In this paper, we study a nonlinear panel data model with time-varying regression coefficients associated with an additive factor structure. In our model, factor loadings are unknown functions of observable variables which can capture time-varying and heterogeneous covariate information. A...

Let (εj)j≥0 be a sequence of independent p-dimensional random vectors and τ≥1 a given integer. From a sample ε1,…,εT+τ of the sequence, the so-called lag-τ auto-covariance matrix is Cτ=T−1∑j=1Tετ+jεjt. When the dimension p is large compared to the sample size T, this paper...

A factor analysis-based approach for estimating high dimensional covariance matrix is proposed and is applied to solve the mean–variance portfolio optimization problem in finance. The consistency of the proposed estimator is established by imposing a factor model structure with a relative weak...

In this paper, the random quadratic form is considered. The main motivation comes from the application to wireless communication. For [tau]>0, it is shown that converges to a fixed quantity with convergence rate oa.s(N1/2-[tau]). Also, convergence in probability is established.

Consider the empirical spectral distribution of complex random nxn matrix whose entries are independent and identically distributed random variables with mean zero and variance 1/n. In this paper, via applying potential theory in the complex plane and analyzing extreme singular values, we prove...

Let , where is a random symmetric matrix, a random symmetric matrix, and with being independent real random variables. Suppose that , and are independent. It is proved that the empirical spectral distribution of the eigenvalues of random symmetric matrices converges almost surely to a non-random...