Searcharxiv⌕ Search

SEARCH · Searcharxiv

Results for “stat.OT”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3Linked to original sources
arXiv2011

Model Selection in Undirected Graphical Models with the Elastic Net

Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associated with a Gaussian Markov Random Field (GMRF), the Ising model and the Potts model, by extending previous work on $l_1$ regularized neighborhood estimation to include the elastic net $l_1+l_2$ penalty. Additionally, we show numerical evidence that the edge density plays a role in the graph recovery process. Finally, we introduce a novel method for augmenting neighborhood estimation by leveraging pair-wise neighborhood union estimates.

stat.OT↗
arXiv2012

Performance-based regularization in mean-CVaR portfolio optimization

We introduce performance-based regularization (PBR), a new approach to addressing estimation risk in data-driven optimization, to mean-CVaR portfolio optimization. We assume the available log-return data is iid, and detail the approach for two cases: nonparametric and parametric (the log-return distribution belongs in the elliptical family). The nonparametric PBR method penalizes portfolios with large variability in mean and CVaR estimations. The parametric PBR method solves the empirical Markowitz problem instead of the empirical mean-CVaR problem, as the solutions of the Markowitz and mean-CVaR problems are equivalent when the log-return distribution is elliptical. We derive the asymptotic behavior of the nonparametric PBR solution, which leads to insight into the effect of penalization, and justification of the parametric PBR method. We also show via simulations that the PBR methods produce efficient frontiers that are, on average, closer to the population efficient frontier than the empirical approach to the mean-CVaR problem, with less variability.

q-fin.PM↗
arXiv2011

On a connection between Stein characterizations and Fisher information

We generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator in terms of a generalized (standardized) score function. We use this result to connect Stein characterizations with information distances such as the generalized (standardized) Fisher information.

math.PR↗
arXiv2012

Grouped sparse paired comparisons in the Bradley-Terry model

In a wide class of paired comparisons, especially in the sports games, in which all subjects are divided into several groups, the intragroup comparisons are dense and the intergroup comparisons are sparse. Typical examples include the NFL regular season. Motivated by these situations, we propose group sparsity for paired comparisons and show the consistency and asymptotical normality of the maximum likelihood estimate in the Bradley-Terry model when the number of parameters goes to infinity in this paper. Simulations are carried out to illustrate the group sparsity and asymptotical results.

stat.OT↗
arXiv2011

Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package

This paper proposes consistent and asymptotically Gaussian estimators for the drift, the diffusion coefficient and the Hurst exponent of the discretely observed fractional Ornstein-Uhlenbeck process. For the estimation of the drift, the results are obtained only in the case when 1/2 < H < 3/4. This paper also provides ready-to-use software for the R statistical environment based on the YUIMA package.

stat.CO↗
arXiv2012

Voting Power : A Generalised Framework

This paper examines an area of Game Theory called Voting Power Theory. With the adoption of a measure theoretic framework it argues that the many different indices and tools currently used for measuring voting power can be replaced by just three simple probabilities. The framework is sufficiently general to be applicable to every conceivable type of voting game, and every possible decision rule.

math.ST↗
arXiv2012

A Brief History of the Statistics Department of the University of California at Berkeley

The early history of our department was dominated by Jerzy Neyman (1894-1981), while the next phase was largely in the hands of Neyman's students, with Erich Lehmann (1917-2009) being a central, long-lived and much-loved member of this group. We are very fortunate in having Constance Reid's biography "Neyman -- From Life" and Erich's "Reminiscences of a Statistician: The Company I Kept" and other historical material documenting the founding and growth of the department, and the people in it. In what follows, we will draw heavily from these sources, describing what seems to us to be a remarkable success story: one person starting "a cell of statistical research and teaching ... not being hampered by any existing traditions and routines" and seeing that cell grow rapidly into a major force in academic statistics worldwide. That it has remained so for (at least) the half-century after its founding is a testament to the strength of Neyman's model for a department of statistics.

stat.OT↗
arXiv2012

Partially-blind Estimation of Reciprocal Channels for AF Two-Way Relay Networks Employing M-PSK Modulation

