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2010年
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| 报告题目： |
On
the Estimation of Integrated Covariance Matrices of High Dimensional
Diffusion Processes |
| 报
告 人： |
Prof.
Yingying Li(Hong Kong University of Science and Technology)
|
| 时间地点： |
2010年6月13日15:00-16:00 思源楼703 |
| 摘 要： |
We
consider the estimation of integrated covariance matrices of
high dimensional diffusion processes by using high frequency
data. We start by studying the most commonly used estimator,
the realized covariance matrix (RCV). We show that in the high
dimensional case when the dimension p and the observation frequency
n grow in the same rate, the limiting empirical spectral distribution
of RCV depends on the covolatility processes not only through
the underlying integrated covariance matrix Sigma, but also
on how the covolatility processes vary in time. In particular,
for two high dimensional diffusion processes with the same integrated
covariance matrix, the empirical spectral distributions of their
RCVs can be very different. Hence in terms of making inference
about the spectrum of the integrated covariance matrix, the
RCV is in general \emph{not} a good proxy to rely on in the
high dimensional case. We then propose an alternative estimator,
the time-variation adjusted realized covariance matrix (TVARCV),
for a class of diffusion processes. We show that the limiting
empirical spectral distribution of our proposed estimator TVARCV
does depend solely on that of Sigma through a Marcenko-Pastur
equation, and hence the TVARCV can be used to recover the empirical
spectral distribution of Sigma by inverting the Marcenko-Pastur
equation, which can then be applied to further applications
such as portfolio allocation, risk management, etc..
This is based on Joint work with Xinghua Zheng..
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2008年
|
| 报告题目： |
One-step
Sparse Estimates in Nonconcave Penalized Likelihood Models |
| 报
告 人： |
Prof.
Runze Li (Associate Professor The Pennsylvania State University)
|
| 时间地点： |
2008年6月27日16:00-17:40 思源楼703 |
| 摘 要： |
Fan
and Li (2001) proposed a family of variable selection methods
via penalized likelihood using concave penalty functions. The
nonconcave penalized likelihood estimators enjoy the oracle
properties, but maximizing the penalized likelihood function
is computationally challenging, because the objective function
is nondifferentiable and nonconcave. In this article we propose
a new unified algorithm based on the local linear approximation
(LLA) for maximizing the penalized likelihood for a broad class
of concave penalty functions. Convergence and other theoretical
properties of the LLA algorithm are established. A distinguished
feature of the LLA algorithm is that at each LLA step, the LLA
estimator can naturally adopt a sparse representation. Thus
we suggest using the one-step LLA estimator from the LLA algorithm
as the final estimates. Statistically, we show that if the regularization
parameter is appropriately chosen, the one-step LLA estimates
enjoy the oracle properties with good initial estimators. Computationally,
the one-step LLA estimation methods dramatically reduce the
computational cost in maximizing the nonconcave penalized likelihood.
We conduct some Monte Carlo simulation to assess the finite
sample performance of the one-step sparse estimation methods.
The results are very encouraging.. |
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| 报告题目： |
Quotient
Correlation: A Sample Based Alternative To Pearson's Correlation |
| 报
告 人： |
Prof.
Zhengjun Zhang (Princeton University, USA) |
| 时间地点： |
2008年6月27日10:40-11:40 思源楼1013 |
| 摘 要： |
The
quotient correlation is defined here as an alternative to Pearson's
correlation that is more intuitive and flexible in cases where
the tail behavior of data is important. It measures nonlinear
dependence where the regular correlation coefficient is generally
not applicable. One of its most useful features is a test statistic
that has high power when testing nonlinear dependence in cases
where the Fisher's $Z$-transformation test may fail to reach
a right conclusion. Unlike most asymptotic test statistics,
which are either normal or $\chi2$, this test statistic has
a limiting gamma distribution (henceforth, the gamma test statistic).
More than the common usages of correlation, the quotient correlation
can easily and intuitively be adjusted to values at tails. This
adjustment generates two new concept -- the tail quotient correlation
and the tail independence test statistics, which are also gamma
statistics. Due to the fact that there is no analogue of the
correlation coefficient in extreme value theory, and there does
not exist an efficient tail independence test statistic, these
two new concepts may open up a new field of study. In addition,
an alternative to Spearman's rank correlation, a rank based
quotient correlation, is also defined. The advantages of using
these new concepts are illustrated with simulated data and real
data analysis of internet traffic and asset returns. |
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|
| 报告题目： |
Statistical
semiparametric detection of significant activation for brain
fMRI |
| 报
告 人： |
Prof.
