Was the conservative majority predictable?

Canada's $41{\rm st}$ national general election saw the Conservative Party increase its seat count from 143 to 166, thus giving it a majority of the national parliament's 308 seats. By contrast, nearly all of the pre‐election seat count forecasts predicted a Conservative minority only. We examine the extent to which simple statistical models could or could not have predicted the Conservative majority prior to the election. We conclude that, by using data from the previous (2008) election appropriately, the Conservative majority should have been anticipated as the most likely outcome. The Canadian Journal of Statistics 39: 721–733; 2011. © 2011 Statistical Society of Canada     

Bias in Multinomial Models

This paper investigates bias in parameter estimates and residual diagnostics for parametric multinomial models by considering the effect of deleting a cell. In particular, it describes the average changes in the standardized residuals and maximum likelihood estimates resulting from conditioning on the given cells. These changes suggest how individual cell observations affect biases. Emphasis is placed on the role of individual cell observations in determining bias and on how bias affects standard diagnostic methods. Examples from genetics and log–linear models are considered. Numerical results show that conditioning on an influential cell results in substantial changes in biases.     

A comparison of the estimative and predictive methods of estimating posterior probabilities

An asymptotic account Is presented on the relative performance of the so-called estimative and predictive methods of estimating the posterior probability that an object belongs to one of two possible multivariate normal populations. For equal prior probabil-ities it is concluded that the predictive method generally gives a less extreme estimate than the estimative. This is supported by previously available results based essentially on simulation studies. Conditions under which the predictive method provides less extreme estimates for arbitrary prior probabilities are considered. Also, the asymptotic biases associated with the two methods are compared.     

Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckman's two-step estimator is widely used to estimate these models. However, Heckman's two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckman's two-step estimator are compared using Monte Carlo experiments and empirical examples.     

Robust Smoothed Rank Estimation Methods for Accelerated Failure Time Model Allowing Clusters

Smoothed Gehan rank estimation methods are widely used in accelerated failure time (AFT) models with/without clusters. However, most methods are sensitive to outliers in the covariates. In order to solve this problem, we propose robust approaches based on the smoothed Gehan rank estimation methods for the AFT model, allowing for clusters by employing two different weight functions. Simulation studies show that the proposed methods outperform existing smoothed rank estimation methods regarding their biases and standard deviations when there are outliers in the covariates. The proposed methods are also applied to a real dataset from the “Major cardiovascular interventions” study.     

Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckman's two-step estimator is widely used to estimate these models. However, Heckman's two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckman's two-step estimator are compared using Monte Carlo experiments and empirical examples.     

Estimating Parliamentary composition through electoral polls

Summary.  All electoral systems have an electoral formula that converts proportions of votes into Parliamentary seats. Pre-electoral polls usually focus on estimating proportions of votes and then apply the electoral formula to give a forecast of Parliamentary composition. We describe the problems that arise from this approach: there will typically be a bias in the forecast. We study the origin of the bias and some methods for evaluating and reducing it. We propose a bootstrap algorithm for computing confidence intervals for the allocation of seats. We show, by Monte Carlo simulation, the performance of the proposed methods using data from Spanish elections in previous years. We also propose graphical methods for visualizing how electoral formulae and Parliamentary forecasts work (or fail).     

Multiple-bias modelling for analysis of observational data

Summary.  Conventional analytic results do not reflect any source of uncertainty other than random error, and as a result readers must rely on informal judgments regarding the effect of possible biases. When standard errors are small these judgments often fail to capture sources of uncertainty and their interactions adequately. Multiple-bias models provide alternatives that allow one systematically to integrate major sources of uncertainty, and thus to provide better input to research planning and policy analysis. Typically, the bias parameters in the model are not identified by the analysis data and so the results depend completely on priors for those parameters. A Bayesian analysis is then natural, but several alternatives based on sensitivity analysis have appeared in the risk assessment and epidemiologic literature. Under some circumstances these methods approximate a Bayesian analysis and can be modified to do so even better. These points are illustrated with a pooled analysis of case–control studies of residential magnetic field exposure and childhood leukaemia, which highlights the diminishing value of conventional studies conducted after the early 1990s. It is argued that multiple-bias modelling should become part of the core training of anyone who will be entrusted with the analysis of observational data, and should become standard procedure when random error is not the only important source of uncertainty (as in meta-analysis and pooled analysis).     

