Outlier‐Robust Bayesian Multinomial Choice Modeling

A Bayesian method for outlier‐robust estimation of multinomial choice models is presented. The method can be used for both correlated as well as uncorrelated choice alternatives and guarantees robustness towards outliers in the dependent and independent variables. To account for outliers in the response direction, the fat‐tailed multivariate Laplace distribution is used. Leverage points are handled via a shrinkage procedure. A simulation study shows that estimation of the model parameters is less influenced by outliers compared to non‐robust alternatives. An analysis of margarine scanner data shows how our method can be used for better pricing decisions. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust Small Area Estimation under Spatial Non‐stationarity

The effective use of spatial information in a regression‐based approach to small area estimation is an important practical issue. One approach to account for geographic information is by extending the linear mixed model to allow for spatially correlated random area effects. An alternative is to include the spatial information by a non‐parametric mixed models. Another option is geographic weighted regression where the model coefficients vary spatially across the geography of interest. Although these approaches are useful for estimating small area means efficiently under strict parametric assumptions, they can be sensitive to outliers. In this paper, we propose robust extensions of the geographically weighted empirical best linear unbiased predictor. In particular, we introduce robust projective and predictive estimators under spatial non‐stationarity. Mean squared error estimation is performed by two analytic approaches that account for the spatial structure in the data. Model‐based simulations show that the methodology proposed often leads to more efficient estimators. Furthermore, the analytic mean squared error estimators introduced have appealing properties in terms of stability and bias. Finally, we demonstrate in the application that the new methodology is a good choice for producing estimates for average rent prices of apartments in urban planning areas in Berlin.     

Outlier Detection in the Lognormal Logarithmic Conditional Autoregressive Range Model

An outlier detection procedure in the lognormal logarithmic conditional autoregressive range (lognormal Log‐CARR) model is proposed. The proposed test statistic is demonstrated to be well‐sized and to have good power using Monte Carlo simulations. Furthermore, the outlier detection procedure suffers less from the masking effect caused by multiple outliers. The results of an empirical investigation show that the proposed method can effectively detect volatility outliers and improve forecasting accuracy.     

Estimation of Randomisation Mean Square Error in Small Area Estimation

In this article, we propose a new method for estimating the randomisation (design‐based) mean squared error (DMSE) of model‐dependent small area predictors. Analogously to classical survey sampling theory, the DMSE considers the finite population values as fixed numbers and accounts for the MSE of small area predictors over all possible sample selections. The proposed method models the true DMSE as computed for synthetic populations and samples drawn from them, as a function of known statistics and then applies the model to the original sample. Several simulation studies for the linear area‐level model and the unit‐level mixed logistic model illustrate the performance of the proposed method and compare it with the performance of other DMSE estimators proposed in the literature.     

Small Area Estimation-New Developments and Directions

The purpose of this paper is to provide a critical review of the main advances in small area estimation (SAE) methods in recent years. We also discuss some of the earlier developments, which serve as a necessary background for the new studies. The review focuses on model dependent methods with special emphasis on point prediction of the target area quantities, and mean square error assessments. The new models considered are models used for discrete measurements, time series models and models that arise under informative sampling. The possible gains from modeling the correlations among small area random effects used to represent the unexplained variation of the small area target quantities are examined. For review and appraisal of the earlier methods used for SAE, see Ghosh & Rao (1994).     

Reliable Robust Regression Diagnostics

Motivated by the requirement of controlling the number of false discoveries that arises in several application fields, we study the behaviour of diagnostic procedures obtained from popular high‐breakdown regression estimators when no outlier is present in the data. We find that the empirical error rates for many of the available techniques are surprisingly far from the prescribed nominal level. Therefore, we propose a simulation‐based approach to correct the liberal diagnostics and reach reliable inferences. We provide evidence that our approach performs well in a wide range of settings of practical interest and for a variety of robust regression techniques, thus showing general appeal. We also evaluate the loss of power that can be expected from our corrections under different contamination schemes and show that this loss is often not dramatic. Finally, we detail some possible extensions that may further enhance the applicability of the method.     

The identification of outliers in exponential samples

In this paper, the task of identifying outliers in exponential samples is treated conceptionally in the sense of DAVIES and GATHER (1989, 1993) by means of a so-called outlier region. In case of an exponential distribution, an empirical version of such a region – also called an outlier identifier – is mainly dependent on some estimator of the unknown scale parameter. The worst-case behaviour of several reasonable outlier identifiers is investigated thoroughly and it is shown that only robust estimators of scale should be used to construct reliable identifiers. These findings lead to the recommendation of an outlier identifier that is based on a standardized version of the sample median.     

