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...

We consider the problem of testing hypotheses regarding the covariance matrix of multivariate normal data, if the sample size s and dimension n satisfy lim [n,s→∞] n/s = y. Recently, several tests have been proposed in the case, where the sample size and dimension are of the same order, that...

We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in which default events and losses are derived from the asset values at...

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...

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...

In this paper we re-visit a recent theoretical idea introduced by Phillips and Lee (2015). They examine an empirically relevant situation when multiple time series under consideration exhibit different degrees of non-stationarity. By bridging the asymptotic theory of the local to unity and...

We propose a nonparametric test for checking parametric hypotheses about the stationary density of weakly dependent observations. The test statistic is based on the L2-distance between a nonparametric and a smoothed version of a parametric estimate of the stationary density. It can be shown that...

Theory in time series analysis is often developed in the context of finite-dimensional models for the data generating process. Whereas corresponding estimators such as those of a conditional mean function are reasonable even if the true dependence mechanism is of a more complex structure, it is...

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we...