Second-order biases of the maximum likelihood estimates in von Mises regression models

This paper discusses issues related to the improvement of maximum likelihood estimates in von Mises regression models. It obtains general matrix expressions for the second-order biases of maximum likelihood estimates of the mean parameters and concentration parameters. The formulae are simple to compute, and give the biases by means of weighted linear regressions. Simulation results are presented assessing the performance of corrected maximum likelihood estimates in these models.     

Least squares parameter estimation in multiplicative noise models

A simple multiplicative noise model with a constant signal has become a basic mathematical model in processing synthetic aperture radar images. The purpose of this paper is to examine a general multiplicative noise model with linear signals represented by a number of unknown parameters. The ordinary least squares (LS) and weighted LS methods are used to estimate the model parameters. The biases of the weighted LS estimates of the parameters are derived. The biases are then corrected to obtain a second-order unbiased estimator, which is shown to be exactly equivalent to the maximum log quasi-likelihood estimation, though the quasi-likelihood function is founded on a completely different theoretical consideration and is known, at the present time, to be a uniquely acceptable theory for multiplicative noise models. Synthetic simulations are carried out to confirm theoretical results and to illustrate problems in processing data contaminated by multiplicative noises. The sensitivity of the LS and weighted LS methods to extremely noisy data is analysed through the simulated examples.     

An Alternative Methodology for Combining Different Forecasting Models

Many economic and financial time series exhibit heteroskedasticity, where the variability changes are often based on recent past shocks, which cause large or small fluctuations to cluster together. Classical ways of modelling the changing variance include the use of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and Neural Networks models. The paper starts with a comparative study of these two models, both in terms of capturing the non-linear or heteroskedastic structure and forecasting performance. Monthly and daily exchange rates for three different countries are implemented. The paper continues with different methods for combining forecasts of the volatility from the competing models, in order to improve forecasting accuracy. Traditional methods for combining the predicted values from different models, using various weighting schemes are considered, such as the simple average or methods that find the best weights in terms of minimizing the squared forecast error. The main purpose of the paper is, however, to propose an alternative methodology for combining forecasts effectively. The new, hereby-proposed non-linear, non-parametric, kernel-based method, is shown to have the basic advantage of not being affected by outliers, structural breaks or shocks to the system and it does not require a specific functional form for the combination.     

A flexible semiparametric regression model for bimodal,asymmetric and censored data

In this paper, we propose a new semiparametric heteroscedastic regression model allowing for positive and negative skewness and bimodal shapes using the B-spline basis for nonlinear effects. The proposed distribution is based on the generalized additive models for location, scale and shape framework in order to model any or all parameters of the distribution using parametric linear and/or nonparametric smooth functions of explanatory variables. We motivate the new model by means of Monte Carlo simulations, thus ignoring the skewness and bimodality of the random errors in semiparametric regression models, which may introduce biases on the parameter estimates and/or on the estimation of the associated variability measures. An iterative estimation process and some diagnostic methods are investigated. Applications to two real data sets are presented and the method is compared to the usual regression methods.     

Approximate bounded influence estimation for longitudinal data with outliers and measurement errors

Mixed effects models or random effects models are popular for the analysis of longitudinal data. In practice, longitudinal data are often complex since there may be outliers in both the response and the covariates and there may be measurement errors. The likelihood method is a common approach for these problems but it can be computationally very intensive and sometimes may even be computationally infeasible. In this article, we consider approximate robust methods for nonlinear mixed effects models to simultaneously address outliers and measurement errors. The approximate methods are computationally very efficient. We show the consistency and asymptotic normality of the approximate estimates. The methods can also be extended to missing data problems. An example is used to illustrate the methods and a simulation is conducted to evaluate the methods.     

