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The observed best predictor (OBP) has been recently offered as a more robust alternative to the remarkable empirical best linear unbiased predictor (EBLUP). Although the latter has become a pervasive tool among applied statisticians, there are critical reasons why the OBP should almost always be used in conjunction with the EBLUP. In particular, mathematical models are often oversimplified or misspecified, lacking key predictors within the available set of data. For more complex models such as time-series applications, model robustness becomes even more imperative. We will provide some results related to the OBP theory and introduce a generalized, or weighted version of the OBP for different loss functions. This will first be defined on the Fay-Herriot model and then extended to the General Linear Mixed model. Finally, we will apply the best predictive estimator (BPE) to both parameter coefficients and variance parameters within the Fay-Herriot and cross-sectional time series models. Model building strategies abound, and have continued to evolve. These are instrumental for applied statisticians and analysts passing judgement on whether statistical models are suitable for drawing conclusions or producing official estimates. A number of methodologies and approaches have been developed to consider this critical question of model selection and diagnostics. We endeavor to view this problem from the perspective of empirical Bayes (EB) - in a similar fashion as the EBLUP. As such, we define and develop an EB parametric bootstrap approach not only to estimate mean squared error, but also for finding the best model from a set of candidates (e.g., variable selection). This could be done for general criteria by considering leave-one-out predictive distributions. Once a viable model is selected, we can continue the model-building process by performing appropriate validation. Thus, the method is not only versatile, but has some computational advantages over other model building

© IWA Publishing 2020. Because of the static nature of conventional principal component analysis (PCA), natural process variations may be interpreted as faults when it is applied to processes with time-varying behavior. In this paper, therefore, we propose a complete adaptive process monitoring framework based on incremental principal component analysis (IPCA). This framework updates the eigenspace by incrementing new data to the PCA at a low computational cost. Moreover, the contribution of variables is recursively provided using complete decomposition contribution (CDC). To impute missing values, the empirical best linear unbiased prediction (EBLUP) method is incorporated into this framework. The effectiveness of this framework is evaluated using benchmark simulation model No. 2 (BSM2). Our simulation results show the ability of the proposed approach to distinguish between time-varying behavior and faulty events while correctly isolating the sensor faults even when these faults are relatively small.

This thesis develops and evaluates Small Area Estimation (SAE) methods to provide estimates of prevalence rates of health risk factors for Local Government Areas (LGAs) in NSW using data from the NSW Population Health Survey. All outcome variables considered are dichotomous. The aim is to produce estimates that are an improvement over direct survey estimates based on a single year of data as well as over direct estimates based on data aggregated over seven years. Modified direct estimators, conventional synthetic and composite estimators, Empirical Best Linear Unbiased Predictors (EBLUP), complex synthetic estimators using a linear model, Empirical Best Predictors (EBP) and associated synthetic estimators based on the logistic model are assessed initially for the outcome variable ‘Current Smoking’ using 2006 survey data. All estimates are produced using SAS Version 9.2. Model-based SAE methods using regression models and area level random effects are found to be the most effective approach to create unbiased LGA-level estimates for ‘Current Smoking’, and are successful in creating estimates with face-validity when based on a single year of data. Of the other methods assessed neither LGA-based weighting nor generalised regression (GREG) estimates are shown to improve the direct LGA-level estimates sufficiently for them to be more useful than the current direct estimates. Conventional synthetic and composite estimators produce over-smoothed LGA-level estimates. In addition the n¨aive estimates of the mean square error (MSE) of these estimators underestimate the bias, and estimation of the root mean square error (RMSE) is difficult. The EBLUP and EBP estimates and their associated synthetic counterparts are created and evaluated for four key outcome variables (‘Current Smoking’, ‘Risk Alcohol Consumption’, ‘Overweight or obese’ and ‘Have difficulties getting health care when needed’), by sex, for survey years 2006, 2007 and 2008. These outcome variables differ in their

This thesis develops and evaluates Small Area Estimation (SAE) methods to provide estimates of prevalence rates of health risk factors for Local Government Areas (LGAs) in NSW using data from the NSW Population Health Survey. All outcome variables considered are dichotomous. The aim is to produce estimates that are an improvement over direct survey estimates based on a single year of data as well as over direct estimates based on data aggregated over seven years. Modified direct estimators, conventional synthetic and composite estimators, Empirical Best Linear Unbiased Predictors (EBLUP), complex synthetic estimators using a linear model, Empirical Best Predictors (EBP) and associated synthetic estimators based on the logistic model are assessed initially for the outcome variable ‘Current Smoking’ using 2006 survey data. All estimates are produced using SAS Version 9.2. Model-based SAE methods using regression models and area level random effects are found to be the most effective approach to create unbiased LGA-level estimates for ‘Current Smoking’, and are successful in creating estimates with face-validity when based on a single year of data. Of the other methods assessed neither LGA-based weighting nor generalised regression (GREG) estimates are shown to improve the direct LGA-level estimates sufficiently for them to be more useful than the current direct estimates. Conventional synthetic and composite estimators produce over-smoothed LGA-level estimates. In addition the n¨aive estimates of the mean square error (MSE) of these estimators underestimate the bias, and estimation of the root mean square error (RMSE) is difficult. The EBLUP and EBP estimates and their associated synthetic counterparts are created and evaluated for four key outcome variables (‘Current Smoking’, ‘Risk Alcohol Consumption’, ‘Overweight or obese’ and ‘Have difficulties getting health care when needed’), by sex, for survey years 2006, 2007 and 2008. These outcome variables differ in their

