We investigate the problem of estimating the Cholesky decomposition in a conditional independent normal model with missing data. Explicit expressions for the maximum likelihood estimators and unbiased estimators are derived. By introducing a special group, we obtain the best equivariant estimators.

In this paper we derive, under the assumption of Gaussian errors with known errorcovariance matrix, asymptotic local power bounds for seasonal unit root tests for bothknown and unknown deterministic scenarios and for an arbitrary seasonal aspect. Wedemonstrate that the optimal test of a unit...

We present the asymptotic properties of double-stage quantile regressionestimators with random regressors, where the first stage is based on quantile regressionswith the same quantile as in the second stage, which ensures robustness of the estimationprocedure. We derive invariance properties...

In this paper we develop the rst estimator of the covariance matrix that relies solely onforward-looking information. This estimator only uses price information from a cross-sectionof plain-vanilla options. In an out-of-sample study for US blue-chip stocks we show that aminimum-variance strategy...

Our context involves Cournot oligopolists producing NM products at constant marginal costs when preferences are quasi-linear. We identify relationships between second moments of unit costs and second moments of firm-level production. For example, a larger variance in unit costs of a product...

Many statistical applications require an estimate of a covariance matrix and/or its inverse.When the matrix dimension is large compared to the sample size, which happensfrequently, the sample covariance matrix is known to perform poorly and may suffer fromill-conditioning. There already exists...

We propose a Conditional Autoregressive Wishart (CAW) model for the analysis of realized covariance matrices of asset returns. Our model assumes a generalized linear autoregressive moving average structure for the scale matrix of the Wishart distribution allowing to accommodate for complex...

This research focuses to develop some new techniques on statistical learning including methodology, computation and application. We also developed statistical quantification in nanomaterials. For a large number of random variables with temporal or spatial structures, we proposed shrink estimates...