163,870 research outputs found
Change point analysis of second order characteristics in non-stationary time series
An important assumption in the work on testing for structural breaks in time
series consists in the fact that the model is formulated such that the
stochastic process under the null hypothesis of "no change-point" is
stationary. This assumption is crucial to derive (asymptotic) critical values
for the corresponding testing procedures using an elegant and powerful
mathematical theory, but it might be not very realistic from a practical point
of view.
This paper develops change point analysis under less restrictive assumptions
and deals with the problem of detecting change points in the marginal variance
and correlation structures of a non-stationary time series. A CUSUM approach is
proposed, which is used to test the "classical" hypothesis of the form vs. , where and
denote second order parameters of the process before and after a
change point. The asymptotic distribution of the CUSUM test statistic is
derived under the null hypothesis. This distribution depends in a complicated
way on the dependency structure of the nonlinear non-stationary time series and
a bootstrap approach is developed to generate critical values. The results are
then extended to test the hypothesis of a {\it non relevant change point}, i.e.
, which reflects the fact that
inference should not be changed, if the difference between the parameters
before and after the change-point is small.
In contrast to previous work, our approach does neither require the mean to
be constant nor - in the case of testing for lag -correlation - that the
mean, variance and fourth order joint cumulants are constant under the null
hypothesis. In particular, we allow that the variance has a change point at a
different location than the auto-covariance.Comment: 64 pages, 5 figure
Inference of synchrosqueezing transform -- toward a unified statistical analysis of nonlinear-type time-frequency analysis
We provide a statistical analysis of a tool in nonlinear-type time-frequency
analysis, the synchrosqueezing transform (SST), for both the null and non-null
cases. The intricate nonlinear interaction of different quantities in the SST
is quantified by carefully analyzing relevant multivariate complex Gaussian
random variables. Several new results for such random variables are provided,
and a central limit theorem result for the SST is established. The analysis
sheds lights on bridging time-frequency analysis to time series analysis and
diffusion geometry
Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget
In stochastic simulation, input uncertainty (IU) is caused by the error in
estimating the input distributions using finite real-world data. When it comes
to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the
failure of many existing selection procedures. In this paper, we study R&S
under IU by allowing the possibility of acquiring additional data. Two
classical R&S formulations are extended to account for IU: (i) for fixed
confidence, we consider when data arrive sequentially so that IU can be reduced
over time; (ii) for fixed budget, a joint budget is assumed to be available for
both collecting input data and running simulations. New procedures are proposed
for each formulation using the frameworks of Sequential Elimination and Optimal
Computing Budget Allocation, with theoretical guarantees provided accordingly
(e.g., upper bound on the expected running time and finite-sample bound on the
probability of false selection). Numerical results demonstrate the
effectiveness of our procedures through a multi-stage production-inventory
problem
A Generic Path Algorithm for Regularized Statistical Estimation
Regularization is widely used in statistics and machine learning to prevent
overfitting and gear solution towards prior information. In general, a
regularized estimation problem minimizes the sum of a loss function and a
penalty term. The penalty term is usually weighted by a tuning parameter and
encourages certain constraints on the parameters to be estimated. Particular
choices of constraints lead to the popular lasso, fused-lasso, and other
generalized penalized regression methods. Although there has been a lot
of research in this area, developing efficient optimization methods for many
nonseparable penalties remains a challenge. In this article we propose an exact
path solver based on ordinary differential equations (EPSODE) that works for
any convex loss function and can deal with generalized penalties as well
as more complicated regularization such as inequality constraints encountered
in shape-restricted regressions and nonparametric density estimation. In the
path following process, the solution path hits, exits, and slides along the
various constraints and vividly illustrates the tradeoffs between goodness of
fit and model parsimony. In practice, the EPSODE can be coupled with AIC, BIC,
or cross-validation to select an optimal tuning parameter. Our
applications to generalized regularized generalized linear models,
shape-restricted regressions, Gaussian graphical models, and nonparametric
density estimation showcase the potential of the EPSODE algorithm.Comment: 28 pages, 5 figure
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