Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Evaluating the Dynamic Nature of Market Risk

This study examines the systematic risk present in major crops for the United States and three corn-belt states. An index of commodities is used in conjunction with cash receipts to generate dynamic estimates of the systematic risk for each crop and state. In our study, we find that beta estimates from a time varying parameter model (FLS) and OLS formulation are substantially different. From our graphs of betas over time, one gains insight into the changing nature of risk and the impact of institutional and macroeconomic events. Systematic risk is shown to increase for most crops over the analyzed period with significant changes in volatility after the collapse of the Bretton Woods Accord.Systematic risk, flexible least squares, single index model, farm policy, macroeconomics, Agribusiness, Agricultural Finance, Consumer/Household Economics, Demand and Price Analysis, Farm Management, Financial Economics, Institutional and Behavioral Economics, Marketing, Risk and Uncertainty,

Identification of time-varying systems using multiresolution wavelet models

Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm

Spillover effects among financial institutions: a state-dependent sensitivity value-at-risk approach : [Version September 2012]

In this paper, we develop a state-dependent sensitivity value-at-risk (SDSVaR) approach that enables us to quantify the direction, size, and duration of risk spillovers among financial institutions as a function of the state of financial markets (tranquil, normal, and volatile). Within a system of quantile regressions for four sets of major financial institutions (commercial banks, investment banks, hedge funds, and insurance companies) we show that while small during normal times, equivalent shocks lead to considerable spillover effects in volatile market periods. Commercial banks and, especially, hedge funds appear to play a major role in the transmission of shocks to other financial institutions. Using daily data, we can trace out the spillover effects over time in a set of impulse response functions and find that they reach their peak after 10 to 15 days

A Comparative Study of Inequality and Corruption

We argue that income inequality increases the level of corruption through material and normative mechanisms. The wealthy have both greater motivation and opportunity to engage in corruption, while the poor are more vulnerable to extortion and less able to monitor and hold the rich and powerful accountable as inequality increases. Inequality also adversely affects peoples social norms about corruption and beliefs about the legitimacy of rules and institutions, and thereby makes it easier to tolerate corruption as acceptable behavior. Our comparative analysis of 129 countries utilizing two-staged least squares methods with a variety of instrumental variables supports our hypotheses, using different measures of corruption (the World Banks Control of Corruption Index and the Transparency Internationals Corruption Perceptions Index). The explanatory power of inequality is at least as important as conventionally accepted causes of corruption such as economic development. We also find a significant interaction effect between inequality and democracy, and evidence that inequality affects norms and perceptions about corruption, using the World Values Survey data. Since corruption also contributes to income inequality, societies often fall into vicious circles of inequality and corruption.This publication is Hauser Center Working Paper No. 22. The Hauser Center Working Paper Series was launched during the summer of 2000. The Series enables the Hauser Center to share with a broad audience important works-in-progress written by Hauser Center scholars and researchers

Dynamics and sparsity in latent threshold factor models: A study in multivariate EEG signal processing

We discuss Bayesian analysis of multivariate time series with dynamic factor models that exploit time-adaptive sparsity in model parametrizations via the latent threshold approach. One central focus is on the transfer responses of multiple interrelated series to underlying, dynamic latent factor processes. Structured priors on model hyper-parameters are key to the efficacy of dynamic latent thresholding, and MCMC-based computation enables model fitting and analysis. A detailed case study of electroencephalographic (EEG) data from experimental psychiatry highlights the use of latent threshold extensions of time-varying vector autoregressive and factor models. This study explores a class of dynamic transfer response factor models, extending prior Bayesian modeling of multiple EEG series and highlighting the practical utility of the latent thresholding concept in multivariate, non-stationary time series analysis.Comment: 27 pages, 13 figures, link to external web site for supplementary animated figure

Nonlinear association structures in flexible Bayesian additive joint models

Joint models of longitudinal and survival data have become an important tool for modeling associations between longitudinal biomarkers and event processes. The association between marker and log-hazard is assumed to be linear in existing shared random effects models, with this assumption usually remaining unchecked. We present an extended framework of flexible additive joint models that allows the estimation of nonlinear, covariate specific associations by making use of Bayesian P-splines. Our joint models are estimated in a Bayesian framework using structured additive predictors for all model components, allowing for great flexibility in the specification of smooth nonlinear, time-varying and random effects terms for longitudinal submodel, survival submodel and their association. The ability to capture truly linear and nonlinear associations is assessed in simulations and illustrated on the widely studied biomedical data on the rare fatal liver disease primary biliary cirrhosis. All methods are implemented in the R package bamlss to facilitate the application of this flexible joint model in practice.Comment: Changes to initial commit: minor language editing, additional information in Section 4, formatting in Supplementary Informatio