A new non‐randomized response model: The parallel model

Despite certain advances for non‐randomized response (NRR) techniques in the past 6 years, the existing non‐randomized crosswise and triangular models have several limitations in practice. In this paper, I propose a new NRR model, called the parallel model with a wider application range. Asymptotical properties of the maximum likelihood estimator (and its modified version) for the proportion of interest are explored. Theoretical comparisons with the crosswise and triangular models show that the parallel model is always more efficient than the two existing NRR models for most of the possible parameter ranges. Bayesian methods for analyzing survey data from the parallel model are developed. A case study on college students' premarital sexual behavior at Wuhan and a case study on plagiarism at the University of Hong Kong are conducted and are used to illustrate the proposed methods. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.     

Evaluating,Comparing, Monitoring,and Improving Representativeness of Survey Response Through R‐Indicators and Partial R‐Indicators

Non‐response is a common source of error in many surveys. Because surveys often are costly instruments, quality‐cost trade‐offs play a continuing role in the design and analysis of surveys. The advances of telephone, computers, and Internet all had and still have considerable impact on the design of surveys. Recently, a strong focus on methods for survey data collection monitoring and tailoring has emerged as a new paradigm to efficiently reduce non‐response error. Paradata and adaptive survey designs are key words in these new developments. Prerequisites to evaluating, comparing, monitoring, and improving quality of survey response are a conceptual framework for representative survey response, indicators to measure deviations thereof, and indicators to identify subpopulations that need increased effort. In this paper, we present an overview of representativeness indicators or R‐indicators that are fit for these purposes. We give several examples and provide guidelines for their use in practice.     

Subsampling Inference with K Populations and a Non‐standard Behrens–Fisher Problem

We revisit the methodology and historical development of subsampling, and then explore in detail its use in hypothesis testing, an area which has received surprisingly modest attention. In particular, the general set‐up of a possibly high‐dimensional parameter with data from K populations is explored. The role of centring the subsampling distribution is highlighted, and it is shown that hypothesis testing with a data‐centred subsampling distribution is more powerful. In addition we demonstrate subsampling’s ability to handle a non‐standard Behrens–Fisher problem, i.e., a comparison of the means of two or more populations which may possess not only different and possibly infinite variances, but may also possess different distributions. However, our formulation is general, permitting even functional data and/or statistics. Finally, we provide theory for K ‐ sample U ‐ statistics that helps establish the asymptotic validity of subsampling confidence intervals and tests in this very general setting.     

Social Intermediation in Base‐of‐the‐Pyramid Markets

Our study explores the structuring decisions made by intermediaries seeking to alleviate poverty by connecting base‐of‐the‐pyramid markets with more developed markets. Using intermediation theory to ground our study, we collected qualitative data on 29 social intermediation projects located within Latin America, Africa, and Asia. Our findings suggest that ‘socializing’ intermediation theory to more accurately explain and predict structural outcomes across more diverse contexts requires three key modifications: (1) the attenuation of opportunism, which creates an internalizing social force; (2) the accommodation of non‐monetary objectives, which creates an externalizing social force; and (3) the perception of transaction capabilities as tractable, which serves as a guidepost for reconciling these two opposing social forces.     

Bayesian Estimation of Willingness‐to‐pay Where Respondents Mis‐report Their Preferences*

We introduce a modified conditional logit model that takes account of uncertainty associated with mis‐reporting in revealed preference experiments estimating willingness‐to‐pay (WTP). Like Hausman et al. [Journal of Econometrics (1988) Vol. 87, pp. 239–269], our model captures the extent and direction of uncertainty by respondents. Using a Bayesian methodology, we apply our model to a choice modelling (CM) data set examining UK consumer preferences for non‐pesticide food. We compare the results of our model with the Hausman model. WTP estimates are produced for different groups of consumers and we find that modified estimates of WTP, that take account of mis‐reporting, are substantially revised downwards. We find a significant proportion of respondents mis‐reporting in favour of the non‐pesticide option. Finally, with this data set, Bayes factors suggest that our model is preferred to the Hausman model.     

Selecting Adaptive Survey Design Strata with Partial R‐indicators

Recent survey literature shows an increasing interest in survey designs that adapt data collection to characteristics of the survey target population. Given a specified quality objective function, the designs attempt to find an optimal balance between quality and costs. Finding the optimal balance may not be straightforward as corresponding optimisation problems are often highly non‐linear and non‐convex. In this paper, we discuss how to choose strata in such designs and how to allocate these strata in a sequential design with two phases. We use partial R‐indicators to build profiles of the data units where more or less attention is required in the data collection. In allocating cases, we look at two extremes: surveys that are run only once, or infrequent, and surveys that are run continuously. We demonstrate the impact of the sample size in a simulation study and provide an application to a real survey, the Dutch Crime Victimisation Survey.     

Simulating non‐normal distributions with specified L‐moments and L‐correlations

This paper derives a procedure for simulating continuous non‐normal distributions with specified L‐moments and L‐correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product‐moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L‐moment‐based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L‐skew and L‐kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, the L‐correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposed L‐moment‐based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.     