A Comparison of Methods for Poverty Estimation in Developing Countries

Small area estimation is a widely used indirect estimation technique for micro‐level geographic profiling. Three unit level small area estimation techniques—the ELL or World Bank method, empirical best prediction (EBP) and M‐quantile (MQ) — can estimate micro‐level Foster, Greer, & Thorbecke (FGT) indicators: poverty incidence, gap and severity using both unit level survey and census data. However, they use different assumptions. The effects of using model‐based unit level census data reconstructed from cross‐tabulations and having no cluster level contextual variables for models are discussed, as are effects of small area and cluster level heterogeneity. A simulation‐based comparison of ELL, EBP and MQ uses a model‐based reconstruction of 2000/2001 data from Bangladesh and compares bias and mean square error. A three‐level ELL method is applied for comparison with the standard two‐level ELL that lacks a small area level component. An important finding is that the larger number of small areas for which ELL has been able to produce sufficiently accurate estimates in comparison with EBP and MQ has been driven more by the type of census data available or utilised than by the model per se.     

Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model

In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation.     

Robust forecast combinations

Forecast outliers commonly occur in economic, financial, and other areas of forecasting applications. In the literature of forecast combinations, there have been only a few studies exploring how to deal with outliers. In this work, we propose two robust combining methods based on the AFTER algorithm (Yang, 2004a). Our approach utilizes robust loss functions in order to reduce the influence of outliers. Oracle inequalities for certain versions of these methods are obtained, which show that the combined forecasts automatically perform as well as the best individual among the pool of original forecasts. Systematic simulations and data examples show that the robust methods outperform the AFTER algorithm when outliers are likely to occur and perform on par with AFTER when there are no outliers. Comparison of the robust AFTERs with some commonly used combining methods also shows their potential advantages.     

Robust testing procedures of process locations

In many manufacturing and service industries, the quality department of the organization works continuously to ensure that the mean or location of the process is close to the target value. In order to understand the process, it is necessary to provide numerical statements of the processes that are being investigated. That is why the researcher needs to check the validity of the hypotheses that are concerned with some physical phenomena. It is usually assumed that the collected data behave well. However, sometimes the data may contain outliers. The presence of one or more outliers might seriously distort the statistical inference. Since the sample mean is very sensitive to outliers, this research will use the smooth adaptive (SA) estimator to estimate the population mean. The SA estimator will be used to construct testing procedures, called smooth adaptive test (SA test), for testing various null hypotheses. A Monte Carlo study is used to simulate the values of the probability of a Type I error and the power of the SA test. This is accomplished by constructing confidence intervals of the process mean by using the SA estimator and bootstrap methods. The SA test will be compared with other tests such as the normal test, t test and a nonparametric statistical method, namely, the Wilcoxon signed-rank test. Also, the cases with and without outliers will be considered. For the right-skewed distributions, the SA test is the best choice. When the population is a right-skewed distribution with one outlier, the SA test controls the probability of a Type I error better than other tests and is recommended.     

Analysis of three tests for one or two outliers

Summary  Three well-known test statistics for the precense of two outliers are studied from the points of views of exact null distribution and power. In a sample case, it is shown that the M urphy two outlier statistic may suffer from masking. A recursive version of the P earson -C handrasekar test is shown to perform well.     

Penalized likelihood smoothing in robust state space models

In likelihood-based approaches to robustify state space models, Gaussian error distributions are replaced by non-normal alternatives with heavier tails. Robustified observation models are appropriate for time series with additive outliers, while state or transition equations with heavy-tailed error distributions lead to filters and smoothers that can cope with structural changes in trend or slope caused by innovations outliers. As a consequence, however, conditional filtering and smoothing densities become analytically intractable. Various attempts have been made to deal with this problem, reaching from approximate conditional mean type estimation to fully Bayesian analysis using MCMC simulation. In this article we consider penalized likelihood smoothers, this means estimators which maximize penalized likelihoods or, equivalently, posterior densities. Filtering and smoothing for additive and innovations outlier models can be carried out by computationally efficient Fisher scoring steps or iterative Kalman-type filters. Special emphasis is on the Student family, for which EM-type algorithms to estimate unknown hyperparameters are developed. Operational behaviour is illustrated by simulation experiments and by real data applications. Received: March 1998     

An outlier test for linear processes

In this paper we introduce an outlier test for linear processes. It is assumed that an upper bound for the number of outliers is known which is not too big in relation to the sample size. The test statistic bases on the comparison of the observations with certain predictors. We discuss the asymptotical behaviour of the test statistic under the null hypothesis ‘no outlier’ and derive the asymptotic distribution for the case that the distribution of the squared white noise process belongs to a certain subset of the domain of attraction of the Gumbel distribution. Especially the most important case in applications, the Gaussian white noise is included.     

