Strong Distributional Assumptions Research Articles

The Constraining Power of International Treaties: Theory and Methods

We acknowledge the contribution of von Stein (2005) in calling attention to the very real problem of selection bias in estimating treaty effects. Nonetheless, we dispute both von Stein's theoretical and empirical conclusions. Theoretically, we contend that treaties can both screen and constrain simultaneously, meaning that findings of screening do nothing to undermine the claim that treaties constrain state behavior as well. Empirically, we question von Stein's estimator on several grounds, including its strong distributional assumptions and its statistical inconsistency. We then illustrate that selection bias does not account for much of the difference between Simmons's (2000) and von Stein's (2005) estimated treaty effects, and instead reframe the problem as one of model dependency. Using a preprocessing matching step to reduce that dependency, we then illustrate treaty effects that are both substantively and statistically significant—and that are quite close in magnitude to those reported by Simmons.

Advanced Statistics: Bootstrapping Confidence Intervals for Statistics with “Difficult” Distributions

The use of confidence intervals in reporting results of research has increased dramatically and is now required or highly recommended by editors of many scientific journals. Many resources describe methods for computing confidence intervals for statistics with mathematically simple distributions. Computing confidence intervals for descriptive statistics with distributions that are difficult to represent mathematically is more challenging. The bootstrap is a computationally intensive statistical technique that allows the researcher to make inferences from data without making strong distributional assumptions about the data or the statistic being calculated. This allows the researcher to estimate confidence intervals for statistics that do not have simple sampling distributions (e.g., the median). The purposes of this article are to describe the concept of bootstrapping, to demonstrate how to estimate confidence intervals for the median and the Spearman rank correlation coefficient for non-normally-distributed data from a recent clinical study using two commonly used statistical software packages (SAS and Stata), and to discuss specific limitations of the bootstrap.

Hierarchical Inverse Gaussian Models and Multiple Testing: Application to Gene Expression Data

Detecting differentially expressed genes in microarray experiments is a topic that has been well studied in the literature. Many hypothesis testing methods have been proposed that rely on strong distributional assumptions for the gene intensities. However, the shape of microarray data may vary substantially from one experiment to another, and model assumptions may be seriously violated in many cases. The literature on microarray data is mainly based on two distributions: the log-normal and the gamma distributions, that often appear to be effective when used in a Bayesian hierarchical framework. However, if a model that fits the data well in a global manner seems attractive, two points should be regarded with attention: the ability of the model to fit the tail of the observed distribution, and its robustness to a wrong specification of the model, in terms of error rates for the hypothesis tests. In order to focus on these aspects, we propose to use Bayesian models involving the inverse Gaussian distribution to describe gene expression data. We show that these models can be good competitors to the traditional Bayesian or random effect gamma or log-normal models in some situations. A multiple testing procedure is then proposed, based on an asymptotic property of the posterior probability of the one-sided alternative hypothesis. We show that the asymptotic property is well approximated for inverse Gaussian models, even when the number of observations available for each test is very small.

Instrumental Variables for Binary Treatments with Heterogenous Treatment Effects: A Simple Exposition

This note provides a simple exposition of what IV can and cannot estimate in a model with binary treatment variable and heterogenous treatment effects. It shows how linear IV is essentially a misspecification of functional form and the reason why linear IV estimates will generally depend on the instrument used is because of this misspecification. It shows that if one can estimate the correct functional form then the treatment effects are independent of the instruments used. However, the data may not be rich enough in practice to be able to identify these treatments effects without strong distributional assumptions. In this case, one will have to settle for estimations of treatment effects that are instrument-dependent.

Application of rough sets analysis to identify polluted aquatic sites based on a battery of biomarkers: a comparison with classical methods

The evaluation of toxicological effects at the cellular and molecular levels in organisms are often used to determine sites subjected to contamination problems that pose a threat to the long-term survival of organisms. However, the integration of multiple measurements on the health status of organisms into a model for site discrimination is challenging. This study compares two discrimination methods which are based on rule inference: rough sets (RS) analysis and classification trees (CT) with classical multivariate discriminant analysis (DA). Site classification was attempted with six biomarkers of effects: metallothionein levels, lipid peroxidation, DNA damage, levels of lipophosphoproteins (i.e., vitellins), phagocytosis activity and haemocyte cell viability on clam ( Mya arenaria) populations from the Saguenay River fjord (Quebec, Canada). Rule based methods have the advantage of complete independence from data distribution constraints in contrast to the classification methods from multivariate analysis that are more commonly used in ecotoxicology. Results show that RS and CT gave better classifications than DA because they do not require strong distributional assumptions. Moreover, RS provided classification rules that could identify the most important biomarker(s) for site discrimination. RS and CT were shown to be simple and efficient methods for classifying multivariable ecotoxicological data. This methodology would be especially useful when freedom from distributional assumptions is required.

