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.     

Resolving a Multi-Million Dollar Contract Dispute With a Latin Square

The City of New York negotiated a dispute over the performance of new garbage trucks purchased from a vehicle manufacturer. The dispute concerned the fulfillment of a specification in the purchase contract that the trucks load a minimum full-load of 12.5 tons of household refuse. On behalf of the City, but in cooperation with the manufacturer, the City's Department of Sanitation and consulting statisticians tested fulfillment of the contract specification, employing a Latin Square design for routing trucks. We present the classical analysis using a linear model and analysis of variance. We also show how fixed, mixed, and random effect models are useful in analyzing the results of the test. Finally, we take a Bayesian perspective to demonstrate how the information from the data overcomes the difference between the prior densities of the city and the manufacturer for the load capacities of the trucks to result in much closer posterior densities. This procedure might prove useful in similar negotiations. Supplementary material including the data and R code for computations in the article are available online.     

A graphical method for comparing trends in series of events

This paper describes a new graphical method for comparing trends in two or more series of events. The method is applicable,e.g., to observations such as the successive times to failure of two or more devices and the arrival times on succeeding days at a service facility. The graphs provide information about the rela-tive trend and can be used to order several series with respect to rates of occurrence of events. The series are assumed independent of one another and are assumed to follow nonhomogeneous Poisson processes with mean functions and rate functions unspeci-fied.