Robustness and the general dynamic factor model with infinite-dimensional space: Identification,estimation, and forecasting

General dynamic factor models have demonstrated their capacity to circumvent the curse of dimensionality in the analysis of high-dimensional time series and have been successfully considered in many economic and financial applications. As second-order models, however, they are sensitive to the presence of outliers—an issue that has not been analyzed so far in the general case of dynamic factors with possibly infinite-dimensional factor spaces (Forni et al. 2000, 2015, 2017). In this paper, we consider this robustness issue and study the impact of additive outliers on the identification, estimation, and forecasting performance of general dynamic factor models. Based on our findings, we propose robust versions of identification, estimation, and forecasting procedures. The finite-sample performance of our methods is evaluated via Monte Carlo experiments and successfully applied to a classical data set of 115 US macroeconomic and financial time series.     

Predictors for the first-order autoregressive process

The error made in predicting a first-order autoregressive process with unknown parameters is investigated. It is shown that the least squares predictor is unbiased for symmetric error distributions. Alternative predictors for stationary and non-stationary processes are studied using the Monte Carlo method. The ordinary least squares statistics perform reasonably well for one period predictions with samples as small as ten for both stationary and non-stationary processes. It is demonstrated that there is a considerable loss in efficiency when outdated estimators are used to construct predictors.     

Conditional feature screening for mean and variance functions in models with multiple-index structure

The existing methods for feature screening focus mainly on the mean function of regression models. The variance function, however, plays an important role in statistical theory and application. We thus investigate feature screening for mean and variance functions with multiple-index framework in high dimensional regression models. Notice that some information about predictors can be known in advance from previous investigations and experience, for example, a certain set of predictors is related to the response. Based on the conditional information, together with empirical likelihood, we propose conditional feature screening procedures. Our methods can consistently estimate the sets of active predictors in the mean and variance functions. It is interesting that the proposed screening procedures can avoid estimating the unknown link functions in the mean and variance functions, and moreover, can work well in the case of high correlation among the predictors without iterative algorithm. Therefore, our proposal is of computational simplicity. Furthermore, as a conditional method, our method is robust to the choice of the conditional set. The theoretical results reveal that the proposed procedures have sure screening properties. The attractive finite sample performance of our method is illustrated in simulations and a real data application.     

On the lack of invariance of some Bayesian outlier models

The property of non-invariance to the scale of the data for the Abraham and Box (1978) Bayesian outlier model, and the model that generalizes the Guttman, Dutter and Freeman (1978) outlier analysis is discussed. This drawback is due to the non-informative prior taken for the parameters. Freeman (1980) expected that most posterior weight would be put on the model with the most outliers if the improper prior is used. We show that this may not be correct. An illustrative example is given.     

Multivariate residual‐based finite‐sample tests for serial dependence and ARCH effects with applications to asset pricing models

In this paper, we propose several finite‐sample specification tests for multivariate linear regressions (MLR). We focus on tests for serial dependence and ARCH effects with possibly non‐Gaussian errors. The tests are based on properly standardized multivariate residuals to ensure invariance to error covariances. The procedures proposed provide: (i) exact variants of standard multivariate portmanteau tests for serial correlation as well as ARCH effects, and (ii) exact versions of the diagnostics presented by Shanken ( 1990 ) which are based on combining univariate specification tests. Specifically, we combine tests across equations using a Monte Carlo (MC) test method so that Bonferroni‐type bounds can be avoided. The procedures considered are evaluated in a simulation experiment: the latter shows that standard asymptotic procedures suffer from serious size problems, while the MC tests suggested display excellent size and power properties, even when the sample size is small relative to the number of equations, with normal or Student‐t errors. The tests proposed are applied to the Fama–French three‐factor model. Our findings suggest that the i.i.d. error assumption provides an acceptable working framework once we allow for non‐Gaussian errors within 5‐year sub‐periods, whereas temporal instabilities clearly plague the full‐sample dataset. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting Bitcoin risk measures: A robust approach

Over the last few years, Bitcoin and other cryptocurrencies have attracted the interest of many investors, practitioners and researchers. However, little attention has been paid to the predictability of their risk measures. This paper compares the predictability of the one-step-ahead volatility and Value-at-Risk of Bitcoin using several volatility models. We also include procedures that take into account the presence of outliers and estimate the volatility and Value-at-Risk in a robust fashion. Our results show that robust procedures outperform non-robust ones when forecasting the volatility and estimating the Value-at-Risk. These results suggest that the presence of outliers plays an important role in the modelling and forecasting of Bitcoin risk measures.