Statistical Inferences in a Partially Linear Model with Autoregressive Errors

In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error.Since the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also developed.We derive the asymptotic properties of the related statistics under mild conditions.Some simulations,as well as a real data example,are conducted to illustrate the finite sample performance.

A Unit Root Test for an AR(1)Process with AR Errors by Using Random Weighted Bootstrap

A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap method.It turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with or without an intercept term.The simulation results show that the statistic has a desired finite sample performance in terms of both size and power.A real data application is also given relying on the inflation rate data of 17 countries.

Statistical inference for multivariate longitudinal data with irregular auto-correlated error process

Multivariate longitudinal data arise frequently in a variety of applications,where multiple outcomes are measured repeatedly from the same subject.In this paper,we first propose a two-stage weighted least square estimation procedure for the regression coefficients when the random error follows an irregular autoregressive(AR)process,and establish asymptotic normality properties for the resulting estimators.We then apply the smoothly clipped absolute deviation(SCAD)variable selection approach to determine the order of the AR error process.We further propose a test statistic to check whether multiple responses are correlated at the same observation time,and derive the asymptotic distribution of the proposed test statistic.Several simulated examples and real data analysis are presented to illustrate the finite-sample performance of the proposed method.