Nonsampling errors in surveys - a review

Response errors have become extremely important in increasingly complex surveys and a review of the ever expanding literature on the subject was judged necessary. The emphasis here is on models for response and nonresponse errors the most recent ones incorporating the concept of response probabilities.     

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.     

Nonparametric standard errors and confidence intervals

We investigate several nonparametric methods; the bootstrap, the jackknife, the delta method, and other related techniques. The first and simplest goal is the assignment of nonparametric standard errors to a real-valued statistic. More ambitiously, we consider setting nonparametric confidence intervals for a real-valued parameter. Building on the well understood case of confidence intervals for the median, some hopeful evidence is presented that such a theory may be possible.     

Ratio and product methods of estimation of population mean in the presence of correlated measurement errors

The properties of the estimators of population mean arising from the ratio and product methods of estimation in the context of sample surveys have been analyzed in this paper when the observations on both the study and auxiliary variables are contaminated with measurement errors. The measurement errors in both the variables are also correlated. The properties of the ratio and product estimators along with the sample mean under the influence of measurement errors are derived and studied. The properties of the estimators in finite samples are studied through Monte-Carlo simulation and its findings are reported.     

Considerations for optimal nonparametric regression under a generalizederror structure

Nonparametric smoothing, such as kernel or spline estimation, has been examined extensively under the assumption of uncorrelated errors. This paper addresses the effects of potential correlation on consistency and other asymptotic properties in a repeated-measures model, using directly optimized linear smoothers of the replicate means. Unrestricted optimal weights, with respect to squared error loss, are used to confirm a lack of consistency for all linear estimators in an autocorrelated errors model. The results indicate kernel methods that work well for an uncorrelated errors model may not have the ability to perform satisfactorily when correlation is introduced, due to an asymmetry in the optimal weights, which disappears for an uncorrelated errors model. These would include data-driven bandwidth selection methods, adjustments of the bandwidth to accommodate correlation, higher-order kernels, and related bias reduction techniques. The analytic results suggest alternative approaches, not considered here in detail, which have shown merit.     

Alternative mean-squared error estimators for synthetic estimators of domain means

In forest management surveys, the mean of a variable of interest (Y) in a population composed of N equal area spatial compact elements is increasingly estimated from a model linking Y to an auxiliary vector X known for all elements in the population. It is also desired to have synthetic estimates of the mean of Y in spatially compact domains (forest stands) with no or at most one sample-based observation of Y. We develop three alternative estimators of mean-squared errors (MSE) that reduce the risk of a serious underestimation of the uncertainty in a synthetic estimate of a domain mean in cases where the employed model does not accounts for domain effects nor spatial autocorrelation in unobserved residual errors. Expansions of the estimators including anticipated effects of a spatial autocorrelation in residual errors are also provided. Simulation results indicate that the conventional model-dependent (MD) population-level estimator of variance in a synthetic estimate of a domain mean underestimates uncertainty by a wide margin. Our alternative estimators mitigated, in settings with weak to moderate domain effects and relatively small sample sizes, to a large extent, the problem of underestimating uncertainty. We demonstrate applications with examples from two actual forest inventories.     

A Bayesian model for measurement and misclassification errors alongside missing data,with an application to higher education participation in Australia

In this paper we consider the impact of both missing data and measurement errors on a longitudinal analysis of participation in higher education in Australia. We develop a general method for handling both discrete and continuous measurement errors that also allows for the incorporation of missing values and random effects in both binary and continuous response multilevel models. Measurement errors are allowed to be mutually dependent and their distribution may depend on further covariates. We show that our methodology works via two simple simulation studies. We then consider the impact of our measurement error assumptions on the analysis of the real data set.     

The non parametric regression estimate with dependent measurement errors

ABSTRACT

Non parametric regression estimation with measurement errors data has received great attention, and deconvolution local polynomial estimators can be used to deal with the problem that the errors are independent of other variables in the literature. In this article, the copula method is applied to tackle the case that the errors may depend on covariates, and the asymptotic properties of the resulting estimators are derived. Two simulations are conducted to illustrate the performance of the proposed estimators.     

Performance of Wald-type estimator for parametric component in partial linear regression with a mixture of Berkson and classical error models

This article discusses a consistent and almost unbiased estimation approach in partial linear regression for parameters of interest when the regressors are contaminated with a mixture of Berkson and classical errors. Advantages of the presented procedure are: (1) random errors and observations are not necessarily to be parametric settings; (2) there is no need to use additional sample information, and to consider the estimation of nuisance parameters. We will examine the performance of our presented estimate in a variety of numerical examples through Monte Carlo simulation. The proposed approach is also illustrated in the analysis of an air pollution data.     

On the Strong Consistency of M‐Estimates in Linear Models for Negatively Superadditive Dependent Errors

In this paper we discuss the strong consistency of M‐estimates of the regression parameters in a linear model with negatively superadditive dependent (NSD) random errors. The result improves the moment condition and generalises the case of independent random errors to that of NSD random errors.     

