Evidence for hedge fund predictability from a multivariate Student's t full-factor GARCH model

Extending previous work on hedge fund return predictability, this paper introduces the idea of modelling the conditional distribution of hedge fund returns using Student's t full-factor multivariate GARCH models. This class of models takes into account the stylized facts of hedge fund return series, that is, heteroskedasticity, fat tails and deviations from normality. For the proposed class of multivariate predictive regression models, we derive analytic expressions for the score and the Hessian matrix, which can be used within classical and Bayesian inferential procedures to estimate the model parameters, as well as to compare different predictive regression models. We propose a Bayesian approach to model comparison which provides posterior probabilities for various predictive models that can be used for model averaging. Our empirical application indicates that accounting for fat tails and time-varying covariances/correlations provides a more appropriate modelling approach of the underlying dynamics of financial series and improves our ability to predict hedge fund returns.     

On inference for Kendall's τ within a longitudinal data setting

Kendall's τ is a non-parametric measure of correlation based on ranks and is used in a wide range of research disciplines. Although methods are available for making inference about Kendall's τ, none has been extended to modeling multiple Kendall's τs arising in longitudinal data analysis. Compounding this problem is the pervasive issue of missing data in such study designs. In this article, we develop a novel approach to provide inference about Kendall's τ within a longitudinal study setting under both complete and missing data. The proposed approach is illustrated with simulated data and applied to an HIV prevention study.     

Demystifying the Integrated Tail Probability Expectation Formula

ABSTRACT

Calculating the expected values of different types of random variables is a central topic in mathematical statistics. Targeted toward students and instructors in both introductory probability and statistics courses and graduate-level measure-theoretic probability courses, this pedagogical note casts light on a general expectation formula stated in terms of distribution and survival functions of random variables and discusses its educational merits. Often consigned to an end-of-chapter exercise in mathematical statistics textbooks with minimal discussion and presented under superfluous technical assumptions, this unconventional expectation formula provides an invaluable opportunity for students to appreciate the geometric meaning of expectations, which is overlooked in most undergraduate and graduate curricula, and serves as an efficient tool for the calculation of expected values that could be much more laborious by traditional means. For students’ benefit, this formula deserves a thorough in-class treatment in conjunction with the teaching of expectations. Besides clarifying some commonly held misconceptions and showing the pedagogical value of the expectation formula, this note offers guidance for instructors on teaching the formula taking the background of the target student group into account.     

The Box–Cox Transformation and Non‐Iterative Estimation Methods for Ordinal Log‐Linear Models

Recently Beh and Farver investigated and evaluated three non‐iterative procedures for estimating the linear‐by‐linear parameter of an ordinal log‐linear model. The study demonstrated that these non‐iterative techniques provide estimates that are, for most types of contingency tables, statistically indistinguishable from estimates from Newton's unidimensional algorithm. Here we show how two of these techniques are related using the Box–Cox transformation. We also show that by using this transformation, accurate non‐iterative estimates are achievable even when a contingency table contains sampling zeros.     

Coupon collector's problem and generalized Pareto distributions

Let N_n={1,2,…,n}. We sample with replacement from the set N_n assuming that each element has probability 1/n of being drawn. Let M_n be the waiting time determined by certain stoping rules in the coupon collector's problem. We investigate models for the asymptotic behavior of the excesses of M_n over the high thresholds.     

Testing for qualitative interaction of multiple sources of informative dropout in longitudinal data

Longitudinal studies suffer from patient dropout. The dropout process may be informative if there exists an association between dropout patterns and the rate of change in the response over time. Multiple patterns are plausible in that different causes of dropout might contribute to different patterns. These multiple patterns can be dichotomized into two groups: quantitative and qualitative interaction. Quantitative interaction indicates that each of the multiple sources is biasing the estimate of the rate of change in the same direction, although with differing magnitudes. Alternatively, qualitative interaction results in the multiple sources biasing the estimate of the rate of change in opposing directions. Qualitative interaction is of special concern, since it is less likely to be detected by conventional methods and can lead to highly misleading slope estimates. We explore a test for qualitative interaction based on simultaneous confidence intervals. The test accommodates the realistic situation where reasons for dropout are not fully understood, or even entirely unknown. It allows for an additional level of clustering among participating subjects. We apply these methods to a study exploring tumor growth rates in mice as well as a longitudinal study exploring rates of change in cognitive functioning for Alzheimer's patients.     

A weighted test of internal symmetry

This study examines extensions of McNemar's Test with multinomial responses, and proposes a linear weighting scheme, based on the distance of the response change, that is applied to one of these extensions (Bowker's test). This weighted version of Bowker's test is then appropriate for ordinal response variables. A Monte Carlo simulation was conducted to examine the Type I error rate of the weighted Bowker's test for a cross-classification table based on a five-category ordinal response scale. The weighted Bowker's test was also applied to a data set involving change in student attitudes towards mathematics. The results of the weighted Bowker's test were compared with the results of Bowker's test applied to the same set of data.     

Reporting cumulative proportion of subjects with an adverse event based on data from multiple studies

Experience has shown us that when data are pooled from multiple studies to create an integrated summary, an analysis based on naïvely‐pooled data is vulnerable to the mischief of Simpson's Paradox. Using the proportions of patients with a target adverse event (AE) as an example, we demonstrate the Paradox's effect on both the comparison and the estimation of the proportions. While meta analytic approaches have been recommended and increasingly used for comparing safety data between treatments, reporting proportions of subjects experiencing a target AE based on data from multiple studies has received little attention. In this paper, we suggest two possible approaches to report these cumulative proportions. In addition, we urge that regulatory guidelines on reporting such proportions be established so that risks can be communicated in a scientifically defensible and balanced manner. Copyright © 2010 John Wiley & Sons, Ltd.     

Estimation of a Conditional Copula and Association Measures

Abstarct. This paper is concerned with studying the dependence structure between two random variables Y ₁ and Y ₂ conditionally upon a covariate X. The dependence structure is modelled via a copula function, which depends on the given value of the covariate in a general way. Gijbels et al. (Comput. Statist. Data Anal., 55, 2011, 1919) suggested two non‐parametric estimators of the ‘conditional’ copula and investigated their numerical performances. In this paper we establish the asymptotic properties of the proposed estimators as well as conditional association measures derived from them. Practical recommendations for their use are then discussed.