Extrapolation‐based Bandwidth Selectors: A Review and Comparative Study with Discussion on Bivariate Applications

Cross‐validation is a widely used tool in selecting the smoothing parameter in a non‐parametric procedure. However, it suffers from large sampling variation and tends to overfit the data set. Many attempts have been made to reduce the variance of cross‐validation. This paper focuses on two recent proposals of extrapolation‐based cross‐validation bandwidth selectors: indirect cross‐validation and subsampling‐extrapolation technique. In univariate case, we notice that using a fixed value parameter surrogate for indirect cross‐validation works poorly when the true density is hard to estimate, while the subsampling‐extrapolation technique is more robust to non‐normality. We investigate whether a hybrid bandwidth selector could benefit from the advantages of both approaches and compare the performance of different extrapolation‐based bandwidth selectors through simulation studies, real data analyses and large sample theory. A discussion on their extension to bivariate case is also presented.     

Aspects of second‐order analysis of structured inhomogeneous spatio‐temporal point processes

Statistical methodology for spatio‐temporal point processes is in its infancy. We consider second‐order analysis based on pair correlation functions and K‐functions for general inhomogeneous spatio‐temporal point processes and for inhomogeneous spatio‐temporal Cox processes. Assuming spatio‐temporal separability of the intensity function, we clarify different meanings of second‐order spatio‐temporal separability. One is second‐order spatio‐temporal independence and relates to log‐Gaussian Cox processes with an additive covariance structure of the underlying spatio‐temporal Gaussian process. Another concerns shot‐noise Cox processes with a separable spatio‐temporal covariance density. We propose diagnostic procedures for checking hypotheses of second‐order spatio‐temporal separability, which we apply on simulated and real data.     

A comment on Mendeş and Yiğit (2013), ‘Type I error and test power of different tests for testing interaction effects in factorial experiments’, Statistica Neerlandica, 67:1–26

In their advocacy of the rank‐transformation (RT) technique for analysis of data from factorial designs, Mende? and Yi?it (Statistica Neerlandica, 67, 2013, 1–26) missed important analytical studies identifying the statistical shortcomings of the RT technique, the recommendation that the RT technique not be used, and important advances that have been made for properly analyzing data in a non‐parametric setting. Applied data analysts are at risk of being misled by Mende? and Yi?it, when statistically sound techniques are available for the proper non‐parametric analysis of data from factorial designs. The appropriate methods express hypotheses in terms of normalized distribution functions, and the test statistics account for variance heterogeneity.     

Alternative Approaches to Multilevel Modelling of Survey Non‐Contact and Refusal

We review three alternative approaches to modelling survey non‐contact and refusal: multinomial, sequential, and sample selection (bivariate probit) models. We then propose a multilevel extension of the sample selection model to allow for both interviewer effects and dependency between non‐contact and refusal rates at the household and interviewer level. All methods are applied and compared in an analysis of household non‐response in the United Kingdom, using a data set with unusually rich information on both respondents and non‐respondents from six major surveys. After controlling for household characteristics, there is little evidence of residual correlation between the unobserved characteristics affecting non‐contact and refusal propensities at either the household or the interviewer level. We also find that the estimated coefficients of the multinomial and sequential models are surprisingly similar, which further investigation via a simulation study suggests is due to non‐contact and refusal having largely different predictors.     

Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

Small area estimation typically requires model‐based methods that depend on isolating the contribution to overall population heterogeneity associated with group (i.e. small area) membership. One way of doing this is via random effects models with latent group effects. Alternatively, one can use an M‐quantile ensemble model that assigns indices to sampled individuals characterising their contribution to overall sample heterogeneity. These indices are then aggregated to form group effects. The aim of this article is to contrast these two approaches to characterising group effects and to illustrate them in the context of small area estimation. In doing so, we consider a range of different data types, including continuous data, count data and binary response data.     

Estimation and testing of crossing‐points in fixed design regression

Many phenomena in the life sciences can be analyzed by using a fixed design regression model with a regression function m that exhibits a crossing‐point in the following sense: the regression function runs below or above its mean level, respectively, according as the input variable lies to the left or to the right of that crossing‐point, or vice versa. We propose a non‐parametric estimator and show weak and strong consistency as long as the crossing‐point is unique. It is defined as maximizing point arg max of a certain marked empirical process. For testing the hypothesis H₀ that the regression function m actually is constant (no crossing‐point), a decision rule is designed for the specific alternative H₁ that m possesses a crossing‐point. The pertaining test‐statistic is the ratio max/argmax of the maximum value and the maximizing point of the marked empirical process. Under the hypothesis the ratio converges in distribution to the corresponding ratio of a reflected Brownian bridge, for which we derive the distribution function. The test is consistent on the whole alternative and superior to the corresponding Kolmogorov–Smirnov test, which is based only on the maximal value max. Some practical examples of possible applications are given where a certain study about dental phobia is discussed in more detail.     