The relationship between crime, punishment and economic conditions: is reliable inference possible when crimes are under-recorded?

We investigate the estimation of dynamic models of criminal activity, when there is significant under-recording of crime. We give a theoretical analysis and use simulation techniques to investigate the resulting biases in conventional regression estimates. We find the biases to be of little practical significance. We develop and apply a new simulated maximum likelihood procedure that estimates simultaneously the measurement error and crime processes, using extraneous survey data. This also confirms that measurement error biases are small. Our estimation results for data from England and Wales imply a significant response of crime to both the economic and the enforcement environment.     

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jørgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n⁻¹) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n⁻¹) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n⁻¹) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n⁻¹) that are based on bootstrap methods. These estimators are compared by simulation.     

Locally Efficient Semiparametric Estimators for Proportional Hazards Models with Measurement Error

We propose a new class of semiparametric estimators for proportional hazards models in the presence of measurement error in the covariates, where the baseline hazard function, the hazard function for the censoring time, and the distribution of the true covariates are considered as unknown infinite dimensional parameters. We estimate the model components by solving estimating equations based on the semiparametric efficient scores under a sequence of restricted models where the logarithm of the hazard functions are approximated by reduced rank regression splines. The proposed estimators are locally efficient in the sense that the estimators are semiparametrically efficient if the distribution of the error‐prone covariates is specified correctly and are still consistent and asymptotically normal if the distribution is misspecified. Our simulation studies show that the proposed estimators have smaller biases and variances than competing methods. We further illustrate the new method with a real application in an HIV clinical trial.     

Multiparameter evidence synthesis in epidemiology and medical decision-making: current approaches

Summary.  Alongside the development of meta-analysis as a tool for summarizing research literature, there is renewed interest in broader forms of quantitative synthesis that are aimed at combining evidence from different study designs or evidence on multiple parameters. These have been proposed under various headings: the confidence profile method, cross-design synthesis, hierarchical models and generalized evidence synthesis. Models that are used in health technology assessment are also referred to as representing a synthesis of evidence in a mathematical structure. Here we review alternative approaches to statistical evidence synthesis, and their implications for epidemiology and medical decision-making. The methods include hierarchical models, models informed by evidence on different functions of several parameters and models incorporating both of these features. The need to check for consistency of evidence when using these powerful methods is emphasized. We develop a rationale for evidence synthesis that is based on Bayesian decision modelling and expected value of information theory, which stresses not only the need for a lack of bias in estimates of treatment effects but also a lack of bias in assessments of uncertainty. The increasing reliance of governmental bodies like the UK National Institute for Clinical Excellence on complex evidence synthesis in decision modelling is discussed.     

Biases and Uncertainty in Climate Projections

Abstract. We study statistical procedures to quantify uncertainty in multivariate climate projections based on several deterministic climate models. We introduce two different assumptions – called constant bias and constant relation respectively – for extrapolating the substantial additive and multiplicative biases present during the control period to the scenario period. There are also strong indications that the biases in the scenario period are different from the extrapolations from the control period. Including such changes in the statistical models leads to an identifiability problem that we solve in a frequentist analysis using a zero sum side condition and in a Bayesian analysis using informative priors. The Bayesian analysis provides estimates of the uncertainty in the parameter estimates and takes this uncertainty into account for the predictive distributions. We illustrate the method by analysing projections of seasonal temperature and precipitation in the Alpine region from five regional climate models in the PRUDENCE project.     

Improved log‐linear model estimators of abundance in capture‐recapture experiments

The authors review log‐linear models for estimating the size of a closed population and propose a new log‐linear estimator for experiments having between animal heterogeneity and a behavioral response. They give a general formula for evaluating the asymptotic biases of estimators of abundance derived from log‐linear models. They propose simple frequency modifications for reducing these asymptotic biases and investigate the modifications in a Monte Carlo experiment which reveals that they reduce both the bias and the mean squared error of abundance estimators.