NZSA Visiting Lecturers

Ray Chambers is Professor of Statistical Methodology at University of Wollongong and has extensive research interests in the design and analysis of sample surveys, official statistics methodology, robust methods for statistical inference and analysis of data with group structure.

Statistics New Zealand hosted Ray Chambers’ visit to New Zealand, and the New Zealand Statistical Association, through its Visiting Lectureship, enabled Ray to visit other New Zealand centres.

A brief preamble to Ray Chambers’ visit was given in Newsletter 67.

Talk Abstracts

Robust Prediction of Small Area Means and Distributions

Small area estimation techniques typically rely on mixed models containing random area effects to characterise between area variability. In contrast, the M-quantile approach to small area estimation avoids conventional Gaussian assumptions and problems associated with specification of random effects and uses M-quantile regression models to characterise small area effects. In this talk I will describe a general framework for robust small area prediction that is based on representing a small area estimator as a functional of a predictor of the within area distribution of the target variable, and is applicable under either a mixed model approach or a M-quantile approach. The usefulness of this framework will be demonstrated through< both model-based as well as design-based simulation, with the latter based on two realistic survey data sets containing small area information. An application to predicting key percentiles of district level distributions of per-capita household consumption expenditure in Albania in 2002 will be described.

Small Area Estimation Via M-quantile Geographically Weighted Regression

Spatially correlated data arise in many situations. When these data are used for small area estimation, a popular approach is to characterise the small area effects using a Simultaneous Autoregressive Regression model. An alternative approach incorporates the spatial information via Geographically Weighted Regression (GWR). In this talk I will describe how the M-quantile approach to small area estimation can be extended to situations where GWR is preferable. An important spin-off from this approach is more efficient synthetic estimation for out of sample areas. The usefulness of this framework will be demonstrated through model-based as well as design-based simulation. An application to predicting average Acid Neutralizing Capacity at 8-digit Hydrologic Unit Code level in the Northeast states of the USA will also be described.

Small Area Estimation Under Transformation To Linearity

Small area estimation based on linear mixed models can be inefficient when the underlying relationships are non-linear. In this talk I will describe small area estimation techniques for variables that can be modelled linearly following a non-linear transformation. In particular, I will show how so-called model-based direct estimation can be used with data that are consistent with a linear mixed model in the logarithmic scale, provided estimation weights are derived using model calibration. Simulation results will be presented which show that this transformation-based estimator is both efficient and robust with respect to the distribution of the random effects in the linear mixed model. An application to business survey data will also be discussed.

Robust Mean Squared Error Estimation for Linear Predictors for Domains

A crucial aspect of small area estimation is estimation of the mean squared error of the resulting small area estimators. In this talk I will discuss robust mean squared error estimation for linear predictors of finite population domain means. The approach that will be taken represents an extension of the well known ‘sandwich’ type variance estimator used in population level sample survey inference, and appears to lead to a mean squared error estimator that is simpler to implement, and potentially more robust, than alternatives suggested in the small area literature. The usefulness of this approach will be demonstrated through both model-based as well as design-based simulation, with the latter based on two realistic survey data sets containing small area information.

Measurement Error in Auxiliary Information

Auxiliary information is information about the target population of a sample survey over and above that contained in the actual data obtained from the sampled population units. The availability of this type of information represents a key distinction between sample survey inference and more mainstream inference scenarios. In particular, modern methods of sampling inference (both model-assisted as well as model-based) depend on the availability of auxiliary information to improve efficiency in survey estimation. However, such information is not always of high quality, and typically contains errors. In this talk I focus on some survey-based situations where auxiliary information is crucial, but where this information is not precise. Estimation methods that allow for this imprecision will be described. In doing so I will not only address the types of inference of concern to sampling statisticians (e.g. prediction of population quantities), but also inference for parameters of statistical models for surveyed populations.

Maximum Likelihood With Auxiliary Information

In this talk I use a general framework for maximum likelihood estimation with complex survey data to develop methods for efficiently incorporating external population information into linear and logistic regression models fitted via sample survey data. In particular, saddlepoint and smearing methods will be used to derive highly accurate approximations to the score and information functions defined by the model parameters under random sampling and under case-control sampling when auxiliary data on population moments are available. Simulation-based results illustrating the resulting gains in efficiency will also be discussed.

Analysis of Probability-Linked Data

Over the last 25 years, advances in information technology have led to the creation of linked individual level databases containing vast amounts of information relevant to research in health, epidemiology, economics, demography, sociology and many other scientific areas. In many cases this linking is not perfect but can be modelled as the outcome of a stochastic process, with a non-zero probability that a unit record in the linked database is actually based on data drawn from distinct individuals. The impact of the resulting linkage errors on analysis of data extracted from such a source is only slowly being appreciated. In this talk I will describe a framework for statistical analysis of such probability-linked data. Applications to linear and logistic regression modelling of this type of data will be discussed.

Estimation of the Finite Population Distribution Function

Although most survey outputs consist of estimates of means and totals, there are important situations where the primary focus is estimation of the finite population distribution function, defined as the proportion of population units with values less than or equal to the argument of this function. In this talk I will describe design-based, model-assisted and model-based methods for predicting a finite population distribution function, focussing on a situation where the underlying regression relationship is non-linear. An application to estimation of the distribution of hourly pay rates will be discussed in some detail.

Maximum Likelihood under Informative Sampling

Loosely speaking, a sampling method is informative if the random variable corresponding to the outcome of the sampling process and the random variable corresponding to the response that is of interest are correlated in some way. An examples of informative sampling is size-biased sampling. In this talk I describe a general framework for likelihood-based inference with sample survey data, including data collected via informative sampling. Some simple examples will then be used to contrast maximum likelihood estimation within this framework with alternative likelihood-based approaches that have been suggested for data collected under informative sampling.