492,502 research outputs found
Minimax Optimality of CUSUM for an Autoregressive Model
Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others the change is in the unconditional distribution. Some models include an observation before the first possible change time â others not. Earlier and new CUSUM type methods are given and minimax optimality is examined. For the conditional model with an observation before the possible change there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.Autoregressive; Change point; Monitoring; Online detection
Correlation Structures of Correlated Binomial Models and Implied Default Distribution
We show how to analyze and interpret the correlation structures, the
conditional expectation values and correlation coefficients of exchangeable
Bernoulli random variables. We study implied default distributions for the
iTraxx-CJ tranches and some popular probabilistic models, including the
Gaussian copula model, Beta binomial distribution model and long-range Ising
model. We interpret the differences in their profiles in terms of the
correlation structures. The implied default distribution has singular
correlation structures, reflecting the credit market implications. We point out
two possible origins of the singular behavior.Comment: 16 pages, 7 figure
Effects of correlation between merging steps on the global halo formation
The excursion set theory of halo formation is modified by adopting the
fractional Brownian motion, to account for possible correlation between merging
steps. We worked out analytically the conditional mass function, halo merging
rate and formation time distribution in the spherical collapse model. We also
developed an approximation for the ellipsoidal collapse model and applied it to
the calculation of the conditional mass function and the halo formation time
distribution. For models in which the steps are positively correlated, the halo
merger rate is enhanced when the accreted mass is less than , while
for the negatively correlated case this rate is reduced. Compared with the
standard model in which the steps are uncorrelated, the models with positively
correlated steps produce more aged population in small mass halos and more
younger population in large mass halos, while for the models with negatively
correlated steps the opposite is true. An examination of simulation results
shows that a weakly positive correlation between successive merging steps
appears to fit best. We have also found a systematic effect in the measured
mass function due to the finite volume of simulations. In future work, this
will be included in the halo model to accurately predict the three point
correlation function estimated from simulations.Comment: 8 pages, submitted to MNRA
Modeling Inter-Dependence Between Time and Mark in Multivariate Temporal Point Processes
Temporal Point Processes (TPP) are probabilistic generative frameworks. They
model discrete event sequences localized in continuous time. Generally,
real-life events reveal descriptive information, known as marks. Marked TPPs
model time and marks of the event together for practical relevance. Conditioned
on past events, marked TPPs aim to learn the joint distribution of the time and
the mark of the next event. For simplicity, conditionally independent TPP
models assume time and marks are independent given event history. They
factorize the conditional joint distribution of time and mark into the product
of individual conditional distributions. This structural limitation in the
design of TPP models hurt the predictive performance on entangled time and mark
interactions. In this work, we model the conditional inter-dependence of time
and mark to overcome the limitations of conditionally independent models. We
construct a multivariate TPP conditioning the time distribution on the current
event mark in addition to past events. Besides the conventional intensity-based
models for conditional joint distribution, we also draw on flexible
intensity-free TPP models from the literature. The proposed TPP models
outperform conditionally independent and dependent models in standard
prediction tasks. Our experimentation on various datasets with multiple
evaluation metrics highlights the merit of the proposed approach
Non-Gaussian buoyancy statistics in fingering convection
We examine the statistics of active scalar fluctuations in high-Rayleigh
number fingering convection with high-resolution three-dimensional numerical
experiments. The one-point distribution of buoyancy fluctuations is found to
present significantly non-Gaussian tails.
A modified theory based on an original approach by Yakhot (1989) is used to
model the active scalar distributions as a function of the conditional
expectation values of scalar dissipation and fluxes in the flow. Simple models
for these two quantities highlight the role of blob-like coherent structures
for scalar statistics in fingering convection
Local identification in nonseparable models
Conditions are derived under which there is local nonpara
metric identification of values of structural functions and of their derivatives in potentially nonlinear nonseparable models. The attack on this problem is via conditional quantile functions and exploits local quantile independence conditions. The identification conditions include local analogues of the order and rank conditions familiar in the analysis of linear simultaneous equations models. The derivatives whose identification is sought are derivatives of structural equations at a point defined by values of covariates and quantiles of the distributions of the stochastic drivers of the system. These objects convey information about the distribution of the exogenous impact of changes in variables potentially endogenous in the data generating process. The identification conditions point directly to analogue estimators of derivatives of structural functions which are functionals of quantile regression function estimators
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