Chunming Zhang (Associate Professor University of Wisconsin
) |
| 时间地点： |
2008年6月27日9:30-10:30 思源楼1013 |
| 摘 要： |
Functional
magnetic resonance imaging (fMRI) aims to locate activated regions
in human brains when specific tasks are performed. The conventional
tool for analyzing fMRI data applies some variant of the linear
model, which is restrictive in modeling assumptions. To yield
more accurate prediction of the time-course behavior of neuronal
responses, the semiparametric inference for the underlying hemodynamic
response function is developed to identify significantly activated
voxels. Under mild regularity conditions, we demonstrate that
a class of the proposed semiparametric test statistics, based
on the local linear estimation technique, follow chi-squared
distributions under null hypotheses for a number of useful hypotheses.
Furthermore, the asymptotic power functions of the constructed
tests are derived under the fixed and contiguous alternatives.
Simulation evaluations and real fMRI data application suggest
that the semiparametric inference procedure provides more efficient
detection of activated brain areas than the popular imaging
analysis tools AFNI and FSL. |
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2007年
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| 报告题目： |
Challenge
of Dimensionaly in Classifications and Feature Selection |
| 报
告 人： |
Prof.
Jianqing Fan(Princeton University, USA) |
| 时间地点： |
2007年12月27日9:30-10:30 思源楼703 |
| 摘 要： |
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| 报告题目： |
Regression
Analysis of Longitudinal Data with Outcome Dependent Observation
and Follow-up Times |
| 报
告 人： |
Prof.(Tony)
Jianguo Sun (University of Missouri, USA ) |
| 时间地点： |
2007年7月13日16:00-17:00
思源楼703 |
| 摘 要： |
Longitudinal
data frequently occur in many studies such as longitudinal follow-up
studies. To develop statistical methods and theory for the analysis
of them, independent or noninformative observation and censoring
times are typically assumed, which naturally leads to inference
procedures conditional on observation and censoring times (Diggle
et al., 1994; Lin and Ying, 2001). In many situations, however,
this may not be true or realistic. That is, longitudinal responses
may be correlated with observation times as well as censoring
time. This paper considers the analysis of longitudinal data
where these correlations may exist and a joint modeling approach
that uses some latent variables to characterize the correlations
is proposed. For inference about regression parameters, estimating
equation approaches are developed and both large and final sample
properties of the proposed estimators are established. The ethodology
is applied to a bladder cancer study that motivated this nvestigation. |
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| 报告题目： |
AGGREGATION
OF NONPARAMETRIC ESTIMATORS FOR VOLATILITY MATRIX |
| 报
告 人： |
Jianqing
Fan, Yingying Fan and Jinchi Lv (Princeton University) |
| 时间地点： |
2007年6月25日16:00-17:30
思源楼712 |
| 摘 要： |
An
aggregated method of nonparametric estimators based on time-domain
and state-domain estimators is proposed and studied. To attenuate
the curse of dimensionality, we propose a factor modeling strategy.
We first investigate the asymptotic behaviors of nonparametric
estimators of the volatility matrix in the time domain and in
the state domain. The asymptotic normality is separately established
for nonparametric estimators in the time domain and state domain.
These two estimators are asymptotically independent. Hence,
they can be combined, through a dynamic weighting scheme, to
improve the efficiency of the estimated volatility matrix. The
optimal dynamic weights are derived and it is shown that the
aggregated estimator uniformly dominates the volatility matrix
estimators using time-domain or state-domain smoothing alone.
