Multivariate boundary kernels and a continuous least squares principle

Whereas there are many references on univariate boundary kernels, the construction of boundary kernels for multivariate density and curve estimation has not been investigated in detail. The use of multivariate boundary kernels ensures global consistency of multivariate kernel estimates as measured by the integrated mean-squared error or sup-norm deviation for functions with compact support. We develop a class of boundary kernels which work for any support, regardless of the complexity of its boundary. Our construction yields a boundary kernel for each point in the boundary region where the function is to be estimated. These boundary kernels provide a natural continuation of non-negative kernels used in the interior onto the boundary. They are obtained as solutions of the same kernel-generating variational problem which also produces the kernel function used in the interior as its solution. We discuss the numerical implementation of the proposed boundary kernels and their relationship to locally weighted least squares. Along the way we establish a continuous least squares principle and a continuous analogue of the Gauss–Markov theorem.     

Model averaging procedure for partially linear single-index models

This paper is concerned with model selection and model averaging procedures for partially linear single-index models. The profile least squares procedure is employed to estimate regression coefficients for the full model and submodels. We show that the estimators for submodels are asymptotically normal. Based on the asymptotic distribution of the estimators, we derive the focused information criterion (FIC), formulate the frequentist model average (FMA) estimators and construct proper confidence intervals for FMA estimators and FIC estimator, a special case of FMA estimators. Monte Carlo studies are performed to demonstrate the superiority of the proposed method over the full model, and over models chosen by AIC or BIC in terms of coverage probability and mean squared error. Our approach is further applied to real data from a male fertility study to explore potential factors related to sperm concentration and estimate the relationship between sperm concentration and monobutyl phthalate.     

Application of copulas to multivariate control charts

The most popular multivariate control chart for monitoring the mean of a distribution is probably the Hotelling T² rule. Unfortunately, this rule relies on the assumption that the distribution under control is Gaussian, which is rarely true in practice. The objective of this paper is to propose a new approach for the non-normal multivariate case. It consists in the construction of a tolerance region obtained from a density level set estimation. The method follows a “plug-in” approach in which the density of the observations is previously estimated. This estimation is conducted using copulas modeling, an increasingly popular tool in multivariate modeling.     

Simulation-Based Density Estimation for Time Series Using Covariate Data

This article proposes a simulation-based density estimation technique for time series that exploits information found in covariate data. The method can be paired with a large range of parametric models used in time series estimation. We derive asymptotic properties of the estimator and illustrate attractive finite sample properties for a range of well-known econometric and financial applications.     

Restricted Estimation in Partially Linear Errors-in-Variables Models

As a compromise between parametric regression and nonparametric regression, partially linear models are frequently used in statistical modelling. This article considers statistical inference for this semiparametric model when the linear covariate is measured with additive error and some additional linear restrictions on the parametric component are assumed to hold. We propose a restricted corrected profile least-squares estimator for the parametric component, and study the asymptotic normality of the estimator. To test hypothesis on the parametric component, we construct a Wald test statistic and obtain its limiting distribution. Some simulation studies are conducted to illustrate our approaches.     

Design-based analysis of embedded experiments with applications in the Dutch Labour Force Survey

Summary.  Previous research has proposed a design-based analysis procedure for experiments that are embedded in complex sampling designs in which the ultimate sampling units of an on-going sample survey are randomized over different treatments according to completely randomized designs or randomized block designs. Design-based Wald and t -statistics are applied to test whether sample means that are observed under various survey implementations are significantly different. This approach is generalized to experimental designs in which clusters of sampling units are randomized over the different treatments. Furthermore, test statistics are derived to test differences between ratios of two sample estimates that are observed under alternative survey implementations. The methods are illustrated with a simulation study and real life applications of experiments that are embedded in the Dutch Labour Force Survey. The functionality of a software package that was developed to conduct these analyses is described.     

The 'heuristics and biases' bias in expert elicitation

Summary.  In the early 1970s Tversky and Kahneman published a series of papers on 'heuristics and biases' describing human inadequacies in assessing probabilities, culminating in a highly popular article in Science . This seminal research has been heavily cited in many fields, including statistics, as the definitive research on probability assessment. Curiously, although this work was debated at the time and more recent work has largely refuted many of the claims, this apparent heuristics and biases bias in elicitation research has gone unremarked. Over a decade of research into the frequency effect, the importance of framing, and cognitive models more generally, has been almost completely ignored by the statistical literature on expert elicitation. To remedy this situation, this review offers a guide to the psychological research on assessing probabilities, both old and new, and gives concrete guidelines for eliciting expert knowledge.     

GEOMETRIC DECAY OF THE STEADY-STATE PROBABILITIES IN A QUASI-BIRTH-AND-DEATH PROCESS WITH A COUNTABLE NUMBER OF PHASES

A sufficient condition is proved for geometric decay of the steady-state probabilities in a quasi-birth-and-death process having a countable number of phases in each level. If there is a positive number η and positive vectors x = (x _i) and y = (y _j ) satisfying some equations and inequalities, the steady-state probability π _mi decays geometrically with rate η in the sense π _mi ～ cη ^m x _i as m → ∞. As an example, the result is applied to a two-queue system with shorter queue discipline.     

Exit polling in a cold climate: the BBC–ITV experience in Britain in 2005

Summary.  Conducting an exit poll to forecast the outcome of a national election in terms of both votes and seats is particularly difficult in Britain. No official information is available on how individual polling stations voted in the past, use of single-member plurality means that there is no consistent relationship between votes and seats, electors can choose to vote by post and most of those who vote in person do so late in the day. In addition, around one in every six intended exit poll respondents refuses to participate. Methods that were developed to overcome these problems, and their use in the successful 2005 British Broadcasting Corporation–Independent Television exit poll, are described and evaluated. The methodology included a panel design to allow the estimation of electoral change at local level, coherent multiple-regression modelling of multiparty electoral change to capture systematic patterns of variation, probabilistic prediction of constituency winners to account for uncertainty in projected constituency level shares, collection of information about the voting intentions of postal voters before polling day and access to interviewer guesses on the voting behaviour of refusals. The coverage and accuracy of the exit poll data are critically examined, the effect of key aspects of the statistical modelling of the data is assessed and some general lessons are drawn for the design and analysis of electoral exit polls.     

Order statistics and test duration

There are two principal issues in statistical planning. One is the accuracy/reliability of statistical inference and the other is the length of test time needed to complete the designed experiment. With regard to the latter, various test schemes have been proposed and applied in statistical literature. These schemes, among others, include type-I censoring, the usual type-II censoring, and progressively type-II censoring. To implement any of these experiments it is necessary that the capacity of the test facility is large enough so that all the items can be tested simultaneously. If, however, instead of having one facility with large capacity there are several facilities with relatively smaller capacities, a differently designed experiment would be necessary. This paper studies and compares elapsed test times and total elapsed test times corresponding to different statistical plans. The results obtained here are useful for performing an experiment that has shorter test time in a certain sense.