The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
Optimizes recommendation models using skew normal distribution.
problem Improving personalized recommendation systems.
method Develops a new optimization criterion based on skew normal distribution.
result Significantly outperforms state-of-the-art models.
The paper improves asset allocation using a skew-normal distribution in the Black-Litterman model.
problem Improving asset allocation under skewed return distributions.
method Using the Black-Litterman model with hidden truncation skew-normal distribution and Simaan's three-moment risk model.
result Optimal portfolios have less risk and higher skewness compared to classical BL model.
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution.…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard …
SkewD robustly discovers causal relationships in skewed noise models.
problem Distinguishing cause from effect in skewed noise models.
method SkewD extends normal-distribution framework to skew-normal setting for reliable inference.
result SkewD remains robust under high skewness, improving reliability.
The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.
problem Examining skewness and kurtosis measures for skew-elliptical distributions.
method Deriving exact expressions for skewness and kurtosis measures for skew-elliptical distributions, constructing test statistics, and comparing measures through simulations and real data analysis.
result Exact expressions and test statistics for skewness and kurtosis measures for various skew-elliptical distributions.
A new clustering method for functional data using skewed distributions.
problem Clustering functional data with skewed distributions.
method Mixtures of functional linear regression models and three skewed multivariate distributions (variance-gamma, skew-t, normal-inverse Gaussian).
result The proposed method funWeightClustSkew performs well on simulated and real data.
Proposes a new model for clustering with heavier tails.
problem Clustering with heavy-tailed data.
method Finite mixture of skewed sub-Gaussian stable distributions, maximum likelihood estimation, EM algorithm.
result The proposed model can robustly handle heavy-tailed data.
In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-w…
Researchers develop a new spatial process model for non-Gaussian data.
problem Non-Gaussian spatial data with asymmetry and heavy-tailedness.
method Re-parameterized Unified Skew-Normal (SUN) distribution, GSUN process, neural Bayes inference with GATs.
result GSUN process captures non-Gaussian spatial data properties and outperforms conventional models.
Many large-scale machine learning (ML) applications need to perform decentralized learning over datasets generated at different devices and locations. Such datasets pose a significant challenge to decentralized learning because their different contexts result in significant data distribution skew across devices/locatio…
SkewPNN uses probabilistic neural networks with skew-normal kernels to improve classification of imbalanced data.
problem Imbalanced data distribution leading to biased predictions for minority classes.
method Probabilistic neural networks with skew-normal kernel function and Bat optimization algorithm for hyperparameter tuning.
result SkewPNN and BA-SkewPNN outperform other methods in both balanced and imbalanced datasets.
Mixture of Experts (MoE) is a popular framework in the fields of statistics and machine learning for modeling heterogeneity in data for regression, classification and clustering. MoE for continuous data are usually based on the normal distribution. However, it is known that for data with asymmetric behavior, heavy tail…
Optimal option portfolios under Sharpe Ratio maximization with skew-elliptical t-distributed returns
problem Optimal option portfolios under Sharpe Ratio maximization
method Formulation for explicit portfolio weights
result Different optimal portfolios for Sharpe Ratio and return-to-Value-at-Risk (VaR) ratio
Unified Skew-Gaussian process framework for various regression and classification tasks.
problem Handling multiple types of regression and classification problems.
method Generalization of Skew-Gaussian processes to handle various types of data and likelihoods.
result Closed-form posterior distributions for multiple tasks.
Improves data normality with robust transformations.
problem Skewed data distribution.
method Modified Box-Cox and Yeo-Johnson transformations with robust parameter estimation.
result Transformed data approximates normality in the center with outliers.
Efficient EP algorithm improves smoothing distribution inference in financial models.
problem Computational intractability of smoothing distribution in high dimensions.
method Adapted expectation propagation (EP) algorithms for the unified skew-normal family.
result Accuracy gains in financial illustrations over existing approximate algorithms.
This paper proposes new GARCH models for cryptocurrency volatility, showing skewed distributions improve prediction accuracy.
problem Predicting cryptocurrency volatility and improving upon normality assumptions.
method Non-Gaussian GARCH models with Skewed Generalized Error Distribution.
result Skewed distributions enhance forecasting accuracy for cryptocurrency exchange rates.
Optimizes option portfolios for skewed-t returns using VaR and variance measures.
problem Optimizing portfolios for skewed-t returns with heavy tails and skewness.
method Uses variance and VaR measures, departing from normal returns, and provides explicit portfolio weights.
result Optimal portfolio weights differ significantly from variance optimal weights due to skewness.
Skew Gaussian Processes improve classification performance by allowing asymmetry.
problem Limited use of Gaussian processes in applications requiring asymmetry.
method Propose Skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions, extending the multivariate Unified Skew-Normal distribution to stochastic processes.
result SkewGPs provide better performance than symmetric Gaussian processes in classification tasks.