A simulation study, based on an essentially affine model for
the term structure, is conducted and it demonstrates convincingly
that the newly proposed procedure outperforms both time- and
state-domain estimators. Empirical studies endorse further the
advantages of our aggregated method |
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| 报告题目： |
Analysis
of Longitudinal Data with Semiparametric Estimation of Covariance
Function |
| 报
告 人： |
Runze
Li: Associate Professor (The Pennsylvania State University)
|
| 时间地点： |
2007年5月18日15:30-16:30
晨兴中心605 |
| 摘 要： |
Improving
efficiency for regression coefficients and predicting trajectories
of individuals are two important aspects in analysis of longitudinal
data. Both involve estimation of the covariance function. Yet,
challenges arise in estimating the covariance function of longitudinal
data collected at irregular time points. A class of semiparametric
models for the covariance function is proposed by imposing a
parametric correlation structure while allowing a nonparametric
variance function. A kernel estimator is developed for the estimation
of the nonparametric variance function. Two methods, a quasi-likelihood
approach and a minimum generalized variance method, are proposed
for estimating parameters in the correlation structure. We introduce
a semiparametric varying coefficient partially linear model
for longitudinal data and propose an estimation procedure for
model coefficients by using a profile weighted least squares
approach. Sampling properties of the proposed estimation procedures
are studied and asymptotic normality of the resulting estimators
is established. Finite sample performance of the proposed procedures
is assessed by Monte Carlo simulation studies. The proposed
methodology is illustrated by an analysis of a real data example. |
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| 报告题目： |
Accelerated
Life and Degradation Models with Dynamic Environment |
| 报
告 人： |
Prof.Mikhail
Nikulin (Statistique Mathématique et ses Applications, Victor
Segalen University) |
| 时间地点： |
2006年12月12日16:00-17:00
思源楼712 |
| 摘 要： |
We
consider here the statistical models with dynamic environment
describing dependence of the lifetime distribution on the time-dependent
explanatory variables. Such models are used in reliability and
survival analysis to study the reliability of aging bio-technical
system, in dependence on their longevity, fatigue and degradation
under different conditions of exploration. The reliability theory
gives a general approach for construction of efficient statistical
models in terms of failure rates to study aging and degradation
problems in different areas such as industrial engineering and
technology, biophysics, biology, demography, radiobiology, genetics,
biostatistics, survival analysis, business and finance, etc...
We shall discuss the problems of statistical modelling and of
choice of design in accelerated life testing to obtain the statistical
estimators of the main reliability characteristics of aging
systems. |
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| 报告题目： |
Nonlinear
Dependency and Its Application |
| 报
告 人： |
Wei
Gang (魏刚).(School of Mathematics and System Sciences Shandong
University ) |
| 时间地点： |
2006年11月17日16:00-17:00
思源楼703 |
| 摘 要： |
The
normal distribution and the linear model have been taken as
the central part classical statistic inference in both theory
and application. In the last decade, with the demand from the
social, medical, and industrial sciences, the nonlinear dependency
characterized by the partial ordering, copula construction,
and nonparametric dependency have shown great potentials in
their theoretical challenges and applied statistics. In this
talk, we particularly demonstrate the rich mathematical structures
constructed with the aid of copula analysis and some simple
but important applications of such non-classical statistical
inference techniques. |
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| 报告题目： |
Tree-Structured
Survival Analysis Based on Variance of Survival Time |
| 报
告 人： |
Hua
Jin, Ph.D.(School of Mathematical Sciences, South China Normal
University) |
| 时间地点： |
2006年10月19日10:30 |
| 摘 要： |
Tree structured
survival analysis (TSSA) is a popular alternative to the Cox
proportional hazards regression in medical research of survival
data. Several methods for constructing a tree of different
survival profiles have been developed, including one based
on two-sample log-rank test statistics and martingale -type
residuals.
Lu, Jin and Mi
used variance of restricted mean lifetimes as an index of
degree of separation (DOS) to measure the efficiency in separations
of survival profiles by a classification method. They proposed
a hypothesis testing procedure for comparison of two classification
rules, especially for non-inferiority test.
Our objective
here is to explore the use of DOS in TSSA. We propose an algorithm
in a similar fashion to the least square regression tree for
survival analysis. We apply the proposed method to prospective
cohort data from the Study of Osteoporotic Fracture that motivated
our research and then compare our classification rule to those
rules based on the log-rank statistics and martingale residuals.
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| 报告题目： |
Bayesian
Methods for Inferring Epistasis |
| 报
告 人： |
Prof.