We consider the problem of channel estimation for amplify-and-forward two-way relays assuming channel reciprocity and M-PSK modulation. In an earlier work, a partially-blind maximum-likelihood estimator was derived by treating the data as deterministic unknowns. We prove that this estimator approaches the true channel with high probability at high signal-to-noise ratio (SNR) but is not consistent. We then propose an alternative estimator which is consistent and has similarly favorable high SNR performance. We also derive the Cramer-Rao bound on the variance of unbiased estimators.

cs.IT↗
arXiv2012

A Concise Resolution to the Two Envelope Paradox

In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically, a subjective probability that is inconsistent with reality can mislead reasoning based on Bayesian decision theory.

stat.OT↗
arXiv2012

A divergence formula for regularization methods with an L2 constraint

We derive a divergence formula for a group of regularization methods with an L2 constraint. The formula is useful for regularization parameter selection, because it provides an unbiased estimate for the number of degrees of freedom. We begin with deriving the formula for smoothing splines and then extend it to other settings such as penalized splines, ridge regression, and functional linear regression.

stat.OT↗
arXiv2012

Note on the closed-form MLEs of k-component load-sharing systems

Recently Kim and Kvam (2004) and Singh, Sharma, Kumar (2008) proposed different load-sharing models and developed parametric inference for the these models. However, their parametric estimates are calculated using iterative numerical methods. In this note, we provide the general closed-form MLEs for the two load-sharing models provided by them.

stat.OT↗
arXiv2012

Parameter Estimation from Censored Samples using the Expectation-Maximization Algorithm

This paper deals with parameter estimation when the data are randomly right censored. The maximum likelihood estimates from censored samples are obtained by using the expectation-maximization (EM) and Monte Carlo EM (MCEM) algorithms. We introduce the concept of the EM and MCEM algorithms and develop parameter estimation methods for a variety of distributions such as normal, Laplace and Rayleigh distributions. These proposed methods are illustrated with three examples.

stat.CO↗
arXiv2012

Estimating a Random Walk First-Passage Time from Noisy or Delayed Observations

A random walk (or a Wiener process), possibly with drift, is observed in a noisy or delayed fashion. The problem considered in this paper is to estimate the first time τthe random walk reaches a given level. Specifically, the p-moment (p\geq 1) optimization problem \inf_η\ex|η-τ|^p is investigated where the infimum is taken over the set of stopping times that are defined on the observation process. When there is no drift, optimal stopping rules are characterized for both types of observations. When there is a drift, upper and lower bounds on \inf_η\ex|η-τ|^p are established for both types of observations. The bounds are tight in the large-level regime for noisy observations and in the large-level-large-delay regime for delayed observations. Noteworthy, for noisy observations there exists an asymptotically optimal stopping rule that is a function of a single observation. Simulation results are provided that corroborate the validity of the results for non-asymptotic settings.

cs.IT↗
arXiv2012

Sparse solution of overdetermined linear systems when the columns of $A$ are orthogonal

In this paper, we consider the problem of obtaining the best $k$-sparse solution of $Ax=y$ subject to the constraint that the columns of $A$ are orthogonal. The naive approach for obtaining a solution to this problem has exponential complexity and there exist $l_1$ regularization methods such as Lasso to obtain approximate solutions. In this paper, we show that we can obtain an exact solution to the problem, with much less computational effort compared to the brute force search when the columns of $A$ are orthogonal.

stat.OT↗
arXiv2012

Why FARIMA Models are Brittle

The FARIMA models, which have long-range-dependence (LRD), are widely used in many areas. Through deriving a precise characterisation of the spectrum, autocovariance function, and variance time function, we show that this family is very atypical among LRD processes, being extremely close to the fractional Gaussian noise in a precise sense. Furthermore, we show that this closeness property is not robust to additive noise. We argue that the use of FARIMA, and more generally fractionally differenced time series, should be reassessed in some contexts, in particular when convergence rate under rescaling is important and noise is expected.

stat.AP↗
arXiv2012

Reading Theorie Analytique des Probabilites

This note is an extended read of my read of Laplace's book Theorie Analytique des Probabilites, when considered from a Bayesian viewpoint but without historical nor comparative pretentions. A deeper analysis is provided in Dale (1999).

stat.OT↗