Statistical Methodology Commons^™

Rejoinder: Estimation Issues For Copulas Applied To Marketing Data, Peter Danaher, Michael Smith

Michael Stanley Smith

Estimating copula models using Bayesian methods presents some subtle challenges, ranging from specification of the prior to computational tractability. There is also some debate about what is the most appropriate copula to employ from those available. We address these issues here and conclude by discussing further applications of copula models in marketing.

Forecasting Television Ratings, Peter Danaher, Tracey Dagger, Michael Smith

Michael Stanley Smith

Despite the state of flux in media today, television remains the dominant player globally for advertising spend. Since television advertising time is purchased on the basis of projected future ratings, and ad costs have skyrocketed, there is increasing pressure to forecast television ratings accurately. Previous forecasting methods are not generally very reliable and many have not been validated, but more distressingly, none have been tested in today’s multichannel environment. In this study we compare 8 different forecasting models, ranging from a naïve empirical method to a state-of-the-art Bayesian model-averaging method. Our data come from a recent time period, 2004-2008 in …

Cross-Validated Targeted Minimum-Loss-Based Estimation, Wenjing Zheng, Mark Van Der Laan

Wenjing Zheng

No abstract provided.

Accurately Sized Test Statistics With Misspecified Conditional Homoskedasticity, Douglas Steigerwald, Jack Erb

Douglas G. Steigerwald

We study the finite-sample performance of test statistics in linear regression models where the error dependence is of unknown form. With an unknown dependence structure there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the amount of heterogeneity in the process. When allowing for heterogeneity, through conditional heteroskedasticity, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags we study test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. …

The Underground Economy Of Fake Antivirus Software, Douglas Steigerwald, Brett Stone-Gross, Ryan Abman, Richard Kemmerer, Christopher Kruegel, Giovanni Vigna

Douglas G. Steigerwald

Fake antivirus (AV) programs have been utilized to defraud millions of computer users into paying as much as one hundred dollars for a phony software license. As a result, fake AV software has evolved into one of the most lucrative criminal operations on the Internet. In this paper, we examine the operations of three large-scale fake AV businesses, lasting from three months to more than two years. More precisely, we present the results of our analysis on a trove of data obtained from several backend servers that the cybercriminals used to drive their scam operations. Our investigations reveal that these …

A Practical Ad-Hoc Adjustment To The Simes P-Value, Chris Lloyd

Chris J. Lloyd

The Simes P-value is more powerful than Bonferroni but still suffers from some conservatism when the tests are correlated. Based on a massive simulation study, I develop a formula that corrects for this conservatism. it requires the number of experimental arms which is known. It also requires the correlation and skewness of the underlying test statistics, which will need analytic approximation in practice.

Windows Executable For Gaussian Copula With Nbd Margins, Michael S. Smith

Michael Stanley Smith

This is an example Windows 32bit program to estimate a Gaussian copula model with NBD margins. The margins are estimated first using MLE, and the copula second using Bayesian MCMC. The model was discussed in Danaher & Smith (2011; Marketing Science) as example 4 (section 4.2).

Modeling Multivariate Distributions Using Copulas: Applications In Marketing, Peter J. Danaher, Michael S. Smith

Michael Stanley Smith

In this research we introduce a new class of multivariate probability models to the marketing literature. Known as “copula models”, they have a number of attractive features. First, they permit the combination of any univariate marginal distributions that need not come from the same distributional family. Second, a particular class of copula models, called “elliptical copula”, have the property that they increase in complexity at a much slower rate than existing multivariate probability models as the number of dimensions increase. Third, they are very general, encompassing a number of existing multivariate models, and provide a framework for generating many more. …

Bicycle Commuting In Melbourne During The 2000s Energy Crisis: A Semiparametric Analysis Of Intraday Volumes, Michael S. Smith, Goeran Kauermann

Michael Stanley Smith

Cycling is attracting renewed attention as a mode of transport in western urban environments, yet the determinants of usage are poorly understood. In this paper we investigate some of these using intraday bicycle volumes collected via induction loops located at ten bike paths in the city of Melbourne, Australia, between December 2005 and June 2008. The data are hourly counts at each location, with temporal and spatial disaggregation allowing for the impact of meteorology to be measured accurately for the first time. Moreover, during this period petrol prices varied dramatically and the data also provide a unique opportunity to assess …

The Generalized Shrinkage Estimator For The Analysis Of Functional Connectivity Of Brain Signals, Mark Fiecas, Hernando Ombao

Mark Fiecas

We develop a new statistical method for estimating functional connectivity between neurophysiological signals represented by a multivariate time series. We use partial coherence as the measure of functional connectivity. Partial coherence identifies the frequency bands that drive the direct linear association between any pair of channels. To estimate partial coherence, one would first need an estimate of the spectral density matrix of the multivariate time series. Parametric estimators of the spectral density matrix provide good frequency resolution but could be sensitive when the parametric model is misspecified. Smoothing-based nonparametric estimators are robust to model misspecification and are consistent but may …

Oracle And Multiple Robustness Properties Of Survey Calibration Estimator In Missing Response Problem, Kwun Chuen Gary Chan

UW Biostatistics Working Paper Series

In the presence of missing response, reweighting the complete case subsample by the inverse of nonmissing probability is both intuitive and easy to implement. However, inverse probability weighting is not efficient in general and is not robust against misspecification of the missing probability model. Calibration was developed by survey statisticians for improving efficiency of inverse probability weighting estimators when population totals of auxiliary variables are known and when inclusion probability is known by design. In missing data problem we can calibrate auxiliary variables in the complete case subsample to the full sample. However, the inclusion probability is unknown in general …

