Journal of Data Science

Minimum Hellinger distance estimation (MHDE) for parametric model is obtained by minimizing the Hellinger distance between an assumed parametric model and a nonparametric estimation of the model. MHDE receives increasing attention for its efficiency and robustness. Recently, it has been extended from parametric models to semiparametric models. This manuscript considers a two-sample semiparametric location-shifted model where two independent samples are generated from two identical symmetric distributions with different location parameters. We propose to use profiling technique in order to utilize the information from both samples to estimate unknown symmetric function. With the profiled estimation of the function, we propose a minimum profile Hellinger distance estimation (MPHDE) for the two unknown location parameters. This MPHDE is similar to but dif- ferent from the one introduced in Wu and Karunamuni (2015), and thus the results presented in this work is not a trivial application of their method. The difference is due to the two-sample nature of the model and thus we use different approaches to study its asymptotic properties such as consistency and asymptotic normality. The efficiency and robustness properties of the proposed MPHDE are evaluated empirically though simulation studies. A real data from a breast cancer study is analyzed to illustrate the use of the proposed method.

Abstract: Additive model is widely recognized as an effective tool for di mension reduction. Existing methods for estimation of additive regression function, including backfitting, marginal integration, projection and spline methods, do not provide any level of uniform confidence. In this paper a sim ple construction of confidence band is proposed for the additive regression function based on polynomial spline estimation and wild bootstrap. Monte Carlo results show three desirable properties of the proposed band: excellent coverage of the true function, width rapidly shrinking to zero with increasing sample size, and minimal computing time. These properties make he pro cedure is highly recommended for nonparametric regression with confidence when additive modelling is appropriate.

Abstract: A seasonal additive nonlinear vector autoregression (SANVAR) model is proposed for multivariate seasonal time series to explore the possible interaction among the various univariate series. Significant lagged variables are selected and additive autoregression functions estimated based on the selected variables using spline smoothing method. Conservative confidence bands are constructed for the additive autoregression function. The model is fitted to two sets of bivariate quarterly unemployment rate data with comparisons made to the linear periodic vector autoregression model. It is found that when the data does not significantly deviate from linearity, the periodic model is preferred. In cases of strong nonlinearity, however, the additive model is more parsimonious and has much higher out-of-sample prediction power. In addition, interactions among various univariate series are automatically detected.