An explanation of generalized profile likelihoods

Let X, T, Y be random vectors such that the distribution of Y conditional on covariates partitioned into the vectors X = x and T = t is given by f(y; x, ), where = (, (t)). Here is a parameter vector and (t) is a smooth, real–valued function of t. The joint distribution of X and T is assumed to be independent of and . This semiparametric model is called conditionally parametric because the conditional distribution f(y; x, ) of Y given X = x, T = t is parameterized by a finite dimensional parameter = (, (t)). Severini and Wong (1992. Annals of Statistics 20: 1768–1802) show how to estimate and (·) using generalized profile likelihoods, and they also provide a review of the literature on generalized profile likelihoods. Under specified regularity conditions, they derive an asymptotically efficient estimator of and a uniformly consistent estimator of (·). The purpose of this paper is to provide a short tutorial for this method of estimation under a likelihood–based model, reviewing results from Stein (1956. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley, pp. 187–196), Severini (1987. Ph.D Thesis, The University of Chicago, Department of Statistics, Chicago, Illinois), and Severini and Wong (op. cit.).     

Nonlinearity testing and modeling for threshold moving average models

In this paper, we suggest a simple test and an easily applicable modeling procedure for threshold moving average (TMA) models. Firstly, based on the fitted residuals by maximum likelihood estimate (MLE) for MA models, we construct a simple statistic, which is obtained by linear arrange regression and follows F-distribution approximately, to test for threshold nonlinearity and specify the threshold variables. And then, we use some scatterplots to identify the number and locations of the potential thresholds. Finally, with the statistic and Akaike information criterion, we propose the procedure to build TMA models. Both the power of test statistic and the convenience of modeling procedure can work very well demonstrated by simulation experiments and the application to a real example.     

Centered-Residuals-Based Moment Estimator and Test for Stochastic Frontier Models

The composed error of a stochastic frontier (SF) model consists of two random variables, and the identification of the model relies heavily on the distribution assumptions for each of these variables. While the literature has put much effort into applying various SF models to a wide range of empirical problems, little has been done to test the distribution assumptions of these two variables. In this article, by exploiting the specification structures of the SF model, we propose a centered-residuals-based method of moments which can be easily and flexibly applied to testing the distribution assumptions on both of the random variables and to estimating the model parameters. A Monte Carlo simulation is conducted to assess the performance of the proposed method. We also provide two empirical examples to demonstrate the use of the proposed estimator and test using real data.