Abstract This paper is devoted to the study of asymptotic properties of the regression function kernel estimate in the setting of continuous time stationary and ergodic data. More precisely, considering the Nadaraya–Watson type estimator, say m̂ T ( x ) , of the l -indexed regression function...

This paper is devoted to the study of asymptotic properties of the regression function kernel estimate in the setting of continuous time stationary and ergodic data. More precisely, considering the Nadaraya–Watson type estimator, say m̂T(x), of the l-indexed regression function...

We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate hyperplanes of an orthogonal basis. We obtain results on...

This note is concerned with estimating censored quantile regressions (CQR). As its major contribution, a' new algorithm, called BRCENS, is developed as an adaption of the Barrodale-Roberts algorithm for the standard quantile regression problem. In a subsequent simulation study, BRCENS performs...

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Aït-Sahalia [J. Finance 54 (1999) 1361–1395; Econometrica 70 (2002) 223–262] proposed asymptotic...

Second-order diffusion process can not only model integrated and differentiated diffusion processes but also overcome the difficulties associated with the nondifferentiability of the Brownian motion, so these models play an important role in econometric analysis. In this paper, we propose a...

The robust estimation for Poisson autoregressive models is studied. As a robust estimator, a minimum density power divergence estimator (MDPDE) is considered. It is shown that under regularity conditions, the MDPDE is strongly consistent and asymptotically normal. Simulation results are provided...

In this paper, we study the robust estimation for the covariance matrix of stationary multivariate time series. As a robust estimator, we propose to use a minimum density power divergence estimator (MDPDE) designed by Basu et al. (1998). To supplement the result of Kim and Lee (2011), we employ...

This note is concerned with estimating censored quantile regressions (CQR). As its major contribution, a' new algorithm, called BRCENS, is developed as an adaption of the Barrodale-Roberts algorithm for the standard quantile regression problem. In a subsequent simulation study, BRCENS performs...