Small Area Estimation for Disease Prevalence Mapping

Small area estimation (SAE) entails estimating characteristics of interest for domains, often geographical areas, in which there may be few or no samples available. SAE has a long history and a wide variety of methods have been suggested, from a bewildering range of philosophical standpoints. We describe design-based and model-based approaches and models that are specified at the area level and at the unit level, focusing on health applications and fully Bayesian spatial models. The use of auxiliary information is a key ingredient for successful inference when response data are sparse, and we discuss a number of approaches that allow the inclusion of covariate data. SAE for HIV prevalence, using data collected from a Demographic Health Survey in Malawi in 2015–2016, is used to illustrate a number of techniques. The potential use of SAE techniques for outcomes related to coronavirus disease 2019 is discussed.     

Ecological Fallacy and Covariates: New Insights based on Multilevel Modelling of Individual Data

The paper provides a new and more explicit formulation of the assumptions needed by the ordinary ecological regression to provide unbiased estimates and clarifies why violations of these assumptions will affect any method of ecological inference. Empirical evidence is obtained by showing that estimates provided by three main ecological inference methods are heavily biased when compared with multilevel logistic regression applied to a unique set of individual data on voting behaviour. The main findings of our paper have two important implications that can be extended to all situations where the assumptions needed to apply ecological inference are violated in the data: (i) only ecological inference methods that allow one to model the effect of covariates have a chance to produce unbiased estimates, and (ii) there are certain data generating mechanisms producing a kind of bias in ecological estimates that cannot be corrected by modelling the effect of covariates.     

Analytical quasi maximum likelihood inference in multivariate volatility models

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension of the parameter space is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian for a variety of multivariate GARCH models including the Vec and BEKK specifications as well as the recent dynamic conditional correlation model. By means of a Monte Carlo investigation of the BEKK–GARCH model we illustrate that employing analytical derivatives for inference is clearly preferable to numerical methods.     

Discussion: Efficiency and Self-efficiency With Multiple Imputation Inference

By closely examining the examples provided in Nielsen (2003), this paper further explores the relationship between self-efficiency (Meng, 1994) and the validity of Rubin's multiple imputation (RMI) variance combining rule. The RMI variance combining rule is based on the common assumption/intuition that the efficiency of our estimators decreases when we have less data. However, there are estimation procedures that will do the opposite, that is, they can produce more efficient estimators with less data. Self-efficiency is a theoretical formulation for excluding such procedures. When a user, typically unaware of the hidden self-inefficiency of his choice, adopts a self-inefficient complete-data estimation procedure to conduct an RMI inference, the theoretical validity of his inference becomes a complex issue, as we demonstrate. We also propose a diagnostic tool for assessing potential self-inefficiency and the bias in the RMI variance estimator, at the outset of RMI inference, by constructing a convenient proxy to the RMI point estimator.     

ALTERNATIVE ESTIMATING AND TESTING EMPIRICAL STRATEGIES FOR FRACTIONAL REGRESSION MODELS

Abstract In many economic settings, the variable of interest is often a fraction or a proportion, being defined only on the unit interval. The bounded nature of such variables and, in some cases, the possibility of nontrivial probability mass accumulating at one or both boundaries raise some interesting estimation and inference issues. In this paper we (i) provide a comprehensive survey of the main alternative models and estimation methods suitable to deal with fractional response variables, (ii) propose a full testing methodology to assess the validity of the assumptions required by each alternative estimator and (iii) examine the finite‐sample properties of most of the estimators and tests discussed through an extensive Monte Carlo study. An application concerning corporate capital structure choices is also provided.     

Testing for multivariate volatility functions using minimum volume sets and inverse regression

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii) of a bathtub shape, and (iii) in a given parametric form. The inference based on those tests may be further enhanced through associated diagnostic plots. Although the potential use of those ideas is much wider, we focus on the inference for multivariate volatility functions in this paper, i.e. we test for (i) heteroscedasticity, (ii) the so-called ‘smiling effect’, and (iii) some parametric volatility models. The asymptotic behavior of the proposed tests is investigated, and practical feasibility is shown via simulation studies. We further illustrate our methods with real financial data.     

