STATISTICS - THEORY AND PRACTICE
Title: Order Thresholding
Mike Akritas,
Abstract: When testing against a
high-dimensional alternative, omnibus test designed to detect any departure
from the null hypothesis have low power. Neyman's
(1937) truncation idea, though motivated by a different type of problem, served
as the spring board for the related approaches of adaptive truncation, and soft
and hard thresholding (cf. Donoho
and Johnstone, 1994, Fan and Lin, 1998, Spokoiny, 1996). This talk presents a new thresholding method, called order thresholding,
based on L-statistics. Numerical comparisons with existing thresholding
methods, and an extension to testing problems in
high-dimensional factorial designs are presented.
Title: Negative Dependence and the Simes Inequality
Henry W.
Block, Thomas H. Savits and Jie
Wang,
Abstract: It is shown that the Simes Inequality is reversed for a broad class of
negatively dependent distributions. This resolves a conjecture of Sarkar (Ann. Stat. 26, 1998, 494-504).
Title: Rich Transformation Models and More.
Kjell Doksum,
Abstract: Regression transformation models are
models where an increasing transformation of the response satisfies a linear
model in terms of increasing transformations of covariates. Richard Johnson and
his collaborators have proposed such models. These will be discussed along with
other proposals such as the Box-Cox transformation model. Properties of
statistical procedures will be considered for two cases: The case where the
transformation is known and the case where the transformation is unknown and
needs to be estimated. Conditions under which properties of statistical
procedures are asymptotically the same for these two cases will be presented.
Title: Finite Markov Chain Imbedding and Its
Application To Matching Probability Between Two Markov
Dependent DNA Sequences
James C.
Fu,
Abstract: In this talk, the concept of finite
Markov chain imbedding technique for studying the distributions of runs and
patterns in a sequence of multi-state trials will be introduced. The method is
extended to study the distribution of the longest matching between two Markov
dependent DNA sequences. The method is very simple, efficient and accurate. To
illustrate the method, numerical results on matching probabilities for both i.i.d. and Markov dependent sequences will be presented.
Title: Regression Model Checking with Long
Memory Design and Errors
Hira L. Koul,
Abstract: This talk will discuss a test for
fitting a parametric regression model with long memory (LM) Gaussian design and
nonparametric heteroscedastic LM moving average
errors. The asymptotic null distribution of these tests will be discussed in
some detail. The proposed test is illustrated by fitting a linear regression
model between the two currency exchange rate data sets that exhibit LM.
Title: Some statistical applications in the
financial services industry
Wenqing Lu, HSBC
Abstract: With rich credit bureau data,
financial service providers rely on statistical analysis and modeling
techniques to make decisions on direct marketing, pricing, and risk management.
This talk reviews some common statistical methods used to improve decision
making in the financial industry. The nature of economical cycle can make the
statistical prediction very challenging as demonstrated in this new credit
crisis. The presenter has work experience at Fair Isaac & Co, Washington
Mutual, and HSBC.
Title: Block sampler for univariate
and multivariate asymmetric stochastic volatility models
Yasuhiro
Omori,
Abstract: We discuss an efficient Markov chain
Title: Revisiting Local Asymptotic Normality
(LAN) and Passing on to Local Asymptotic Mixed Normality (LAMN)
George G.
Roussas,
Abstract: The standard set-up of Locally
Asymptotically Normal families of probability measures is revisited, and the
basic asymptotic results are reviewed. In the form of applications, some
statistical examples are considered, in the framework of hypotheses testing and
asymptotic efficiency of estimates. Also, some generalizations are mentioned.
Certain families of probability measures do not enjoy the property of being
Locally Asymptotically Normal, but rather they are what has
been termed as Locally Asymptotically Mixed Normal. Such families are briefly
considered, and some general results are indicated.
Title: Confidence Regions for Parameters of
Linear Models
Andrew L.
Rukhin, National Institute of Standards and Technology
and
Abstract: A method is suggested for constructing
a conservative confidence region for the parameters of a general linear model
on the basis of a linear estimator. In meta-analytical applications, when the
results of independent but heterogeneous studies are to be combined, this
region can be employed with little to no
knowledge of error variances. The required optimization
problem is formulated and some properties of its solution are described. The
motivating example is a study in which several laboratories performed
measurements via different techniques of gold vapor pressure as a function of
the absolute temperature.
