This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is...

This paper generalises Boswijk and Zu (2018)'s adaptive unit root test for time series with nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix of a vector autoregressive model lead to size distortions in conventional cointegration tests,...

Design of nonlinear observers has received considerable attention since the early development of methods for linear state estimation. The most popular approach is the extended Kalman filter (EKF), that goes through significant degradation in the presence of nonlinearities, particularly if...

Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be writtenin terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A model selection approach made up oftwo steps is investigated. The first step...

Two-stage sampling usually leads to higher variances for estimators of means and regression coefficients, because of intra-cluster homogeneity. One way of allowing for clustering in fitting a linear regression model is to use a linear mixed model with two levels. If the estimated intra-cluster...

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...

The paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares...

The problem of estimation of the finite dimensional parameter in a partial linear model is considered. We derive upper and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum likelihood estimator. It is well known that the...

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...