Jun Liu (Department of Statistics, Harvard University) |
| 时间地点： |
2006年7月24日（周一）
下午2:00 思源楼712 |
| 摘 要： |
I
will discuss a Bayesian approach in detecting multi-locus interactions
(Epistasis) for case-control association studies. Existing methods
are either of low power or computationally infeasible when facing
of a large number of markers. Using MCMC sampling techniques,
the method can efficiently detect interactions among thousands
of markers. I will also discuss the issue of statistical significance
and how to adjust multiple comparisons in this situation (much
of these are conjectures, though). |
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| 报告题目： |
Embracing
Statistical Challenges in the Information Technology Age |
| 报
告 人： |
Prof.
Bin Yu(Department of Statistics, University of California, Berkeley
) |
| 时间地点： |
2006年7月20日（周四） 上午10：00 思源楼703 |
| 摘 要： |
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| 报告题目： |
Bayesian
Hierarchical Modeling for Integrating Low-accuracy and High-accuracy
Experiments |
| 报
告 人： |
Prof.Jeff
Wu (Georgia Institute of Technology School of Industrial and
Systems Engineering ) |
| 时间地点： |
2006年7月14日（周五）
上午10：00 思源楼712 |
| 摘 要： |
Standard
practice in analyzing data from different types of experiments
is to treat data from each type separately. By borrowing strength
across multiple sources, an integrated analysis can produce
better results. Careful adjustments need to be made to incorporate
the systematic differences among various experiments. To this
end, some Bayesian hierarchical Gaussian process models (BHGP)
are proposed. The heterogeneity among different sources is accounted
for by performing flexible location and scale adjustments. The
approach tends to produce prediction closer to that from the
high-accuracy experiment. The Bayesian computations are aided
by the use of Markov chain Monte Carlo and Sample Average Approximation
algorithms. The proposed method is illustrated with two examples:
one with detailed and approximate finite elements simulations
for mechanical material design and the other with physical and
computer experiments. |
| |
| 报告题目： |
Fast
Functional MRI |
| 报
告 人： |
Prof.
Cun-Hui Zhang (Department of Statistics, Rutgers University,
USA ) |
| 时间地点： |
2006年6月22日（星期四)
下午 4:00--5:00 思源楼703 |
| 摘 要： |
We
develop fast functional MRI methods to improve the time-resolution
of the current functional MRI technology by sampling a small
fraction of the Fourier transform of the spin density, and using
a prolate wave filter to approximately obtain, not the usual
susceptibility map, but instead the integral of this quantity
over regions of interest in the brain at successive time-points.
The aim of this space/time trade-off is to obtain, at high time-resolution,
the total activity in these regions which processes the specific
stimulus/task, and more important in studying higher cognition,
the sequence of occurrences of these processes. An fMRI experiment
will be reviewed and discussed. This is joint work with Gary
Glover, Martin Lindquist and Larry Shepp. |
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| 报告题目： |
Statistical
Challenges with High Dimensionality in Feature Selection |
| 报
告 人： |
Prof.
Jianqing Fan (Princeton University, USA ) |
| 时间地点： |
2006年6月2日（星期五)
上午 10:00--11:00 思源楼712 |
| 摘 要： |
Technological
innovations have revolutionized the process of scientific research
and knowledge discovery. The availability of massive data and
challenges from frontiers of research and development have reshaped
statistical thinking, data analysis and theoretical studies.
The challenges of high-dimensionality arise in diverse fields
of sciences and the humanities, ranging from computational biology
and health studies to financial engineering and risk management.
In all of these fields, variable selection and feature extraction
are crucial for knowledge discovery. We first give a comprehensive
overview of statistical challenges with high dimensionality
in these diverse disciplines. We then approach the problem of
variable selection and feature extraction using a unified framework:
penalized likelihood methods. Issues relevant to the choice
of penalty functions are addressed. We demonstrate that for
a host of statistical problems, as long as the dimensionality
is not excessively large, we can estimate the model parameters
as well as if the best model is known in advance. The persistence
property in risk minimization is also addressed. The applicability
of such a theory and method to diverse statistical problems
is demonstrated. Other related problems with high-dimensionality
are also discussed. |
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|
| 报告题目： |
Semi/Non-parametric
Dynamic Quantile Regression Models and Their Applications |
| 报
告 人： |
Prof.
