Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.
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48 results for “Asymptotic Distribution”
Barrieu, Rouault, and Yor [J. Appl. Probab. 41 (2004)] determined asymptotics for the logarithm of the distribution function of the Hartman-Watson distribution. We determine the asymptotics of the density. This refinement can be applied to the pricing of Asian options in the Black-Scholes model.
In this paper we discuss the asymptotic behaviour of random contractions , where , with distribution function , is a positive random variable independent of . Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X…
Normal distributions ensure asymptotic variance reduction in moment matching Monte Carlo.
problem Asymptotic variance reduction in general integration problems.
method Characterization of conditions for asymptotic variance reduction using normal distributions.
result Asymptotic variance reduction is guaranteed for normal distributions in moment matching Monte Carlo.
Asymptotic Analysis of Sampling Estimators for Randomized Numerical Linear Algebra Algorithmsmath.ST
Develops asymptotic analysis for RandNLA sampling estimators in least-squares problems.
problem Lack of distributional information for RandNLA estimators in statistical inference.
method Asymptotic analysis of sampling estimators for least-squares problems in two settings.
result Sampling estimators are asymptotically normally distributed under mild conditions.
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors …
Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.
problem Online statistical inference of model parameters in stochastic optimization problems.
method Kiefer-Wolfowitz algorithm with random search directions, asymptotic distribution analysis.
result Developed valid confidence intervals for online statistical inference.
Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvaturegr-qc
We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.
Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimalitymath.OC
Stochastic algo learns from evolving data, achieving optimal performance.
problem Performative prediction and multiplayer extensions.
method Stochastic approximation with decision-dependent distributions.
result Asymptotic normality and optimality of the algorithm's performance.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
The paper develops AMP theory for sparse and robust regression with polynomial iterations.
problem Challenges in high-dimensional statistical estimation due to asymptotic theory breakdown.
method Non-asymptotic distributional theory of AMP for sparse and robust regression.
result First finite-sample non-asymptotic distributional theory of AMP for polynomial iterations.
This paper establishes non-asymptotic learning bounds for the DR covariate shift adaptation.
problem Distribution shift between training and test domains in machine learning.
method Doubly-robust (DR) estimator combining density ratio estimation and pilot regression model.
result First non-asymptotic learning bounds for DR covariate shift adaptation.
Study slopes of direct images in complex manifolds, proving a Mehta-Ramanathan type theorem.
problem Distribution of Harder-Narasimhan slopes in direct image sheaves.
method Analyzing asymptotic distributions of slopes under base changes of families of complex projective manifolds.
result Asymptotic distribution of slopes can be recovered from base changes over generic curves.
Study non-asymptotic Langevin Monte Carlo for Gibbs distributions.
problem Sampling from Gibbs distributions with dissipative potentials.
method Langevin-type algorithms based on Liptser--Shiryaev theory and Poincaré inequalities.
result Upper bound on 2-Wasserstein distance for accurate approximation.
The paper develops a method to create non-asymptotic confidence ellipsoids for linear regression without strong noise distribution assumptions.
problem Constructing reliable confidence regions for linear regression with finite sample sizes and general noise distributions.
method The paper introduces the SPS EOA algorithm to create non-asymptotically guaranteed confidence ellipsoids for linear regression problems.
result The sizes of SPS outer ellipsoids are shown to decrease at the optimal rate for linear regression problems.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
Continuous-time distributed mirror descent with integral feedback converges to global optimum.
problem Distributed optimization of a global strongly convex function with local convex components.
method Continuous-time distributed mirror descent with integral feedback.
result Asymptotic convergence to global optimum with constant step-size.
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model…
A Geometric Analysis of PCAmath.ST
The paper analyzes the excess risk of PCA and provides a precise characterization.
problem Understanding the excess risk of principal component analysis (PCA).
method Established a central limit theorem for PCA error and derived the excess risk distribution.
result Obtained a non-asymptotic upper bound on the excess risk of PCA.
We give an asymptotic probabilistic real Riemann-Hurwitz formula computing the expected real ramification index of a random covering over the Riemann sphere. More generally, we study the asymptotic expected number and distribution of critical points of a random real Lefschetz pencil over a smooth real algebraic variety…
Unified framework for FDR control in knockoffs, validating Gaussian knockoffs.
problem Asymptotic FDR control in knockoffs with user-specified distributions.
method Unified theoretical framework, three conditions on approximate knockoff statistics, Gaussian knockoffs generator based on moments matching.
result Gaussian knockoffs generator achieves asymptotic FDR control.
New test for conditional independence using kernel embeddings.
problem Testing conditional independence in high-dimensional settings.
method Analytic kernel embeddings, asymptotic distribution.
result New test outperforms existing methods in high-dimensional settings.
The paper analyzes the randomized midpoint method for Langevin diffusions, revealing biases and asymptotic properties.
problem Analyzing biases and asymptotic properties of the randomized midpoint method for Langevin diffusions.
method Characterization of stationary distribution and asymptotic normality for numerical integration.
result The step-size needs to go to zero for the method to be asymptotically unbiased.
This paper presents the asymptotic behavior of a linear instrumental variables (IV) estimator that uses a ridge regression penalty. The regularization tuning parameter is selected empirically by splitting the observed data into training and test samples. Conditional on the tuning parameter, the training sample creates …
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how…
Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic modelsq-fin.PR
In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-diffusion mode…
Study improves BN TTA under distribution shift using higher-order asymptotics.
problem Improving BN TTA for changing data distributions.
method Integrates Edgeworth expansion and saddlepoint approximation with one-step M-estimation.
result Derives optimal weighting parameter for minimized mean-squared error.
