Related papers: Local Quadratic Spectral and Covariance Matrix Est…
We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…
We consider the problem of regression with selectively observed covariates in a nonparametric framework. Our approach relies on instrumental variables that explain variation in the latent covariates but have no direct effect on selection.…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…
This paper deals with the nonparametric estimation in heteroscedastic regression $ Y_i=f(X_i)+\xi_i, \: i=1,...,n $, with incomplete information, i.e. each real random variable $ \xi_i $ has a density $ g_{i} $ which is unknown to the…
The author establishes a new mathematical expression for the Frequency Polygon. He uses it to prove the strong uniform consistency of the Frequency Polygon marginal density estimator for non-anticipative stationary stochastic processes…
We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…
The ensemble covariance matrix of a wide sense stationary signal spatially sampled by a full linear array is positive semi-definite and Toeplitz. However, the direct augmented covariance matrix of an augmentable sparse array is Toeplitz but…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…
The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed periodogram estimator of the spectral coherency matrix of a complex Gaussian high-dimensional time series $(\y_n)_{n \in \mathbb{Z}}$ with independent components…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
We investigate the computational issues related to the memory size in the estimation of quadratic covariation, taking into account the specifics of financial ultra-high-frequency data. In multivariate price processes, we consider both…
This paper introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require pre-binning or any other…