Testing heteroskedasticity in predictive regression.• Specification test for testing constancy of conditional variance when regressor is nonstationary.• Heteroskedasticity exists for predictive regression of stock return with dividend-price ratio and earning price ratio as the predictors.

In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this difficulty and propose a unifying inference procedure for the coefficients. To be specific, we propose a profile weighted estimation equation method that facilitates the unifying inference. The proposed method is applied to the predictive regressions of stock returns, and an empirical likelihood procedure is developed to test the predictability. It is shown that the Wilks theorem holds for the empirical likelihood ratio regardless of predictors being stationary or not, which provides a unifying method for constructing confidence regions of the coefficients of state variables. Simulations show that the proposed method works well and has favorable finite sample performance over some existing approaches. An empirical application examining the predictability of equity returns highlights the value of our methodology.

We study the identification and estimation of graphical models with nonignorable nonresponse. An observable variable correlated to nonresponse is added to identify the mean of response for the unidentifiable model. An approach to estimating the marginal mean of response is proposed, based on simulation imputation methods which are introduced for a variety of models including linear, generalized linear, and monotone nonlinear models. The proposed mean estimators are N -consistent, where N is the sample size. Finite sample simulations confirm the effectiveness of the proposed method. Sensitivity analysis for the untestable assumption on our augmented model is also conducted. A real data example is employed to illustrate the use of the proposed methodology.

In this paper, we develop statistical inference for an important health inequality index proposed by Lv, Wang and Xu [1] for ordinal data. Asymptotic distributions of the indices are established. This allows us to make inference for the indices. Generalizations of the indices to multiple population setting are also studied. We demonstrate the effectiveness of our procedure using the health inequality data of several areas in Switzerland, and our results classify these areas into three classes based on their health inequalities.