Nonparametric Analysis of Longitudinal Binary Data: An Application to the Intergroup Prisoner's Dilemma Game

The intergroup prisoner's dilemma game was suggested by Bornstein (1992, Journal of Personality and Social Psychology. 7, 597–606) for modelling intergroup conflicts over continuous public goods. We analyse data of an experiment in which the game was played for 150 rounds, under three matching conditions. The objective is to study differences in the investment patterns of players in the different groups. A repeated measures analysis was conducted by Goren and Bornstein (1999, Games and Human Behaviour: Essays in Honor of Amnon Rapoport, pp. 299–314), involving data aggregation and strong distributional assumptions. Here we introduce a nonparametric approach based on permutation tests. Two new measures, the cumulative investment and the normalised cumulative investment, provide additional insight into the differences between groups. The proposed tests are based on the area under the investment curves. They identify an overall difference between the groups as well as pairwise differences. A simultaneous confidence band for the mean difference curve is used to detect the games which account for any pairwise difference.

Modeling gene expression measurement error: a quasi-likelihood approach

BackgroundUsing suitable error models for gene expression measurements is essential in the statistical analysis of microarray data. However, the true probabilistic model underlying gene expression intensity readings is generally not known. Instead, in currently used approaches some simple parametric model is assumed (usually a transformed normal distribution) or the empirical distribution is estimated. However, both these strategies may not be optimal for gene expression data, as the non-parametric approach ignores known structural information whereas the fully parametric models run the risk of misspecification. A further related problem is the choice of a suitable scale for the model (e.g. observed vs. log-scale).ResultsHere a simple semi-parametric model for gene expression measurement error is presented. In this approach inference is based an approximate likelihood function (the extended quasi-likelihood). Only partial knowledge about the unknown true distribution is required to construct this function. In case of gene expression this information is available in the form of the postulated (e.g. quadratic) variance structure of the data.As the quasi-likelihood behaves (almost) like a proper likelihood, it allows for the estimation of calibration and variance parameters, and it is also straightforward to obtain corresponding approximate confidence intervals. Unlike most other frameworks, it also allows analysis on any preferred scale, i.e. both on the original linear scale as well as on a transformed scale. It can also be employed in regression approaches to model systematic (e.g. array or dye) effects.ConclusionsThe quasi-likelihood framework provides a simple and versatile approach to analyze gene expression data that does not make any strong distributional assumptions about the underlying error model. For several simulated as well as real data sets it provides a better fit to the data than competing models. In an example it also improved the power of tests to identify differential expression.

A Composite Likelihood Approach to Semivariogram Estimation

This article proposes the use of estimating functions based on composite likelihood for the estimation of isotropic as well as geometrically anisotropic semivariogram parameters. The composite likelihood approach is objective, eliminating the specification of distance lags and lag tolerances associated with the commonly used moment estimator. Extensions to the geometric anisotropy case include a parameterized transformed distance function, which eliminates the subjective estimation of the parameters of geometric anisotropy. The composite likelihood approach requires no matrix inversions and the estimators are shown to be consistent in a fashion similar to maximum likelihood and restricted maximum likelihood but without reliance on strong distributional assumptions. Predictions based on composite likelihood estimates performed very well using isotropic and geometric anisotropic simulated data and compared favorably to predictions based on the traditional approach in the isotropic case. Comparisons were also made using data collected on iron-ore measurements where previous analyses determined a geometric anisotropic semivariogram model to be appropriate.

A non-parametric order statistics software reliability model

This paper addresses a family of probability models for the failure time process known as order statistics models. Conventional order statistics models make rather strong distributional assumptions about the detection times: typically they assume that these come from some parametric family of distributions. In this paper a new model is presented that relaxes these distributional assumptions, and—in the tradition of non-parametric statistics generally—‘allows the data to speak for themselves’. The accuracy of the new model is compared on some real data sets with the predictions that come from several of the better parametric reliability growth models © 1998 John Wiley & Sons, Ltd.

