Testing for symmetry and conditional symmetry using asymmetric kernels

The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-014-0469-6.e financial support from the ESRC under the grant RES-062-23-0311 (Fernandes), from the ARC grant DP0988579 (Mendes), and from the SNSF through the NCCR Finrisk (Scaillet).ESRC under the grant RES-062-23-0311 (Fernandes), from the ARC grant DP0988579 (Mendes), and from the SNSF through the NCCR Finrisk (Scaillet)

"Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes"

This paper considers a nonstandard kernel regression for strongly mixing processes when the regressor is nonnegative. The nonparametric regression is implemented using asymmetric kernels [Gamma (Chen, 2000b), Inverse Gaussian and Reciprocal Inverse Gaussian (Scaillet, 2004) kernels] that possess some appealing properties such as lack of boundary bias and adaptability in the amount of smoothing. The paper investigates the asymptotic and finite-sample properties of the asymmetric kernel Nadaraya-Watson, local linear, and re-weighted Nadaraya-Watson estimators. Pointwise weak consistency, rates of convergence and asymptotic normality are established for each of these estimators. As an important economic application of asymmetric kernel regression estimators, we reexamine the problem of estimating scalar diffusion processes.

Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators

We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [0, ¥). We provide a unifying framework which contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature. This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification. We further develop a specification test to determine if a density belongs to a particular parametric family. The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are simple to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.semiparametric density estimation; asymmetric kernel; income distribution; loss distribution; health insurance; specification testing

Capturing the zero: a new class of zero-augmented distributions and multiplicative error processes

We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed on high frequencies, such as cumulated trading volumes or the time between potentially simultaneously occurring market events. We introduce a flexible pointmass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of liquid NYSE stocks, we show that the model captures both the dynamic and distribution properties of the data very well and is able to correctly predict future distributions. Keywords: High-frequency Data , Point-mass Mixture , Multiplicative Error Model , Excess Zeros , Semiparametric Specification Test , Market Microstructure JEL Classification: C22, C25, C14, C16, C5

Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes

We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed on high frequencies, such as cumulated trading volumes or the time between potentially simultaneously occurring market events. We introduce a flexible point-mass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of liquid NYSE stocks, we show that the model captures both the dynamic and distribution properties of the data very well and is able to correctly predict future distributions.high-frequency data, point-mass mixture, multiplicative error model, excess zeros, semiparametric specification test, market microstructure

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications

The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of computers. Multiple sources in the literature deal with local approximations of the noncentral Wishart distribution with respect to its central counterpart. However, no source has yet developed explicit local approximations for the (central) Wishart distribution in terms of a normal analogue, which is important since Gaussian distributions are at the heart of the asymptotic theory for many statistical methods. In this paper, we prove a precise asymptotic expansion for the ratio of the Wishart density to the symmetric matrix-variate normal density with the same mean and covariances. The result is then used to derive an upper bound on the total variation between the corresponding probability measures and to find the pointwise variance of a new density estimator on the space of positive definite matrices with a Wishart asymmetric kernel. For the sake of completeness, we also find expressions for the pointwise bias of our new estimator, the pointwise variance as we move towards the boundary of its support, the mean squared error, the mean integrated squared error away from the boundary, and we prove its asymptotic normality.Comment: 17 pages, 2 figure

A study of seven asymmetric kernels for the estimation of cumulative distribution functions

In Mombeni et al. (2019), Birnbaum-Saunders and Weibull kernel estimators were introduced for the estimation of cumulative distribution functions (c.d.f.s) supported on the half-line $[0,\infty)$. They were the first authors to use asymmetric kernels in the context of c.d.f. estimation. Their estimators were shown to perform better numerically than traditional methods such as the basic kernel method and the boundary modified version from Tenreiro (2013). In the present paper, we complement their study by introducing five new asymmetric kernel c.d.f. estimators, namely the Gamma, inverse Gamma, lognormal, inverse Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these five new estimators, we prove the asymptotic normality and we find asymptotic expressions for the following quantities: bias, variance, mean squared error and mean integrated squared error. A numerical study then compares the performance of the five new c.d.f. estimators against traditional methods and the Birnbaum-Saunders and Weibull kernel c.d.f. estimators from Mombeni et al. (2019). By using the same experimental design, we show that the lognormal and Birnbaum-Saunders kernel c.d.f. estimators perform the best overall, while the other asymmetric kernel estimators are sometimes better but always at least competitive against the boundary kernel method.Comment: 38 pages, 2 tables, 9 figure

Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds

We describe the quantization of 2-plectic manifolds as they arise in the context of the quantum geometry of M-branes and non-geometric flux compactifications of closed string theory. We review the groupoid approach to quantizing Poisson manifolds in detail, and then extend it to the loop spaces of 2-plectic manifolds, which are naturally symplectic manifolds. In particular, we discuss the groupoid quantization of the loop spaces of R^3, T^3 and S^3, and derive some interesting implications which match physical expectations from string theory and M-theory.Comment: 71 pages, v2: references adde