High Dimensional Statistical Analysis and Related Topics
January 6-7, 2014, Waseda University
Building 63- 1 Meeting Room
( Supported by (A) 23244011 ( M. Taniguchi, Waseda Univ. )
早稲田大学理工研プロジェクト研究共催 ( Supported by GPIF )
早稲田大学理工学術院談話会共催
Program
January 6, 2014
13:30 - 14:15 : Discussion on “ High Dimensional Statistical Analysis “
Chaired by Masanobu Taniguchi ( Waseda Univ. )
14:15 - 15:00
Efficient influence function of coefficient functions of quantile regression
By Hiroyuki Taniai ( Waseda Univ. )
15:00 - 15:30
Coffee Break
15:30 - 16:15
Locally stationary time series factor models
By Junichi Hirukawa ( Niigata Univ. )
16:15 - 17:00
Generalized Least Squares Model Averaging,
By Qingfeng Liu ( Otaru University of Commerce ), Ryo Okui ( Kyoto Univ. )
and Arihiro Yoshimura ( Kyoto Univ. )
17:30 Buffet Style Dinner
January 7, 2014
10:30 - 11:00
Robust spectral estimation in time series analysis
By Yan Liu ( Waseda Univ. )
11:00 - 11:30
Nonparametric LAN approach for frequency domain GMM-type hypothesis testing
By Fumiya Akashi ( Waseda Univ. )
11:30 - 12:15 : General Discussion
12:15 - 13:45 : Lunch
13:45 - 14:45
Testing second order dynamics for autoregressive processes in presence of
time-varying variance.
By Hamdi Raissi ( Univ. Europeenne de Bretagne, France )
14:45 - 15:00 : Coffee Break
15:00 - 16:00
Nonparametric estimation of probability density functions for irregularly observed
spatial data
By Zudi Lu ( University of Southampton, U.K. )
16:00 - 17:00
The dynamic structure of high-dimensional factor models
By Marco Lippi ( Università di Roma - La Sapienza and EIEF )
Abstract ( High Dim Workshop )
(1) Efficient influence function of coefficient functions of quantile regression
By Hiroyuki Taniai ( Waseda Univ. )
Abstract.
As in Koenker and Xiao (2006), the Quantile Regression model has an interpretation as
the Random Coefficient Regression model where the coefficients are function of uniform
random variables. In this talk, we regard this as a kind of Mixture model by looking at
the covariate as a ``random nuisance parameter" whose distribution serves as mixing
distribution. So this can be seen as a infinite-dimensional version of Pfanzagl (1982),
Chapter 14. Consequently I derive the tangent space for the coefficient functions
(infinite-dimensional), and then present the form of efficient influence function (for
fixed probability $u$) as well. This will yield, together with the Donsker result for the
Regression Quantile Process indexed by $u$, the efficient inference of the coefficients as
functions. Further, if time allows, the corresponding estimation scheme may also be
discussed.
(2) Locally stationary time series factor models
By Junichi Hirukawa ( Niigata Univ.)
Abstract.
The factor modeling for multivariate time series from a dimension-reduction viewpoint
has been well developed under stationary and non-stationary setting. The inference is
simple in the sense that both the number of factors and the factor loadings are
estimated in terms of an eigenanalysis for a nonnegative definite matrix. However,
many results are described by the consistency of the estimators. In this talk we will
consider the factor modeling for multivariate locally stationary processes. Since we are
interested in the comparison between stationary setting and locally stationary setting,
the consistency results are not enough. The asymptotic normality or the mean squares
error will be required. Here, we will consider the asymptotic normality of the estimators
for locally stationary factor models.
(3) Generalized Least Squares Model Averaging,
By Qingfeng Liu ( Otaru University of Commerce ), Ryo Okui ( Kyoto Univ. )
and Arihiro Yoshimura ( Kyoto Univ. )
Abstract.
In this paper, we propose a method of averaging generalized least squares estimators
for linear regression models with heteroscedastic errors. The averaging weights are
chosen to minimize Mallows’ Cp-like criterion. We show that this method achieves
asymptotic optimality. It is also shown that asymptotic optimality holds even when the
variances of the error terms are estimated and the feasible generalized least squares
estimators are averaged. The variances can be estimated parametrically or
nonparametrically. Monte Carlo simulation results are encouraging. An empirical
example illustrates that the proposed method is useful for predicting a measure of firms’
performance.
