County level estimates of mean sheet and rill erosion from the Conservation Effects Assessment Project (CEAP) survey are useful for program development and evaluation. As a result of small county sample sizes, small area estimation procedures are needed.One variable that is related to sheet and rill erosion is the quantity of water runoff. The runoff is collected in the CEAP survey but is unavailable for the full population. We use an estimate of mean runoff from the CEAP survey as a covariate in a small area model for sheet and rill erosion. The measurement error in the covariate is important, as is the correlation between the measurement error and the sampling error. We conduct a detailed investigation of small area estimation in the presence of a correlation between the measurement error in the covariate and the sampling error in the response. The proposed methodology has a genuine need in CEAP, where the same survey that supplies the response also provides auxiliary information. In simulations, the proposed predictor is superior to small area predictors that assume the response and covariate are uncorrelated or that ignore the measurement error entirely. We conclude with practical recommendations.

This article focuses on cointegrating regression models in which covariate processes exhibit long range or semi-long range memory behaviors, and may involve endogeneity in which covariate and response error terms are not independent. We assume semilong range memory is produced in the covariate process by tempering of random shock coefficients. The fundamental properties of long memory processes are thus retained in the covariate process. We modify a test statistic proposed for the long memory case by Wang and Phillips (2016) to be suitable in the semi-long range memory setting.The limiting distribution is derived for this modified statistic and shown to depend only on the local memory process of standard Brownian motion. Because, unlike the original statistic of Wang and Phillips (2016), the limit distribution is independent of the differencing parameter of fractional Brownian motion, it is pivotal. Through simulation we investigate properties of nonparametric function estimation for semilong range memory cointegrating models, and consider behavior of both the modified test statistic under semi-long range memory and the original statistic under long range memory. We also provide a brief empirical example.

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Statistical agencies are often asked to produce small area estimates (SAEs) for positively skewed variables. When domain sample sizes are too small to support direct estimators, effects of skewness of the response variable can be large. As such, it is important to appropriately account for the distribution of the response variable given available auxiliary information. Motivated by this issue and in order to stabilize the skewness and achieve normality in the response variable, we propose an area-level logmeasurement error model on the response variable. Then, under our proposed modeling framework, we derive an empirical Bayes (EB) predictor of positive small area quantities subject to the covariates containing measurement error. We propose a corresponding mean squared prediction error (MSPE) of EB predictor using both a jackknife and a bootstrap method. We show that the order of the bias is O(m −1 ), where m is the number of small areas. Finally, we investigate the performance of our methodology using both design-based and model-based simulation studies.

Abstract. Census counts are subject to different types of nonsampling errors. One of these main errors is coverage error. Undercount and overcount are two types of coverage error. Undercount usually occurs more than the other, thus net undercount estimation is important. There are various methods for estimating the coverage error in censuses. One of these methods is dual system (DS) that usually uses data from the census and a postenumeration survey (PES). In this paper, the coverage error and necessity of its evaluation, PES design and DS method are explained. Then PES associated approaches and their effects on DS estimation are illustrated and these approaches are compared. Finally, we explain the Statistical Center of Iran method of estimating net undercount in Iran 2006 population and dwelling census and a suggestion will be given for improving net undercount estimation in population and dwelling censuses of Iran.