of parameters based on classical Whittle estimator. finite sample size performances proposed are analyzed under scenarios PARMA processes with and without additive out...

M-estimators are widely used in active noise control (ANC) systems order to update the adaptive FIR filter taps. ANC reduce level by generating anti-noise signals. Up now, evaluation of capabilities has shown that there exists a need for further improvements this area. In paper, new improved M-estimator is proposed. The sensitivity proposed algorithm variations its constant parameter checked fe...

In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and can appear either at the group level or within certain groups. such cases, an ideal model should be able to encourage variable selection consistently. Bi-level has become even more challenging have heavy-tailed distribution outliers exist in random errors covariates. this paper, we st...