The Generalized Conditional Autoregressive Wishart Model for Multivariate Realized Volatility

It is well known that in finance variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high-frequency returns as the ex-post realization of the covariance matrix of low-frequency returns. For the analysis of dynamics of RCOV matrices, we propose the generalized conditional autoregressive Wishart (GCAW) model. Both the noncentrality matrix and scale matrix of the Wishart distribution are driven by the lagged values of RCOV matrices, and represent two different sources of dynamics, respectively. The GCAW is a generalization of the existing models, and accounts for symmetry and positive definiteness of RCOV matrices without imposing any parametric restriction. Some important properties such as conditional moments, unconditional moments, and stationarity are discussed. Empirical examples including sequences of daily RCOV matrices from the New York Stock Exchange illustrate that our model outperforms the existing models in terms of model fitting and forecasting.     

Penalised spline estimation for generalised partially linear single-index models

Generalised linear models are frequently used in modeling the relationship of the response variable from the general exponential family with a set of predictor variables, where a linear combination of predictors is linked to the mean of the response variable. We propose a penalised spline (P-spline) estimation for generalised partially linear single-index models, which extend the generalised linear models to include nonlinear effect for some predictors. The proposed models can allow flexible dependence on some predictors while overcome the “curse of dimensionality”. We investigate the P-spline profile likelihood estimation using the readily available R package mgcv, leading to straightforward computation. Simulation studies are considered under various link functions. In addition, we examine different choices of smoothing parameters. Simulation results and real data applications show effectiveness of the proposed approach. Finally, some large sample properties are established.     

The expected bit complexity of the von Neumann rejection algorithm

In 1952, von Neumann introduced the rejection method for random variate generation. We revisit this algorithm when we have a source of perfect bits at our disposal. In this random bit model, there are universal lower bounds for generating a random variate with a given density to within an accuracy \(\epsilon \) derived by Knuth and Yao, and refined by the authors. In general, von Neumann’s method fails in this model. We propose a modification that insures proper behavior for all Riemann-integrable densities on compact sets, and show that the expected number of random bits needed behaves optimally with respect to universal lower bounds. In particular, we introduce the notion of an oracle that evaluates the supremum and infimum of a function on any rectangle of \({\mathbb {R}}^{d}\), and develop a quadtree-style extension of the classical rejection method.     

Prior specification of neighbourhood and interaction structure in binary Markov random fields

We formulate a prior distribution for the energy function of stationary binary Markov random fields (MRFs) defined on a rectangular lattice. In the prior we assign distributions to all parts of the energy function. In particular we define priors for the neighbourhood structure of the MRF, what interactions to include in the model, and for potential values. We define a reversible jump Markov chain Monte Carlo (RJMCMC) procedure to simulate from the corresponding posterior distribution when conditioned to an observed scene. Thereby we are able to learn both the neighbourhood structure and the parametric form of the MRF from the observed scene. We circumvent evaluations of the intractable normalising constant of the MRF when running the RJMCMC algorithm by adopting a previously defined approximate auxiliary variable algorithm. We demonstrate the usefulness of our prior in two simulation examples and one real data example.     

Additive mixed effect model for recurrent gap time data

Gap times between recurrent events are often of primary interest in medical and observational studies. The additive hazards model, focusing on risk differences rather than risk ratios, has been widely used in practice. However, the marginal additive hazards model does not take the dependence among gap times into account. In this paper, we propose an additive mixed effect model to analyze gap time data, and the proposed model includes a subject-specific random effect to account for the dependence among the gap times. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The finite sample behavior of the proposed methods is evaluated through simulation studies, and an application to a data set from a clinic study on chronic granulomatous disease is provided.     

Variable selection in discrete survival models including heterogeneity

Several variable selection procedures are available for continuous time-to-event data. However, if time is measured in a discrete way and therefore many ties occur models for continuous time are inadequate. We propose penalized likelihood methods that perform efficient variable selection in discrete survival modeling with explicit modeling of the heterogeneity in the population. The method is based on a combination of ridge and lasso type penalties that are tailored to the case of discrete survival. The performance is studied in simulation studies and an application to the birth of the first child.     

Joint modeling of longitudinal and survival data with the Cox model and two-phase sampling

A common objective of cohort studies and clinical trials is to assess time-varying longitudinal continuous biomarkers as correlates of the instantaneous hazard of a study endpoint. We consider the setting where the biomarkers are measured in a designed sub-sample (i.e., case-cohort or two-phase sampling design), as is normative for prevention trials. We address this problem via joint models, with underlying biomarker trajectories characterized by a random effects model and their relationship with instantaneous risk characterized by a Cox model. For estimation and inference we extend the conditional score method of Tsiatis and Davidian (Biometrika 88(2):447–458, 2001) to accommodate the two-phase biomarker sampling design using augmented inverse probability weighting with nonparametric kernel regression. We present theoretical properties of the proposed estimators and finite-sample properties derived through simulations, and illustrate the methods with application to the AIDS Clinical Trials Group 175 antiretroviral therapy trial. We discuss how the methods are useful for evaluating a Prentice surrogate endpoint, mediation, and for generating hypotheses about biological mechanisms of treatment efficacy.     

When and how to satisfice: an experimental investigation

This paper is about satisficing behaviour. Rather tautologically, this is when decision-makers are satisfied with achieving some objective, rather than in obtaining the best outcome. The term was coined by Simon (Q J Econ 69:99–118, 1955), and has stimulated many discussions and theories. Prominent amongst these theories are models of incomplete preferences, models of behaviour under ambiguity, theories of rational inattention, and search theories. Most of these, however, seem to lack an answer to at least one of two key questions: when should the decision-maker (DM) satisfice; and how should the DM satisfice. In a sense, search models answer the latter question (in that the theory tells the DM when to stop searching), but not the former; moreover, usually the question as to whether any search at all is justified is left to a footnote. A recent paper by Manski (Theory Decis. doi: 10.1007/s11238-017-9592-1, 2017) fills the gaps in the literature and answers the questions: when and how to satisfice? He achieves this by setting the decision problem in an ambiguous situation (so that probabilities do not exist, and many preference functionals can therefore not be applied) and by using the Minimax Regret criterion as the preference functional. The results are simple and intuitive. This paper reports on an experimental test of his theory. The results show that some of his propositions (those relating to the ‘how’) appear to be empirically valid while others (those relating to the ‘when’) are less so.