Abstract. This paper gives a brief overview of the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inference for instantaneous returns and volatility functions of time-homogeneous and time-dependent diffusion processes, and estimation of transition densities and state price densities. We first briefly describe the problems and then outline the main techniques and main results. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.

We consider the asymptotic joint distribution of the eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues become infinitely dispersed. We show that the normalized sample eigenvalues and the relevant elements of the sample eigenvectors are asymptotically all mutually independently distributed. The limiting distributions of the normalized sample eigenvalues are chi-squared distributions with varying degrees of freedom and the distribution of the relevant elements of the eigenvectors is the standard normal distribution. As an application of this result, we investigate tail minimaxity in the estimation of the population covariance matrix of Wishart distribution with respect to Stein's loss function and the quadratic loss function. Under mild regularity conditions, we show that the behavior of a broad class of minimax estimators is identical when the sample eigenvalues become infinitely dispersed. Keywords and phrases asymptotic distribution, covariance matrix, minimax estimator, quadratic loss, singular parameter, Stein's loss, tail minimaxity. 1

The concept of the spectral envelope was introduced as a statistical basis for the frequency domain analysis and scaling of qualitative-valued time series.

We are gratefull to Marine Carrasco, Russell Davidson and Raymond Kan for helpful comments as well as seminar

This paper examines the information provided to the private sector by central banks. By using the principal component analysis, we investigated the variance of the procedural rules followed by nine major central banks about information treatments. We investigate problems related to the information coming from the central banks by focusing on the quantity and quality perspectives and highlight the methodological complexity of the investigation. We find that a synthetic quantitative index of transparency is not enough to represent the phenomenon since it can result misleading in understanding the behavior of institutionally different central banks associated with the same index values. Keywords: policy. Central bank transparency, principal components, monetary