A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intraday structures in the financial time series. The present study is based on the...

There is considerable literature on matrix-variate gamma distributions, also known as Wishart distributions, which are driven by a shape parameter with values in the (Gindikin) set {i/2, i = 1, . . . , k−1}∪((k−1)/2, É). We provide an extension of this class to the case where the shape...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e. sup-norm) convergence rate (n= log n)..p=(2p+d) of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal rate...

This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of...

For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with the same covariance structure. This class contains both...

We show that spline and wavelet series regression estimators for weakly dependent regressors attain the optimal uniform (i.e., sup-norm) convergence rate (n/log n)^{-p/(2p+d)} of Stone (1982), where d is the number of regressors and p is the smoothness of the regression function. The optimal...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

We apply random matrix theory to compare correlation matrix estimators C obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral...

The statistics of the eigenvalues of symmetric random matrices, composed by real and statistically independent elements following the distribution that maximizes Tsallis's entropy, is carried numerically in the limit of large matrices. For entropic indexes in the interval −∞<q<53, by using a convenient rescale of variables, it is possible to show that such matrices fall in the same class of the Gaussian orthogonal ensemble (GOE). For the entropic index 53⩽q<3, the density of eigenvalues and the distribution of level spacings do not seem to follow a simple rescale of variables involving different values of q, and exhibit a behavior very distinct from the GOE: both quantities present long tails for 53⩽q⩽2, and such long tails die out when q>2. The density of...</q<53,>