Moment estimation in discrete shifting level model applied to fast array‐CGH segmentation

We develop a mathematical theory needed for moment estimation of the parameters in a general shifting level process (SLP) treating, in particular, the finite state space case geometric finite normal (GFN) SLP. For the SLP, we give expressions for the moment estimators together with asymptotic (co)variances, following, completing, and correcting Cline (Journal of Applied Probability 20, 1983, 322–337); formulae are then made more explicit for the GFN‐SLP. To illustrate the potential uses, we then apply the moment estimation method to a GFN‐SLP model of array comparative genomic hybridization data. We obtain encouraging results in the sense that a segmentation based on the estimated parameters turns out to be faster than with other currently available methods, while being comparable in terms of sensitivity and specificity.     

Stable Asymptotics for M‐estimators

We review some first‐order and higher‐order asymptotic techniques for M‐estimators, and we study their stability in the presence of data contaminations. We show that the estimating function (ψ) and its derivative with respect to the parameter play a central role. We discuss in detail the first‐order Gaussian density approximation, saddlepoint density approximation, saddlepoint test, tail area approximation via the Lugannani–Rice formula and empirical saddlepoint density approximation (a technique related to the empirical likelihood method). For all these asymptotics, we show that a bounded ψ (in the Euclidean norm) and a bounded (e.g. in the Frobenius norm) yield stable inference in the presence of data contamination. We motivate and illustrate our findings by theoretical and numerical examples about the benchmark case of one‐dimensional location model.     

Application of one‐step method to parameter estimation in ODE models

In this paper, we study application of Le Cam's one‐step method to parameter estimation in ordinary differential equation models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular non‐linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system. The one‐step method starts from a preliminary ‐consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size n →∞ ) equivalent of the least squares estimator through a numerically straightforward procedure. We demonstrate performance of the one‐step estimator via extensive simulations and real data examples. The method enables the researcher to obtain both point and interval estimates. The preliminary ‐consistent estimator that we use depends on non‐parametric smoothing, and we provide a data‐driven methodology for choosing its tuning parameter and support it by theory. An easy implementation scheme of the one‐step method for practical use is pointed out.     

Evaluating asset‐pricing models using the Hansen–Jagannathan bound: a Monte Carlo investigation

We use recent statistical tests, based on a ‘distance’ between the model and the Hansen–Jagannathan bound, to compute the rejection rates of true models. For asset‐pricing models with time‐separable preferences, the finite‐sample distribution of the test statistic associated with the risk‐neutral case is extreme, in the sense that critical values based on this distribution deliver type I errors no larger than intended—regardless of risk aversion or the rate of time preference. We also show that these maximal‐type‐I‐error critical values are appropriate for both time and state non‐separable preferences and that they yield acceptably small type II error rates. Copyright © 2002 John Wiley & Sons, Ltd.     

Factor‐Based Identification‐Robust Interference in IV Regressions

Robust methods for instrumental variable inference have received considerable attention recently. Their analysis has raised a variety of problematic issues such as size/power trade‐offs resulting from weak or many instruments. We show that information reduction methods provide a useful and practical solution to this and related problems. Formally, we propose factor‐based modifications to three popular weak‐instrument‐robust statistics, and illustrate their validity asymptotically and in finite samples. Results are derived using asymptotic settings that are commonly used in both the factor and weak‐instrument literature. For the Anderson–Rubin statistic, we also provide analytical finite‐sample results that do not require any underlying factor structure. An illustrative Monte Carlo study reveals the following. Factor‐based tests control size regardless of instruments and factor quality. All factor‐based tests are systematically more powerful than standard counterparts. With informative instruments and in contrast to standard tests: (i) power of factor‐based tests is not affected by k even when large; and (ii) weak factor structure does not cost power. An empirical study on a New Keynesian macroeconomic model suggests that our factor‐based methods can bridge a number of gaps between structural and statistical modeling. Copyright © 2015 John Wiley & Sons, Ltd.     

Stratification of Skewed Populations: A Comparison of Optimisation‐based versus Approximate Methods

Survey statisticians use either approximate or optimisation‐based methods to stratify finite populations. Examples of the former are the cumrootf (Dalenius & Hodges, 1957 ) and geometric (Gunning & Horgan, 2004 ) methods, while examples of the latter are Sethi ( 1963 ) and Kozak ( 2004 ) algorithms. The approximate procedures result in inflexible stratum boundaries; this lack of flexibility results in non‐optimal boundaries. On the other hand, optimisation‐based methods provide stratum boundaries that can simultaneously account for (i) a chosen allocation scheme, (ii) overall sample size or required reliability of the estimator of a studied parameter and (iii) presence or absence of a take‐all stratum. Given these additional conditions, optimisation‐based methods will result in optimal boundaries. The only disadvantage of these methods is their complexity. However, in the second decade of 21st century, this complexity does not actually pose a problem. We illustrate how these two groups of methods differ by comparing their efficiency for two artificial populations and a real population. Our final point is that statistical offices should prefer optimisation‐based over approximate stratification methods; such a decision will help them either save much public money or, if funds are already allocated to a survey, result in more precise estimates of national statistics.