Modification And Improvement Of Empirical Likelihood For Missing Response Problem, Kwun Chuen Gary Chan

UW Biostatistics Working Paper Series

An empirical likelihood (EL) estimator was proposed by Qin and Zhang (2007) for a missing response problem under a missing at random assumption. They showed by simulation studies that the finite sample performance of EL estimator is better than some existing estimators. However, the empirical likelihood estimator does not have a uniformly smaller asymptotic variance than other estimators in general. We consider several modifications to the empirical likelihood estimator and show that the proposed estimator dominates the empirical likelihood estimator and several other existing estimators in terms of asymptotic efficiencies. The proposed estimator also attains the minimum asymptotic variance among …

Modification And Improvement Of Empirical Liklihood For Missing Response Problem, Gary Chan

UW Biostatistics Working Paper Series

An empirical likelihood (EL) estimator was proposed by Qin and Zhang (2007) for a missing response problem under a missing at random assumption. They showed by simulation studies that the finite sample performance of EL estimator is better than some existing estimators. However, the empirical likelihood estimator does not have a uniformly smaller asymptotic variance than other estimators in general. We consider several modifications to the empirical likelihood estimator and show that the proposed estimator dominates the empirical likelihood estimator and several other existing estimators in terms of asymptotic efficiencies. The proposed estimator also attains the minimum asymptotic variance among …

Minimum Description Length Measures Of Evidence For Enrichment, Zhenyu Yang, David R. Bickel

COBRA Preprint Series

In order to functionally interpret differentially expressed genes or other discovered features, researchers seek to detect enrichment in the form of overrepresentation of discovered features associated with a biological process. Most enrichment methods treat the p-value as the measure of evidence using a statistical test such as the binomial test, Fisher's exact test or the hypergeometric test. However, the p-value is not interpretable as a measure of evidence apart from adjustments in light of the sample size. As a measure of evidence supporting one hypothesis over the other, the Bayes factor (BF) overcomes this drawback of the p-value but lacks …

Efficient Measurement Error Correction With Spatially Misaligned Data, Adam A. Szpiro, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

Association studies in environmental statistics often involve exposure and outcome data that are misaligned in space. A common strategy is to employ a spatial model such as universal kriging to predict exposures at locations with outcome data and then estimate a regression parameter of interest using the predicted exposures. This results in measurement error because the predicted exposures do not correspond exactly to the true values. We characterize the measurement error by decomposing it into Berkson-like and classical-like components. One correction approach is the parametric bootstrap, which is effective but computationally intensive since it requires solving a nonlinear optimization problem …

Bayesian Logistic Regression Model For Siting Biomass-Using Facilities, Xia Huang

Masters Theses

Key sources of oil for western markets are located in complex geopolitical environments that increase economic and social risk. The amalgamation of economic, environmental, social and national security concerns for petroleum-based economies have created a renewed emphasis on alternative sources of energy which include biomass. The stability of sustainable biomass markets hinges on improved methods to predict and visualize business risk and cost to the supply chain.

This thesis develops Bayesian logistic regression models, with comparisons of classical maximum likelihood models, to quantify significant factors that influence the siting of biomass-using facilities and predict potential locations in the 13-state Southeastern …

Modeling Longitudinal Data Using A Pair-Copula Decomposition Of Serial Dependence, Michael S. Smith, Aleksey Min, Carlos Almeida, Claudia Czado

Michael Stanley Smith

Copulas have proven to be very successful tools for the flexible modelling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a ‘vine’ in the graphical models literature, where each copula is entitled a ‘pair-copula’. We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence pair-copulas, with the end result being a parsimonious representation of a time-inhomogeneous Markov process of varying order. Estimates are …

Minimum Description Length And Empirical Bayes Methods Of Identifying Snps Associated With Disease, Ye Yang, David R. Bickel

COBRA Preprint Series

The goal of determining which of hundreds of thousands of SNPs are associated with disease poses one of the most challenging multiple testing problems. Using the empirical Bayes approach, the local false discovery rate (LFDR) estimated using popular semiparametric models has enjoyed success in simultaneous inference. However, the estimated LFDR can be biased because the semiparametric approach tends to overestimate the proportion of the non-associated single nucleotide polymorphisms (SNPs). One of the negative consequences is that, like conventional p-values, such LFDR estimates cannot quantify the amount of information in the data that favors the null hypothesis of no disease-association.

We …

Improving The Power Of Chronic Disease Surveillance By Incorporating Residential History, Justin Manjourides, Marcello Pagano

Harvard University Biostatistics Working Paper Series

No abstract provided.

Geographic Factors Of Residential Burglaries - A Case Study In Nashville, Tennessee, Jonathan A. Hall

Masters Theses & Specialist Projects

This study examines geographic patterns and geographic factors of residential burglary at the Nashville, TN area for a twenty year period at five year interval starting in 1988. The purpose of this study is to identify what geographic factors have impacted on residential burglary rates, and if there were changes in the geographic patterns of residential burglary over the study period. Several criminological theories guide this study, with the most prominent being Social Disorganization Theory and Routine Activities Theory. Both of these theories focus on the relationships of place and crime. A number of spatial analysis methods are hence adopted …