Calibration for Randomized Response Estimators

In the present article, we consider the calibration procedure for the Warner's and Mangat–Singh's (:M–S) randomized response survey estimators using auxiliary information associated with the variable of interest. In the calibration procedure, we can use auxiliary information such as age, gender, and income for the respondents of RR questions from an external source, and then the classical RR estimators can be improved with respect to the problems of noncoverage or nonresponse. From the efficiency comparison study, we show that the calibration estimators are more efficient than those of Warner's and Mangat-Singh's when the known population cell and marginal counts of auxiliary information are used for the calibration procedure.     

How Do Nonlinear Unit Root Tests Perform with Non Normal Errors?

This article examines how popular nonlinear unit root tests perform in the presence of non normal errors. Non normal errors normally do not pose a problem in the usual linear unit root tests since the least squares estimator will still be the most efficient under certain ideal conditions regardless of normal or non normal errors. Whether similar results will carry over to nonlinear unit root tests with non normal errors is a question that merits examination. We find that in contrast to the linear tests, the presence of non normal errors in nonlinear unit root tests will lead to a significant loss of power.     

A residual-based test for autocorrelation in quantile regression models

Quantile regression (QR) models have been increasingly employed in many applied areas in economics. At the early stage, applications in the QR literature have usually used cross-sectional data, but the recent development has seen an increase in the use of QR in both time-series and panel data sets. However, testing for possible autocorrelation, especially in the context of time-series models, has received little attention. As a rule of thumb, one might attempt to apply the usual Breusch–Godfrey LM test to the residuals of a baseline QR. In this paper, we demonstrate analytically and by Monte Carlo simulations that such an application of the LM test can result in potentially large size distortions, especially in either low or high quantiles. We then propose a correct test (named the QF test) for autocorrelation in QR models, which does not suffer from size distortion. Monte Carlo simulations demonstrate that the proposed test performs fairly well in finite samples, across either different quantiles or different underlying error distributions.     

Parameter change test for zero-inflated generalized Poisson autoregressive models

In this paper, we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Based on these results, we construct CMLE- and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. The simulation results are provided for illustration. A real data analysis is performed on some crime data of Australia.     

Performance of threshold cointegration tests

In this paper, we examine and compare the performance of ordinary least squares (OLS) and instrumental variables (IVs) based single-equation Engle–Granger, error correction model (ECM), and autoregressive-distributed lag (ADL) threshold cointegration tests. Results are additionally compared with the system-equation OLS–ECM test. Finite sample properties of size and power are examined in simulations. The single-equation ECM test performs well, but has certain limitations to resolve. The system-equation ECM test has good power, but suffers from mild size distortions that lead to over-rejections. Overall, the single-equation OLS–ADL test has the most desirable properties among the OLS-based tests and the IV–ADL test has the most desirable properties among the IV-based tests. The IV-based tests are invariant to nuisance parameters and have a standard normal distribution in each case, while the OLS-based tests are non-standard so that critical values must be simulated in different models.     

On the consistency of rank transformed regression

Rank-transformed regression (RTR) was proposed by Iman and Conover (1979) as an alternative to isotonic regression. This paper studies the consistency of the estimate obtained by RTR and show that, in general case, the estimate is not mean-square-error (MSE) consistent. The bias of the estimate is also studied by simulation.     

On two-step estimation for varying coefficient models

In this note we discuss two-step kernel estimation of varying coefficient regression models that have a common smoothing variable. The method allows one to use different bandwidths for different coefficient functions. We consider local polynomial fitting and present explicit formulas for the asymptotic biases and variances of the estimators.     

Logistic regression analysis of randomized response data with missing covariates

Randomized response is an interview technique designed to eliminate response bias when sensitive questions are asked. In this paper, we present a logistic regression model on randomized response data when the covariates on some subjects are missing at random. In particular, we propose Horvitz and Thompson (1952)-type weighted estimators by using different estimates of the selection probabilities. We present large sample theory for the proposed estimators and show that they are more efficient than the estimator using the true selection probabilities. Simulation results support theoretical analysis. We also illustrate the approach using data from a survey of cable TV.     

Exponentiated-exponential geometric regression model

A regression model, based on the exponentiated-exponential geometric distribution, is defined and studied. The regression model can be applied to count data with under-dispersion or over-dispersion. Some forms of its modifications to truncated or inflated data are mentioned. Some tests to discriminate between the regression model and its competitors are discussed. Real numerical data sets are used to illustrate the applications of the regression model.