On Extreme Value Asymptotics of Projected Sample Covariances in High
Dimensions with Applications in Finance and Convolutional Networks
- URL: http://arxiv.org/abs/2310.08150v1
- Date: Thu, 12 Oct 2023 09:17:46 GMT
- Title: On Extreme Value Asymptotics of Projected Sample Covariances in High
Dimensions with Applications in Finance and Convolutional Networks
- Authors: Ansgar Steland
- Abstract summary: We show that Gumbel-type extreme values holds true within a linear time series framework.
As applications we discuss long-only mimimal-variance portfolio optimization and sub-portfolio analysis with respect to idiosyncratic risks.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Maximum-type statistics of certain functions of the sample covariance matrix
of high-dimensional vector time series are studied to statistically confirm or
reject the null hypothesis that a data set has been collected under normal
conditions. The approach generalizes the case of the maximal deviation of the
sample autocovariances function from its assumed values. Within a linear time
series framework it is shown that Gumbel-type extreme value asymptotics holds
true. As applications we discuss long-only mimimal-variance portfolio
optimization and subportfolio analysis with respect to idiosyncratic risks, ETF
index tracking by sparse tracking portfolios, convolutional deep learners for
image analysis and the analysis of array-of-sensors data.
Related papers
- Entrywise Inference for Missing Panel Data: A Simple and Instance-Optimal Approach [27.301741710016223]
We consider inferential questions associated with the missing data version of panel data induced by staggered adoption.
We develop and analyze a data-driven procedure for constructing entrywise confidence intervals with pre-specified coverage.
We prove non-asymptotic and high-probability bounds on its error in estimating each missing entry.
arXiv Detail & Related papers (2024-01-24T18:58:18Z) - Conformal inference for regression on Riemannian Manifolds [49.7719149179179]
We investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space.
We prove the almost sure convergence of the empirical version of these regions on the manifold to their population counterparts.
arXiv Detail & Related papers (2023-10-12T10:56:25Z) - Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region.
Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
arXiv Detail & Related papers (2022-02-23T06:11:49Z) - Nonconvex Stochastic Scaled-Gradient Descent and Generalized Eigenvector
Problems [98.34292831923335]
Motivated by the problem of online correlation analysis, we propose the emphStochastic Scaled-Gradient Descent (SSD) algorithm.
We bring these ideas together in an application to online correlation analysis, deriving for the first time an optimal one-time-scale algorithm with an explicit rate of local convergence to normality.
arXiv Detail & Related papers (2021-12-29T18:46:52Z) - Optimal regularizations for data generation with probabilistic graphical
models [0.0]
Empirically, well-chosen regularization schemes dramatically improve the quality of the inferred models.
We consider the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models.
arXiv Detail & Related papers (2021-12-02T14:45:16Z) - On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series [12.94486861344922]
We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional stationary time series.
A sparse-group lasso-based frequency-domain formulation of the problem is presented.
We also empirically investigate selection of the tuning parameters based on Bayesian information criterion.
arXiv Detail & Related papers (2021-11-15T16:52:02Z) - Heavy-tailed Streaming Statistical Estimation [58.70341336199497]
We consider the task of heavy-tailed statistical estimation given streaming $p$ samples.
We design a clipped gradient descent and provide an improved analysis under a more nuanced condition on the noise of gradients.
arXiv Detail & Related papers (2021-08-25T21:30:27Z) - Entropy Minimizing Matrix Factorization [102.26446204624885]
Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks.
In this study, an Entropy Minimizing Matrix Factorization framework (EMMF) is developed to tackle the above problem.
Considering that the outliers are usually much less than the normal samples, a new entropy loss function is established for matrix factorization.
arXiv Detail & Related papers (2021-03-24T21:08:43Z) - Asymptotic Errors for Teacher-Student Convex Generalized Linear Models
(or : How to Prove Kabashima's Replica Formula) [23.15629681360836]
We prove an analytical formula for the reconstruction performance of convex generalized linear models.
We show that an analytical continuation may be carried out to extend the result to convex (non-strongly) problems.
We illustrate our claim with numerical examples on mainstream learning methods.
arXiv Detail & Related papers (2020-06-11T16:26:35Z) - Asymptotic Analysis of an Ensemble of Randomly Projected Linear
Discriminants [94.46276668068327]
In [1], an ensemble of randomly projected linear discriminants is used to classify datasets.
We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator.
We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
arXiv Detail & Related papers (2020-04-17T12:47:04Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.