Effects of non-normality on the power function in a one-way random model

The effects of non-normality on type-I and type-II errors in a one-way random model are investigated for moderate departures from normality. It is found that the probabilities of both errors are more sensitive to the kurtosis of between group effects than that of within group effects.     

Bias of S 2 in Linear Regressions with Dependent Errors

Bounds are given for the expected value of the estimator of the error variance in linear regressions, when the errors are dependent or heteroscedastic. The bounds are valid irrespective of the covariance structure between the errors. Necessary and sufficient conditions to attain the bounds are supplied.     

The impact of integrated measurement errors on modeling long-run macroeconomic time series

ABSTRACT

Data spanning long time periods, such as that over 1860–2012 for the UK, seem likely to have substantial errors of measurement that may even be integrated of order one, but which are probably cointegrated for cognate variables. We analyze and simulate the impacts of such measurement errors on parameter estimates and tests in a bivariate cointegrated system with trends and location shifts which reflect the many major turbulent events that have occurred historically. When trends or shifts therein are large, cointegration analysis is not much affected by such measurement errors, leading to conventional stationary attenuation biases dependent on the measurement error variance, unlike the outcome when there are no offsetting shifts or trends.     

Geometric View of Measurement Errors

The slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of various slope estimators for the measurement error model including an adjusted fourth moment estimator introduced by Gillard and Iles (2005 Gillard , J. , Iles , T. ( 2005 ). Method of moments estimation in linear regression with errors in both variables, Cardiff University School of Mathematics Technical Report, Cardiff, Wales, UK . [Google Scholar]) to remove the jump discontinuity in the estimator of Copas (1972 Copas , J. ( 1972 ). The likelihood surface in the linear functional relationship problem . Journal of the Royal Statistical Society. Series B (Methodological) 34 : 274 – 278 . [Google Scholar]). The polynomial of degree four is associated with a minimun deviation estimator. A simulation study compares these estimators showing improvement in bias and mean squared error.     

Bootstrapping a time series model: some empirical results

The bootstrap is a methodology for estimating standard errors. The idea is to use a Monte Carlo simulation experiment based on a nonparametric estimate of the error distribution. The main objective of this article is to demonstrate the use of the bootstrap to attach standard errors to coefficient estimates in a second-order autoregressive model fitted by least squares and maximum likelihood estimation. Additionally, a comparison of the bootstrap and the conventional methodology is made. As it turns out, the conventional asymptotic formulae (both the least squares and maximum likelihood estimates) for estimating standard errors appear to overestimate the true standard errors. But there are two problems:i. The first two observations y₁ and y₂ have been fixed, and ii. The residuals have not been inflated. After these two factors are considered in the trial and bootstrap experiment, both the conventional maximum likelihood and bootstrap estimates of the standard errors appear to be performing quite well.     

Analysis of mixed outcomes: misclassified binary responses and measurement error in covariates

This paper considers regression models for mixed binary and continuous outcomes, when the true predictor is measured with error and the binary responses are subject to classification errors. The focus of the paper is to study the effects of these errors on the estimates of the model parameters and also to propose a model that incorporates both these errors. The proposed model results in a substantial improvement in the estimates as shown by extensive simulation studies.     

A Simple Estimator of Error Correlation in Non-parametric Regression Models

Abstract.  It is well known that major strength of non-parametric regression function estimation breaks down when correlated errors exist in the data. Positively (negatively) correlated errors tend to produce undersmoothing (oversmoothing). Several remedies have been proposed in the context of bandwidth selection problem, but they are hard to implement without prior knowledge of error correlations. In this paper we propose a simple estimator of error correlation which is ready to implement and reports a reasonably good performance.     

Minimum distance estimation in linear regression with strong mixing errors

Abstract

Minimum distance estimation on the linear regression model with independent errors is known to yield an efficient and robust estimator. We extend the method to the model with strong mixing errors and obtain an estimator of the vector of the regression parameters. The goal of this article is to demonstrate the proposed estimator still retains efficiency and robustness. To that end, this article investigates asymptotic distributional properties of the proposed estimator and compares it with other estimators. The efficiency and the robustness of the proposed estimator are empirically shown, and its superiority over the other estimators is established.     

Prediction Performance of Correlated Error Procedures for Spatial Counts

Abstract

Few guidelines exist for the application of geostatistical methods to spatial counts and the prediction to unsampled areas is an important aspect of experimental field research. The prediction performances of kriging and a correlated errors Poisson model are compared through simulation. Counts with a known spatial covariance structure are generated in an investigation involving several factors: area size, overall mean, range of correlation, spatial covariance function, and the presence of trend. The correlated errors Poisson model generally gives superior prediction performance when an exponential covariance structure is used.     

The effects of data input errors on subsequent statistical inference

Data input errors can potentially affect statistical inferences, but little research has been published to date on this topic. In the present paper, we report the effect of data input errors on the statistical inferences drawn about population parameters in an empirical study involving 280 students from two Polish universities, namely the Warsaw University of Life Sciences – SGGW and the University of Information Technology and Management in Rzeszow. We found that 28% of the students committed at least one data error. While some of these errors were small and did not have any real effect, a few of them had substantial effects on the statistical inferences drawn about the population parameters.