The precision of data obtained in large‐scale science assessments: An investigation of bootstrapping and half‐sample replication methods

Powerful computational procedures are now available to better determine the accuracy of statistical estimates derived from data that have unknown distributions or do not meet parametric requirements. These techniques are generally called resampling plans and include the recently developed bootstrap. Science educators often face the problem of nonnormal distributions especially when conducting large-scale assessments or evaluating national curriculum projects that require complex sampling plans. Resampling techniques permit the researcher to make inferences without the strong distributional assumptions needed for more traditional parametric approaches. In this study, the bootstrap and a simplified version of a half-sample replication are used to examine the precision of science test scores obtained in a large-scale evaluation of Scope, Sequence, and Coordination, a national science curriculum project. The resampling plans are described in some detail and the results are compared with those obtained from parametric methods. © 1998 John Wiley & Sons, Inc. J Res Sci Teach 35: 697–704, 1998.

On the Efficiency of Conditional Heteroskedasticity Models

This paper discusses how conditional heteroskedasticity models can be estimated efficiently without imposing strong distributional assumptions such as normality. Using the generalized method of moments (GMM) principle, we show that for a class of models with a symmetric conditional distribution, the GMM estimates obtained from the joint estimating equations corresponding to the conditional mean and variance of the model are efficient when the instruments are chosen optimally. A simple ARCH(1) model is used to illustrate the feasibility of the proposed estimation procedure.

Production frontiers with cross-sectional and time-series variation in efficiency levels

In this paper we consider the efficient instrumental variables estimation of a panel data model with heterogeneity in slopes as well as intercepts. Using a panel of U.S. airlines, we apply our methodology to a frontier production function with cross-sectional and temporal variation in levels of technical efficiency. Our approach allows us to estimate time-varying efficiency levels for individual firms without invoking strong distributional assumptions for technical inefficiency or random noise. We do so by including in the production function a flexible function of time whose parameterization depends on the firm. We also generalize the results of Hausman and Taylor (1981) to exploit assumptions about the uncorrelatedness of certain exogenous variables with the temporal pattern of the firm's technical inefficiency. Our empirical analysis of the airline industry over two periods of regulation yields believable evidence on the pattern of changes in efficiency across regulatory environments.

A New Test of the Three-Moment Capital Asset Pricing Model

This paper tests the Kraus-Litzenberger (1976) three-moment capital asset pricing model using Hansen's (1982) generalized method-of-moments (GMM). The GMM approach does not impose strong distributional assumptions on the asset returns. This is an interest? ing issue since there is no obvious multivariate distribution for returns that also exhibits co-skewness. Using monthly stock returns to test the model, there is some evidence that systematic skewness is priced.

Comparison of Three-Class Attributes Sampling Plans and Variables Sampling Plans for Lot Acceptance Sampling in Food Microbiology

Lot acceptance sampling is an established method of assessing the microbiological quality and safety of batches or consignments of food, but the choice between three-class attributes plans and variables plans is not always clear. Application of variables plans requires that the microorganism of concern be distributed normally, or log-normally. When such is not true, variables plans may place either the consumer or the producer at increased risk. Validation of normality is therefore essential when using variables plans. However, with small numbers of sample units as are typically analyzed in microbiological testing of food, statistical tests are unlikely to detect non-normality. Three-class attributes plans do not require strong distributional assumptions for correct application, and as well they have several practical and operational advantages over variables plans. Moreover, three-class attributes plans assess lot quality in a fashion fundamentally different from variables plans, and this difference precludes the usual statistical comparisons based on relative discriminatory ability. We conclude that when selecting acceptance sampling plans for microbiological testing of food, whether the plans be for regulatory, port-of-entry or in-plant purposes, three-class plans are generally preferable to variables plans.

A Comparison of Alternative Models for the Demand for Medical Care

We have tested alternative models of the demand for medical care using experimental data. The estimated response of demand to insurance plan is sensitive to the model used. We therefore use a split-sample analysis and find that a model that more closely approximates distributional assumptions and uses a nonparametric retransformation factor performs better in terms of mean squared forecast error. Simpler models are inferior either because they are not robust to outliers (e.g., ANOVA, ANOCOVA), or because they are inconsistent when strong distributional assumptions are violated (e.g., a two-parameter Box-Cox transformation).