This thesis develops and evaluates Small Area Estimation (SAE) methods to provide estimates of prevalence rates of health risk factors for Local Government Areas (LGAs) in NSW using data from the NSW Population Health Survey. All outcome variables considered are dichotomous. The aim is to produce estimates that are an improvement over direct survey estimates based on a single year of data as well as over direct estimates based on data aggregated over seven years. Modified direct estimators, conventional synthetic and composite estimators, Empirical Best Linear Unbiased Predictors (EBLUP), complex synthetic estimators using a linear model, Empirical Best Predictors (EBP) and associated synthetic estimators based on the logistic model are assessed initially for the outcome variable ‘Current Smoking’ using 2006 survey data. All estimates are produced using SAS Version 9.2. Model-based SAE methods using regression models and area level random effects are found to be the most effective approach to create unbiased LGA-level estimates for ‘Current Smoking’, and are successful in creating estimates with face-validity when based on a single year of data. Of the other methods assessed neither LGA-based weighting nor generalised regression (GREG) estimates are shown to improve the direct LGA-level estimates sufficiently for them to be more useful than the current direct estimates. Conventional synthetic and composite estimators produce over-smoothed LGA-level estimates. In addition the n¨aive estimates of the mean square error (MSE) of these estimators underestimate the bias, and estimation of the root mean square error (RMSE) is difficult. The EBLUP and EBP estimates and their associated synthetic counterparts are created and evaluated for four key outcome variables (‘Current Smoking’, ‘Risk Alcohol Consumption’, ‘Overweight or obese’ and ‘Have difficulties getting health care when needed’), by sex, for survey years 2006, 2007 and 2008. These outcome variables differ in their

Many different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable estimates for small domains. Often, the required data for various research purposes are available at different levels of aggregation. Based on the available data, individual-level or aggregated-level models are used in SAE. If unit-level data are available, SAE is usually based on models formulated at the unit level but they are ultimately used to produce estimates at the area level. However, parameter estimates obtained from individual and aggregated level analysis may be different in practice. Individual-level analysis usually results in small area estimates with smaller variances. However, if the unit-level working model is misspecified by exclusion of important auxiliary variables, parameter estimates obtained from the individual and aggregated level analysis will have different expectations. This thesis investigates the circumstances when using an area-level model may be more effective. This may happen due to some substantial contextual or area-level effects in the covariates which may be misspecified in an individual-level model. Ignoring these contextual effects leads to biased estimates. In particular, if an existing contextual variable is ignored, the parameter estimates calculated from an individual-level analysis will be biased, whereas an aggregated-level analysis can lead to small area estimates with less bias. Even if contextual variables are included in unit-level modeling, there may be an increase in the variance of parameter estimates due to increased number of variables in the working model. In this thesis, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are evaluated in SAE based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual effects is examined for models used in SAE.

Many different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable estimates for small domains. Often, the required data for various research purposes are available at different levels of aggregation. Based on the available data, individual-level or aggregated-level models are used in SAE. If unit-level data are available, SAE is usually based on models formulated at the unit level but they are ultimately used to produce estimates at the area level. However, parameter estimates obtained from individual and aggregated level analysis may be different in practice. Individual-level analysis usually results in small area estimates with smaller variances. However, if the unit-level working model is misspecified by exclusion of important auxiliary variables, parameter estimates obtained from the individual and aggregated level analysis will have different expectations. This thesis investigates the circumstances when using an area-level model may be more effective. This may happen due to some substantial contextual or area-level effects in the covariates which may be misspecified in an individual-level model. Ignoring these contextual effects leads to biased estimates. In particular, if an existing contextual variable is ignored, the parameter estimates calculated from an individual-level analysis will be biased, whereas an aggregated-level analysis can lead to small area estimates with less bias. Even if contextual variables are included in unit-level modeling, there may be an increase in the variance of parameter estimates due to increased number of variables in the working model. In this thesis, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are evaluated in SAE based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual effects is examined for models used in SAE.