Zongwu Cai (Department of Mathematics and Statistics & Department
of Economics, University of North Carolina, Charlotte, USA) |
| 时间地点： |
2006年4月8日（星期六)
下午 4:00--5:00 思源楼712 |
| 摘 要： |
In
this talk, first I will briefly review some semiparametric and
nonparametric regression models for time series data and their
applications such as value-at-risk. In particular, I will focus
on a class of smooth coefficient quantile regression time series
models based on some applications. We employ a local linear
fitting scheme to estimate the smooth coefficients in the quantile
framework. The programming involved in the local linear quantile
estimation is relatively simple and it can be modified with
few efforts from the existing programs for the linear quantile
model. We derive the local Bahadur representation of the local
linear estimator for alpha-mixing time series and establish
the asymptotic normality of the resulting estimator. The asymptotic
behaviors of the estimator at the boundaries are examined. A
comparison of the local linear quantile estimator with the local
constant estimator is presented. A simulation study is carried
out to illustrate the performance of the estimates. An empirical
application of the model to the exchange rate time series data
and the well-known Boston house price data further demonstrates
the potential of the proposed modeling procedures. |
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|
| 报告题目： |
Additive
models for spatial processes |
| 报
告 人： |
Dag
Tjostheim 院士（Department of Mathematics,University of Bergen,
Norway） |
| 时间地点： |
2006年4月11日（星期二）下午 4:00--5:00 思源楼712
|
| 摘 要： |
|
|
|
| 报告题目： |
Estimating
Marginal Survival Under Dependent Censoring |
| 报
告 人： |
Donglin
Zeng (Assistant Professor)(Department of Biostatistics, University
of North Carolina (Chapel Hill) ) |
| 时间地点： |
2006年4月13日（星期四）下午
2:00--3:00 思源楼712 |
| 摘 要： |
One
goal in survival analysis of right censored data is to estimate
marginal survival function in the presence of dependent censoring.
When many auxiliary covariates are sufficient to explain the
dependent censoring, estimation based on either semiparametric
model or nonparametric model of the conditional survival function
can be problematic due to the high-dimensionality of the auxiliary
information. In this paper, we use two working models to condense
these high-dimensional covariates in dimension reduction; then
an estimate of the marginal survival function can be derived
non-parametrically in a low-dimension space. We show that such
an estimator has the following double robust property: when
either working model is correct, the estimator is consistent
and asymptotically Gaussian; when both working models are correct,
the asymptotic variance attains the efficiency bound. |
| |
| 报告题目： |
Maximum
Likelihood Estimation in Semiparametric Transformation Models
for Counting Processes |
| 报
告 人： |
Donglin
Zeng (Assistant Professor) (Department of Biostatistics, University
of North Carolina (Chapel Hill) ) |
| 时间地点： |
2006年4月18日（星期二）下午
2:00--3:00 思源楼712 |
| 摘 要： |
A
class of semiparametric transformation models is proposed to
characterize the effects of possibly time-varying covariates
on the intensity functions of counting processes. The class
includes the proportional intensity model and linear transformation
models as special cases. Nonparametric maximum likelihood estimators
are developed for the regression parameters and cumulative intensity
functions of these models based on censored data. The estimators
are shown to be consistent and asymptotically normal. The limiting
variances for the estimators of the regression parameters achieve
the semiparametric efficiency bounds and can be consistently
estimated. The limiting variances for the estimators of smooth
functionals of the cumulative intensity function can also be
consistently estimated. Simulation studies reveal that the proposed
inference procedures perform well in practical settings. Two
medical studies are provided. |
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|
| 报告题目： |
Semiparametric
Transformation Models for Survival Data with a Cure Fraction |
| 报
告 人： |
Donglin
Zeng (Assistant Professor) (Department of Biostatistics, University
of North Carolina (Chapel Hill) ) |
| 时间地点： |
2006年4月19日（星期三）下午
2:00--3:00 思源楼712 |
| 摘 要： |
We
propose a class of transformation models for survival data with
a cure fraction. The class of transformation models is motivated
by biological considerations, and it includes both the proportional
hazards and the proportional odds cure models as two special
cases. An efficient recursive algorithm is proposed to calculate
the maximum likelihood estimators. Furthermore, the maximum
likelihood estimators for the regression coefficients are shown
to be consistent and asymptotically normal, and their asymptotic
variances attain the semiparametric efficiency bound. Simulation
studies are conducted to examine the finite sample properties
of the proposed estimators. The method is illustrated on data
from a clinical trial involving the treatment of melanoma. |