Title: System Signatures in Dynamic Reliability
Settings
Francisco
J. Samaniego,
Abstract: The concept of the 'signature' of an
engineered system is described, and some basic representation and preservation
theorems concerning them are reviewed. We then define the dynamic signature of
a system, conditioned on the events that the system is working at the
inspection time t and that exactly i components have
failed by time t, assuming these events are compatible. Applications of dynamic
signatures to nonparametric modeling in reliability and to the engineering practice
of "burn in" are treated is some detail. This work is joint with N. Balakrishnan and J.
Navarro.
Title: Rates of convergence for estimators of
convolutions of densities
Anton
Schick, SUNY Binghampton
Abstract: The goal of this talk is to give an
overview of various types of convergence results for estimating the convolution
of a density with itself. The estimator of this convolution is a local
U-statistic based on a random sample from the base density. The surprising fact
is that under rather mild assumptions on the base density this estimator has a
convergence rate of the order root-n, point-wise and in various norms, and
(functional) central limit theorems can be proved in the corresponding normed spaces. Integrability
conditions on the base density are key to these
results. A violation of these conditions results in slower rates of
convergence. The behavior of the local U-statistic is now similar to that of
kernel estimators with the customary trade-off between bias and variance terms.
These slower rates of convergence, however, are still faster than the optimal
rates of convergence for kernel estimators based on a sample from the
convolution.
TIitle: Intrinsic Aging and Classes of Nonparametric
Distributions
Moshe Shaked, Rhonda
Righter and J. George Shanthikumar),
Abstract: A general framework is developed for
understanding the nonparametric (aging) properties of nonnegative random
variables. For this purpose considered are aging properties of various residual
and conditional lifetimes. The notion of intrinsic aging is also used, and the
aging properties of the intrinsic life and the actual life are related. Some
new concepts of aging are introduced as a result of the general setup. Several
recent results in the literature are special cases of the general results.
Title: A Bivariate
Generalized von Mises Distribution with Applications
to Circular Genomes
Grace S. Shieh, Academia
Abstract: Recent studies show that gene order is
extensively conserved between closely related species, but rapidly became less
conserved among more distantly related species. Furthermore, this trend is
likely to be universal in prokaryotes (Tamames, 2001;
Wolf, 2001). Therefore, gene order conservation is a valid phylogenetic
measure (Bentley and Pankhillm, 2004), and we propose
to infer evolutionary independence and distance of any pair of circular
genomes, which constitute 476 (each having single chromosome) among 566
prokaryotic Genomes (NCBI,
bivariate distribution with generalized von Mises distributions (BGVM) is proposed to model a pair of
circular genomes. Some distributional properties of BGVM are addressed. Maximum
likelihood estimation and a likelihood ratio test for independence are
developed. The procedures are applied to three pairs of circular genomes to
infer their evolutionary independence; after the independence hypothesis has
been rejected, their evolutionary distances are also estimated. These results
are consistent with those based on different types of data or different
methods. Future work on a new measure of association between paired circular
genomes will also be discussed.
Title: On Competing Risks and Degradation
Processes: Modeling and Inferential Issues
Nozer Singpurwalla,
Title: The Five Most Consequential Ideas in the
History of Statistics
Stephen
M. Stigler,
Abstract: Modern statistics invariably and
understandably focuses upon the latest in technique and technology. The history
of statistics permits a broader view and can identify ideas that not only have
driven development but also retain contemporary relevance. The five most
influential of these are identified. What are they? Surely, you may say, they
would include Bayes’s Theorem? But
no. Nor does the list include important ideas such as cross-validation
or the bootstrap, rank or robust statistics, simulation or loglinear
models. What then would be on the list? You may be surprised.
Title: Model estimation, checking and evaluation
via prediction
L.J. Wei,
Abstract: Recent technology
advancements for obtaining bio- and genetic-markers have drastically enhanced
the knowledge of certain disease processes and the potential for accurately
predicting patient’s clinical outcomes. Traditional statistical methods for the
so-called individualized/personalized medicine with such markers are derived
under a rather strong assumption, that is, one can accurately identify the true
model (at least for the large sample case), which relates the predictors to
their corresponding clinical phenotype variable(s). In practice, however, it is
difficult if not impossible, even to identify the class of models which
contains the true one. Therefore, it is interesting and important to
investigate whether the standard statistical methods for model estimation,
evaluation and comparisons can be modified when the fitted model may not be
correctly specified. In this talk, we discuss new procedures for predicting
future observations and for evaluating and comparing prediction rules. One key
feature of the proposals is that their validity does not require that
assumption that the fitted models are correct. Moreover, the new proposal
provides a reliability measure of the estimated prediction precision, an important
component for model evaluation and checking. The new methods are illustrated
with examples with continuous, binary and censored responses.