Many different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable estimates for small domains. Often, the required data for various research purposes are available at different levels of aggregation. Based on the available data, individual-level or aggregated-level models are used in SAE. If unit-level data are available, SAE is usually based on models formulated at the unit level but they are ultimately used to produce estimates at the area level. However, parameter estimates obtained from individual and aggregated level analysis may be different in practice. Individual-level analysis usually results in small area estimates with smaller variances. However, if the unit-level working model is misspecified by exclusion of important auxiliary variables, parameter estimates obtained from the individual and aggregated level analysis will have different expectations. This thesis investigates the circumstances when using an area-level model may be more effective. This may happen due to some substantial contextual or area-level effects in the covariates which may be misspecified in an individual-level model. Ignoring these contextual effects leads to biased estimates. In particular, if an existing contextual variable is ignored, the parameter estimates calculated from an individual-level analysis will be biased, whereas an aggregated-level analysis can lead to small area estimates with less bias. Even if contextual variables are included in unit-level modeling, there may be an increase in the variance of parameter estimates due to increased number of variables in the working model. In this thesis, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are evaluated in SAE based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual effects is examined for models used in SAE.

Outliers are a well-known problem in survey estimation, and a variety of approaches have been suggested for dealing with them in this context. However, when the focus is on small area estimation using the survey data, much less is known – even though outliers within a small area sample are clearly much more influential than they are in the larger overall sample. To the best of our knowledge, Chambers and Tzavidis (2006) was the first published paper in small area estimation that explicitly addressed the issue of outlier robustness, using an approach based on fitting outlier robust M-quantile models to the survey data. Recently, Sinha and Rao (2009) have also addressed this issue from the perspective of linear mixed models. Both these approaches, however, use plug-in robust prediction. That is, they replace parameter estimates in optimal, but outlier sensitive, predictors by outlier robust versions. Unfortunately, this approach may involve an unacceptable prediction bias (but a low prediction variance) in situations where the outliers are drawn from a distribution that has a different mean to the rest of the survey data (Chambers, 1986), which then leads to the suggestion that outlier robust prediction should include an additional term that makes a correction for this bias. In this paper, we explore the extension of this idea to the small area estimation situation and we propose two different analytical mean squared error (MSE) estimators for outlier robust predictors of small area means. We use simulation based on realistic outlier contaminated data to evaluate how the extended small area estimation approach compares with the plug-in robust methods described earlier. The empirical results show that the biascorrected predictive estimators are less biased than the projective estimators especially when there are outliers in the area effects. Moreover, in the simulation experiments we contrast the proposed MSE estimators with those generally utilized for the plug-in rob

Outliers are a well-known problem in survey estimation, and a variety of approaches have been suggested for dealing with them in this context. However, when the focus is on small area estimation using the survey data, much less is known – even though outliers within a small area sample are clearly much more influential than they are in the larger overall sample. To the best of our knowledge, Chambers and Tzavidis (2006) was the first published paper in small area estimation that explicitly addressed the issue of outlier robustness, using an approach based on fitting outlier robust M-quantile models to the survey data. Recently, Sinha and Rao (2009) have also addressed this issue from the perspective of linear mixed models. Both these approaches, however, use plug-in robust prediction. That is, they replace parameter estimates in optimal, but outlier sensitive, predictors by outlier robust versions. Unfortunately, this approach may involve an unacceptable prediction bias (but a low prediction variance) in situations where the outliers are drawn from a distribution that has a different mean to the rest of the survey data (Chambers, 1986), which then leads to the suggestion that outlier robust prediction should include an additional term that makes a correction for this bias. In this paper, we explore the extension of this idea to the small area estimation situation and we propose two different analytical mean squared error (MSE) estimators for outlier robust predictors of small area means. We use simulation based on realistic outlier contaminated data to evaluate how the extended small area estimation approach compares with the plug-in robust methods described earlier. The empirical results show that the biascorrected predictive estimators are less biased than the projective estimators especially when there are outliers in the area effects. Moreover, in the simulation experiments we contrast the proposed MSE estimators with those generally utilized for the plug-in rob

Unbiased direct estimators for small area quantities are usually considered too variable to be of any practical use. In this paper we propose a class of model-based direct estimators for small area quantities that appears to overcome this objection, in the sense that these estimators are comparable in efficiency to the indirect model-based small area estimators (e.g. empirical best linear unbiased predictors, or EBLUPs) that are now widely used. There are many practical advantages associated with such model-based direct (MBD) estimators, arising from the fact that they are computed as weighted linear combinations of the actual sample data from the small areas of interest. Note that in this case the weights ‘borrow strength’ via a model that explicitly allows for small area effects. One particular advantage that we explore in this paper is that estimation of mean squared error (MSE) is then straightforward, using well-known methods that are in common use for population level estimates. Empirical results reported in this paper show that the MBD estimator represents a real alternative to the EBLUP, with the simple MSE estimator associated with the MBD estimator providing good coverage performance. We also report results that indicate that the MBD estimator may be more robust than the EBLUP when the small area model is incorrectly specified. Furthermore, the MBD approach is easily extended to provide multi-purpose weights that are efficient across a range of variables, including variables that are unsuitable for EBLUP, e.g. variables that contain a significant proportion of zeros.