Keywords: model averaging, GLS, FGLS, asymptotic optimality, Mallows’ Cp
JEL Classification: C51, C52
(4) Robust spectral estimation in time series analysis
By Yan Liu ( Waseda Univ. )
Abstract.
Periodogram plays a crucial role in the parameter estimation in time series analysis.
We generalize the idea of periodogram from a unified point of view of time series
regression. Central limit theorem for time series regression is discussed and some
robust aspects of the idea such as Laplace periodogram and generally quantile
periodogram are provided. We also link the idea with high dimensional time series data
and talk about the asymptotics of periodogram.
(5) Nonparametric LAN approach for frequency domain GMM-type hypothesis testing
By Fumiya Akashi ( Waseda Univ. )
Abstract.
This talk provides the asymptotic theory of testing for time series models. The approach
is mainly based on the concept of local asymptotic normality (LAN). The model
concerned is defined non-parametrically and the functional of the spectral density
summarizes information about pivotal quantities of the model. We consider test
statistics based on the generalized method of moments (GMM) and frequency domain
generalized empirical likelihood (FDGEL) saddle-point problem as in Kakizawa (2013).
Nonparametric alternatives are introduced to elucidate the local power of the tests, and
we discuss the local asymptotic optimality of the test statistics.
(6) Testing second order dynamics for autoregressive processes in presence of
time-varying variance.
By Hamdi Raissi ( Univ. Europeenne de Bretagne, France )
The volatility modeling for autoregressive univariate time series is considered. A
benchmark approach is the stationary ARCH model of Engle (1982).
Motivated by real data evidence, processes with nonconstant unconditional variance
and ARCH effects have been recently introduced. We take into account such possible
nonstationarity and propose simple testing procedures for ARCH effects. Adaptive
McLeod and Li's portmanteau and ARCH-LM tests for checking for second order
dynamics are provided. The standard versions of these tests, commonly used by
practitioners, suppose constant unconditional variance. We prove the failure of these
standard tests with time-varying unconditional variance. The theoretical results are
illustrated by mean of simulated and real data.
References:
Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the
variance of United Kingdom inflation. Econometrica 50, 987-1007.
(7) Nonparametric estimation of probability density functions for irregularly observed
spatial data
By Zudi Lu ( University of Southampton, U.K. )
Abstract.
Nonparametric estimation of probability density functions, both marginal and joint
densities, is a very useful tool in statistical modelling and computation. The kernel
method is popular and applicable to dependent data, including time series and spatial
data. But at least for the joint density, one has had to assume that data are observed at
regular time intervals or on a regular grid in space. Though this is not very restrictive
in the time series case, it often is in the spatial case. In fact, to a large degree it has
precluded applications of nonparametric methods to statistical modelling and
computation for spatial data because such data often are irregularly positioned over
space.
In this paper, we propose nonparametric kernel estimators for both the marginal and in
particular the joint probability density functions for non-gridded spatial data. Large
sample distributions of the proposed estimators are established under mild conditions,
and a new framework of expanding-domain infill asymptotics is suggested to overcome
the shortcomings of spatial asymptotics in the existing literature. A practical,
reasonable selection of the bandwidths on the basis of cross-validation is also proposed.
We illustrate by both simulations and real data examples of moderate sample size that
the proposed methodology is executive and useful in uncovering nonlinear spatial
dependence for general, including non-Gaussian, distributions.
This is a joint work with Dag Tjøstheim from Bergen, Norway. Lu's research was
financially supported from the Australian Research Council's Discovery Project and
Future Fellowships Grants, which are acknowledged.
(8) The dynamic structure of high-dimensional factor models
By Marco Lippi ( Università di Roma - La Sapienza and EIEF )
Abstract.
The talk will give a short, selected review of the literature on large dynamic factor
models: the basic representation results, applications to forecasting and structural
macroeconomic analysis, recent results and open problems. I will insist on the dynamic
structure of the model, special assumptions and their relaxation, the theory of tall
stochastic vectors, autoregressive representations for the common components. I will
provide motivation for models that cannot be put in the static form, both theoretical and
based on Monte Carlo experiments. I will also present results for the I(1) case and on
cointegration for tall stochastic vectors.