This paper analyzes the distribution of genera in 2-bridge knots and proves their asymptotic normality.
problem Analyzing the distribution of genera in 2-bridge knots.
method Proving asymptotic normality through median, mode, and variance calculations.
result The distribution of genera of 2-bridge knots is asymptotically normal.
Unified asymptotic treatment for VaR- and expectile-based systemic risk measures.
problem Analyzing systemic risk measures under extreme system-wide disasters.
method Classified systemic risk measures into VaR- and expectile-based families, introduced new ICE and SICE measures, and provided second-order asymptotic results.
result Second-order asymptotics provide more accurate tail approximations for systemic risk measures.
We analyze the eigenvalue distribution of a neural network's kernel under specific scaling.
problem Analyzing the eigenvalue distribution of the Neural Tangent Kernel (NTK) of a neural network.
method Asymptotic analysis of the NTK matrix under given scaling conditions.
result The eigenvalue distribution is described as a free multiplicative convolution of the Marchenko-Pastur distribution and a deterministic distribution.
The study computes Bergman kernels and point process asymptotics on Kähler manifolds.
problem Computing asymptotics of Bergman kernels and point process distributions on Kähler manifolds.
method Equivariant and partial Bergman kernels, determinantal point processes, asymptotic analysis.
result The distribution of linear statistics converges to a centered normal variable with specific variances.
The paper compares Bayesian uncertainty to MAP estimator in random features regression.
problem Comparing Bayesian uncertainty to MAP estimator in random features regression.
method Analyzing the variance of the posterior predictive distribution and comparing it to the risk of the MAP estimator.
result Asymptotic agreement between Bayesian uncertainty and MAP estimator under specific signal-to-noise ratios and sample sizes.
This paper improves reinforcement learning by estimating return distributions using quantiles.
problem Improving reinforcement learning by estimating return distributions.
method Quantile-based distributional reinforcement learning, using quantile-projected distributional Bellman equations.
result The quantile-based approach achieves optimal sample efficiency and asymptotic efficiency.
Paper develops a robust PP distributed quasi-Newton estimation for Byzantine machines.
problem Byzantine machines in distributed computing under Privacy Protection constraints.
method Robust PP distributed quasi-Newton estimation method that transmits only five vectors.
result Reduces privacy budgeting and transmission cost compared to gradient descent and Newton iteration.
This paper improves reinforcement learning by estimating return distributions using quantiles.
problem Improving reinforcement learning by estimating return distributions.
method The paper uses quantile-based distributional reinforcement learning to characterize return distributions.
result The quantile-based approach achieves optimal sample efficiency and asymptotic efficiency.
This paper analyzes the bias of inexact MCMC methods in high dimensions.
problem Understanding the bias of inexact MCMC methods in high-dimensional spaces.
method Establishing bounds on Wasserstein distances between inexact MCMC methods and target distributions.
result The asymptotic bias of ULA and uHMC depends on key quantities related to the target distribution or the stationary probability measure of the scheme.
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.
CD algorithm achieves near-optimal convergence rate for unnormalized models.
problem Training unnormalized models with high efficiency.
method Non-asymptotic analysis of contrastive divergence algorithm.
result CD can achieve convergence rate under regularity assumptions.
Finite-Time Regret of Thompson Sampling Algorithms for Exponential Family Multi-Armed Banditsstat.ML
New Thompson sampling algorithm reduces regret for exponential family bandits.
problem Minimizing regret in multi-armed bandit problems with exponential family rewards.
method Proposes ExpTS and ExpTS algorithms using novel sampling distributions.
result Minimizes both finite-time and asymptotic regret for exponential family rewards.
This paper corrects an error in [Keller-Ressel, M. and Steiner T. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models." Finance and Stochastics 12.2 (2008): 149-172]. The error concerns the correct expression for the boundary between normal and humped yield curve behavior in affin…
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of populations, specified by unknown distributions. Over some time horizon, at each time , the controller wishes to select a population to sample, with the goal of sampling fro…
The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be c…
We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well ap…
Study examines implied volatility behavior in Bachelier model.
problem Characterizing implied volatility in Bachelier model for large strikes.
method Exploiting regular variation theory, derived explicit expressions for Bachelier implied volatility.
result Established a rigorous connection between characteristic function analyticity and volatility smile asymptotic slope.
We develop asymptotically optimal policies for the multi armed bandit (MAB), problem, under a cost constraint. This model is applicable in situations where each sample (or activation) from a population (bandit) incurs a known bandit dependent cost. Successive samples from each population are iid random variables with u…
Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificitycs.LG
Paper addresses trade-off between robustness and specificity in machine learning.
problem Combating distributional uncertainties in training data compared to population distributions.
method Unified framework that unifies Bayesian, distributionally robust optimization, and regularization methods.
result Reveals the trade-off between robustness and specificity.
This paper improves offline contextual bandits using distributional robustness.
problem Improving offline contextual bandits with robustness.
method Extends Distributionally Robust Optimization (DRO) for offline contextual bandits, introducing a convex reformulation of Counterfactual Risk Minimization.
result Automatic calibration of asymptotic confidence intervals for policy optimization.