Review Of Regression (censored The Regression) Model Parameters, The Semi-parametric And Nonparametric Estimation And Consistency Of The Model Specification Test

In an attempt to balance protect for respondents'privacy and gratification of users'demand for public survey data, many famous microdata survey, such as March Current Population Survey, restrict high income information by top coding. When studying economic behavior underlining medical expenditure by survey data, such as China's Health and Nutrition Survey, we would find a large proportion of zero medical expenditure due to non-negative constraint. To model such two censored phenomena and their mixed type, econometricians usually adopt censored regression model with latent regression. However, even when the same model specification is discussed, the parameters or functions of interest probably vary with the research object.Censored regression has the specific and general model specification relying on the assumptions for distribution function of the error term and latent regression function. This paper derives all the conditional expectation and quantile functions of interest under the specific and general assumptions, and examines the quanlitative and quantitative properties. The relationship between various condtional expectation and quantile functions discussed here base the identification for parameters or functions of interest, and then facilitate the corresponding estimation.For standard censored regression, this paper makes a qualitative comparison between the asymptotic properties of various parametric estimators, and employs Monte Carlo simulation to evaluate their finite-sample performance under standard and non-standard assumptions. It shows in theory and simulation that all parametric estimators are consistent under standard assumptions with MLE estimator performing best in statistical efficiency; however, when the standard assumptions are violated, especially when the error term is heteroskedastic or has a non-normal distribution, all parametric estimators except the method of moments estimators are inconsistent.The weaker model specification of censored regression than the parametric form is semi-parametric censored regression, and this paper investigates the general semi-parametric censored regression with partially linear component and unknown disturbance distribution. Unlike the implementation of quantile restriction to identify and estimate the parameters in linear component of latent regression function by Chen and Khan (2001), we propose semi-parametric estimation by imposing mean restriction, based on the intuition of Lewbel and Linton(2000, 2002)and the estimation method of average derivatives by Li, Lu and Ullah(2003). We take a strict mathematical proof of its asymptotic distribution and conduct a Monte Carlo simulation indicating that this semi-parametic estimator has a highly better small-sample performance than that proposed by Chen and Khan (2001).When the latent regression and the distribution function of the error term are unkown, we have non-parametric censored regression that needs estimating by non-parametric methods. Lewbel and Linton (2000, 2002) examine non-parametric censored regression model with continuous covariates and homokesdatic variance, this paper extends their estimation method to the weaker model specification with continuous and discrete covariates and heteoroskedastic variance. We mathematically derive the asymptotic distribution of the estimated latent regression and its derivatives. A small scale Monte Carlo simulation indicates that the proposed estimator has relatively improved and even superior performance as the sample number increases, though it performs a bit worse than that proposed by Chen and Khan (2002), and what is more, it has superior computational efficiency.Since parametric, semiparametric and nonparametric censored regression estimators only perform best under the corresponding assumed population model specification, we have to test whether this model specification holds to select the suitable estimation method. This paper investigates consistent model specification test of parametric censored regression, single index model and censored quantile regression. The Monte Carlo simulation suggests that the test statistic would underestimate the nominal size using asymptotic standard normal critical values, but it would have more severely distored size with critical values of resampled distribution. In addition, the bandwidth selected by cross-validation works better than that by Rule of Thumb in that it not only reduces the size distortion, but also increases test power.