Sample surveys are generally multivariate, in the sense that they collect data on more than one response variable. In theory, each variable can then be assigned an optimal weight for estimation purposes. However, it is a distinct practical advantage to have a single weight for all variables collected in the survey. This paper describes how such multipurpose sample weights can be constructed when small area estimates of the survey variables are required. The approach is based on the model-based direct (MBD) method of small area estimation described in Chambers and Chandra (2006). Empirical results reported in this paper show that MBD estimators for small areas based on multipurpose weights perform well across a range of variables that are often of interest in business surveys. Furthermore, these results show that the proposed approach is robust to model misspecification and also efficient when used with variables that are not suited to standard methods of small area estimation (e.g. variables that contain a significant proportion of zeros).

Unbiased direct estimators for small area quantities are usually considered too variable to be of any practical use. In this paper we propose a class of model-based direct estimators for small area quantities that appears to overcome this objection, in the sense that these estimators are comparable in efficiency to the indirect model-based small area estimators (e.g. empirical best linear unbiased predictors, or EBLUPs) that are now widely used. There are many practical advantages associated with such model-based direct (MBD) estimators, arising from the fact that they are computed as weighted linear combinations of the actual sample data from the small areas of interest. Note that in this case the weights ‘borrow strength’ via a model that explicitly allows for small area effects. One particular advantage that we explore in this paper is that estimation of mean squared error (MSE) is then straightforward, using well-known methods that are in common use for population level estimates. Empirical results reported in this paper show that the MBD estimator represents a real alternative to the EBLUP, with the simple MSE estimator associated with the MBD estimator providing good coverage performance. We also report results that indicate that the MBD estimator may be more robust than the EBLUP when the small area model is incorrectly specified. Furthermore, the MBD approach is easily extended to provide multi-purpose weights that are efficient across a range of variables, including variables that are unsuitable for EBLUP, e.g. variables that contain a significant proportion of zeros.

Sample surveys are generally multivariate, in the sense that they collect data on more than one response variable. In theory, each variable can then be assigned an optimal weight for estimation purposes. However, it is a distinct practical advantage to have a single weight for all variables collected in the survey. This paper describes how such multipurpose sample weights can be constructed when small area estimates of the survey variables are required. The approach is based on the model-based direct (MBD) method of small area estimation described in Chambers and Chandra (2006). Empirical results reported in this paper show that MBD estimators for small areas based on multipurpose weights perform well across a range of variables that are often of interest in business surveys. Furthermore, these results show that the proposed approach is robust to model misspecification and also efficient when used with variables that are not suited to standard methods of small area estimation (e.g. variables that contain a significant proportion of zeros).

In a large scale survey, we are usually concerned with estimation of some characteristics of interest for a large area (e.g., a country). But we are frequently interested in estimating similar characteristics for a subpopulation using the same survey data. The direct survey estimator which utilizes data only from the small area of interest has been found to be highly unreliable due to small sample size. Model-based methods have been used in small area estimation in order to combine information available from the survey data and various administrative and census data. We study the empirical best linear unbiased prediction (EBLUP) and its inferences under the general Fay-Herriot small area model. Considering that the currently used variance estimation methods could produce zero estimates, we propose the adjusted density method (ADM) following Morris' comments. This new method always produces positive estimates. Morris only suggested such adjustment to the restricted maximum likelihood. Asymptotic theory of ADM is unknown. We prove the consistency for the ADM estimator. We also propose an alternate consistent ADM estimator by adjusting the maximum likelihood. By comparing these two ADM estimators both in theory and simulation, we find that the ADM estimator using maximum likelihood is better than the one using the restricted likelihood in terms of bias. We provide a concrete proof for the positiveness and consistency of both ADM estimators. We also propose EBLUP estimator of $\theta_i$ where we use two ADM estimators of $A$. The associated second-order unbiased Taylor linearization MSE estimators are also proposed. In addition, a new parametric bootstrap prediction interval method using ADM estimator is proposed. The positiveness of ADM estimators is emphasized in the construction of the prediction interval. We also show that the coverage probability of this new method is accurate up to $O(m^{-3/2})$. Extensive Monte Carlo simulations are conducted. A data analysis for