A composite indicator for the waste management in the EU via Hierarchical Disjoint Non-Negative Factor Analysis

In the last years, the quantity of information and statistics about waste management are more and more consistent but so far, few studies are available in this field. The goal of this paper is of producing a model-based Composite Indicator of “good” Waste Management, in order to provide a useful tool of support for EU countries’ policy-makers and institutions.Composite Indicators (CIs), usually, are multidimensional concepts with a hierarchical structure characterized by the presence of a set of specific dimensions, each one corresponding to a subsets of manifest variables. Thus, we propose a CI for Waste Management in Europe by using a hierarchical model-based approach with positive loadings. This approach guarantees to comply with all the good properties on which a composite indicator should be based and to detect the main dimensions (i.e., aspects) of the Waste Management phenomenon.In other terms, this paper provides a hierarchically aggregated index that best describes the Waste Management in EU with its main features by identifying the most important high order (i.e., hierarchical) relationships among subsets of manifest variables. All the parameters are estimated according to the maximum likelihood estimation method (MLE) in order to make inference on the parameters and on the validity of the model.     

Testing for Linearity

The problem of testing for linearity and the number of regimes in the context of self‐exciting threshold autoregressive (SETAR) models is reviewed. We describe least‐squares methods of estimation and inference. The primary complication is that the testing problem is non‐standard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is non‐standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications — annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes.     

On randomization, modeling and experimental design; a new example in an old discussion

Fisher and "Student" quarreled in the early days of statistics about the design of experiments, meant to measure the difference in yield between to breeds of corn. This discussion comes down to randomization versus model building. More than half a century has passed since, but the different views remain. In this paper the discussion is put in terms of artificial randomization and natural randomization, the latter being what remains after appropriate modeling. Also the Bayesian position is discussed. An example in terms of the old corn-breeding discussion is given, showing that a simple robust model may lead to inference and experimental design that outperforms the inference from randomized experiments by far. Finally similar possibilities are suggested in statistical auditing.     

Bootstrapping Financial Time Series

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate.     

On a 2 × 2 factorial design where the use of randomized response is one of the factors

This paper discusses a survey where some respondents were asked sensitive questions directly and others were asked the same questions using randomized response. The use of randomized response was a factor in a 2 × 2 factorial design and dice were used to perform the randomization. First, the paper shows that the perturbation due to the dice can be described using the concept of misclassification and known conditional misclassification probabilities. Second, the paper formulates the likelihood for loglinear models and shows that latent class software can be used to analyse the data. An example including a power analysis is discussed.     

Randomization in the Design of Experiments

A general review is given of the role of randomization in experimental design. Three objectives are distinguished, the avoidance of bias, the establishment of a secure base for the estimation of error in traditional designs, and the provision of formally exact tests of significance and confidence limits. The approximate randomization theory associated with analysis of covariance is outlined and conditionality considerations are used to explain the limited role of randomization in experiments with very small numbers of experimental units. The relation between the so-called design-based and model-based analyses is discussed. Corresponding results in sampling theory are mentioned briefly.     

Processing consistency in non-Bayesian inference

We propose a coherent inference model that is obtained by distorting the prior density in Bayes’ rule and replacing the likelihood with a so-called pseudo-likelihood. This model includes the existing non-Bayesian inference models as special cases and implies new models of base-rate neglect and conservatism. We prove a sufficient and necessary condition under which the coherent inference model is processing consistent, i.e., implies the same posterior density however the samples are grouped and processed retrospectively. We further show that processing consistency does not imply Bayes’ rule by proving a sufficient and necessary condition under which the coherent inference model can be obtained by applying Bayes’ rule to a false stochastic model.     

Predictive regression under various degrees of persistence and robust long-horizon regression

The paper proposes a novel inference procedure for long-horizon predictive regression with persistent regressors, allowing the autoregressive roots to lie in a wide vicinity of unity. The invalidity of conventional tests when regressors are persistent has led to a large literature dealing with inference in predictive regressions with local to unity regressors. Magdalinos and Phillips (2009b) recently developed a new framework of extended IV procedures (IVX) that enables robust chi-square testing for a wider class of persistent regressors. We extend this robust procedure to an even wider parameter space in the vicinity of unity and apply the methods to long-horizon predictive regression. Existing methods in this model, which rely on simulated critical values by inverting tests under local to unity conditions, cannot be easily extended beyond the scalar regressor case or to wider autoregressive parametrizations. In contrast, the methods developed here lead to standard chi-square tests, allow for multivariate regressors, and include predictive processes whose roots may lie in a wide vicinity of unity. As such they have many potential applications in predictive regression. In addition to asymptotics under the null hypothesis of no predictability, the paper investigates validity under the alternative, showing how balance in the regression may be achieved through the use of localizing coefficients and developing local asymptotic power properties under such alternatives. These results help to explain some of the empirical difficulties that have been encountered in establishing predictability of stock returns.     

Short Time Series Analysis: C Statistic vs Edgington Model

Young's C statistic (1941) makes it possible to compare the randomization of a set of sequentially organized data and constitutes an alternative of appropriate analysis in short time series designs. On the other hand, models based on the randomization of stimuli are also very important within the behavioral content applied. For this reason, a comparison is established between the C statistic and the Edgington model. The data analyzed in the comparative study have been obtained from graphs in studies published in behavioral journals. According to the results obtained, it is concluded that the Edgington model in experimental designs AB involves many measurements while the C statistic requires fewer observations to reach the conventional significance level.     

Inference by the <Emphasis Type="Italic">m</Emphasis> out of <Emphasis Type="Italic">n</Emphasis> bootstrap in nonparametric frontier models

It is well-known that the naive bootstrap yields inconsistent inference in the context of data envelopment analysis (DEA) or free disposal hull (FDH) estimators in nonparametric frontier models. For inference about efficiency of a single, fixed point, drawing bootstrap pseudo-samples of size m < n provides consistent inference, although coverages are quite sensitive to the choice of subsample size m. We provide a probabilistic framework in which these methods are shown to valid for statistics comprised of functions of DEA or FDH estimators. We examine a simple, data-based rule for selecting m suggested by Politis et al. (Stat Sin 11:1105–1124, 2001), and provide Monte Carlo evidence on the size and power of our tests. Our methods (i) allow for heterogeneity in the inefficiency process, and unlike previous methods, (ii) do not require multivariate kernel smoothing, and (iii) avoid the need for solutions of intermediate linear programs.     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.     

Bayesian and Frequentist Inference for Ecological Inference: The R×C Case

In this paper we propose Bayesian and frequentist approaches to ecological inference, based on R × C contingency tables, including a covariate. The proposed Bayesian model extends the binomial-beta hierarchical model developed by K ing , R osen and T anner (1999) from the 2×2 case to the R × C case. As in the 2×2 case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods. As such, the resulting MCMC analysis is rich but computationally intensive. The frequentist approach, based on first moments rather than on the entire likelihood, provides quick inference via nonlinear least-squares, while retaining good frequentist properties. The two approaches are illustrated with simulated data, as well as with real data on voting patterns in Weimar Germany. In the final section of the paper we provide an overview of a range of alternative inferential approaches which trade-off computational intensity for statistical efficiency.     

Conditionally heteroscedastic intensity‐dependent marking of log Gaussian Cox processes

Spatial marked point processes are models for systems of points which are randomly distributed in space and provided with measured quantities called marks. This study deals with marking, that is methods of constructing marked point processes from unmarked ones. The focus is density‐dependent marking where the local point intensity affects the mark distribution. This study develops new markings for log Gaussian Cox processes. In these markings, both the mean and variance of the mark distribution depend on the local intensity. The mean, variance and mark correlation properties are presented for the new markings, and a Bayesian estimation procedure is suggested for statistical inference. The performance of the new approach is studied by means of simulation experiments. As an example, a tropical rainforest data is modelled.     

Likelihood inference in some finite mixture models

Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is well known that likelihood inference in mixture models is complicated due to (1) lack of point identification, and (2) parameters (for example, mixing probabilities) whose true value may lie on the boundary of the parameter space. These issues cause the profiled likelihood ratio (PLR) statistic to admit asymptotic limits that differ discontinuously depending on how the true density of the data approaches the regions of singularities where there is lack of point identification. This lack of uniformity in the asymptotic distribution suggests that confidence intervals based on pointwise asymptotic approximations might lead to faulty inferences. This paper examines this problem in details in a finite mixture model and provides possible fixes based on the parametric bootstrap. We examine the performance of this parametric bootstrap in Monte Carlo experiments and apply it to data from Beauty Contest experiments. We also examine small sample inferences and projection methods.