It is well known that the distribution of returns from various financial instruments are leptokurtic, meaning that the distributions have "fatter tails" than a Normal distribution, and have skew toward zero. This paper presents a graceful micro-level explanation for such fat-tailed outcomes, using agents whose private …
A new method generates synthetic data with realistic marginal distributions.
problem Generating synthetic data with bimodal and skewed marginal distributions.
method Pre-transformation variational autoencoders (PTVAEs) with separate parameter optimization for each variable.
result PTVAEs outperform other methods in generating synthetic data with bimodal and skewed distributions.
Develops a robust model for skewed and heavy-tailed data in periodontal studies.
problem Skewed and heavy-tailed data in periodontal pocket depth measurements.
method Flexible two-piece scale Student-t error distribution and deep neural network with monotonicity constraints.
result Robust mode-based estimation resistant to outliers with clinical interpretability.
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the …
Electromyogram (EMG) classification is a key technique in EMG-based control systems. The existing EMG classification methods do not consider the characteristics of EMG features that the distribution has skewness and kurtosis, causing drawbacks such as the requirement of hyperparameter tuning. In this paper, we propose …
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
Layer normalization improves federated learning with skewed labels.
problem Label skewness in federated learning datasets.
method Identified feature normalization as key mechanism; applied to latent features before classifier.
result Normalization accelerates global training and improves convergence under extreme label shift.
In this paper, an application of three GARCH-type models (sGARCH, iGARCH, and tGARCH) with Student t-distribution, Generalized Error distribution (GED), and Normal Inverse Gaussian (NIG) distribution are examined. The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skew…
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.
Improved portfolio optimization using VaR and CVaR with NMVM models.
problem Optimizing portfolios with VaR and CVaR under NMVM distributions.
method Transformed mean-CVaR-skewness problems into quadratic optimization with closed-form solutions for NMVM models.
result Approximate closed-form expressions for VaR and CVaR of NMVM portfolios.
EP method speeds up Bayesian probit regression in high dimensions.
problem Computational challenges in high-dimensional Bayesian probit regression.
method Adapting EP approximation to multivariate Gaussian prior and skew-normal distribution.
result EP routine is computationally feasible in high-dimensional settings.
This work accelerates constrained sampling using large deviation principles.
problem Sampling constrained probability distributions efficiently.
method Large deviation principles applied to skew-reflected non-reversible Langevin dynamics.
result The skew-symmetric matrix accelerates convergence and reduces asymptotic variance.
A new method tracks market performance without active management.
problem Active portfolio management does not outperform benchmarks.
method Developed a hybrid PCA-based tracking portfolio strategy.
result The hybrid PCA strategy outperforms optimization-based approaches.
We classify the connected pseudo-Riemannian manifolds of signature (p,q) with q≥5 so that at each point of M the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes and so that the skew-symmetric curvature operator is not nilpotent for at least …
Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our approximations are …
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
problem Capturing empirical phenomena like return skewness, heavy tails, and volatility asymmetry in option pricing models.
method Developing the Geometric Asymmetric Brownian Motion (GABM) within the Bachelier--Black--Scholes--Merton framework.
result Deriving closed-form option pricing formulas and a discrete-time binomial tree algorithm that converges to the GABM limit.
GG distribution improves option pricing for negatively skewed spot price distributions.
problem Inaccurate Black-Scholes model for negatively skewed spot price distributions.
method Applied Generalized Gamma (GG) distribution as a Risk-Neutral Density (RND) for Heston's SV model.
result GG distribution better matches market option data with negatively skewed spot price distributions.
Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification and clustering. For continuous data which we consider here in the context of regression and cluster analysis, MoE usually use normal experts, that is, expert components following the Gaussian distribution. …
The study revisits portfolio diversification by relaxing assumptions for skewed, multi-regime, and leptokurtic asset returns.
problem Underestimation of risk in portfolio diversification due to assumptions that are inconsistent with real-world asset returns.
method Calibrated a Markov-modulated Levy process model to equity market data to demonstrate the merits of the approach.
result The calibrated models effectively match empirical moments and show the importance of relaxing assumptions in portfolio diversification.
We construct almost complex algebraic curvature tensors for pseudo Hermitian inner products whose skew-symmetric curvature operator has constant Jordan normal form on the set of non-degenerate complex lines.
New RESK distributions improve robust clustering of skewed data.
problem Robustly clustering non-symmetric, heavy-tailed data clusters.
method Proposes RESK distributions and an EM algorithm with robust skew-Huber M-estimator.
result Numerical experiments confirm the effectiveness of the proposed methods.
As all physical adaptive quantum-enhanced metrology schemes operate under noisy conditions with only partially understood noise characteristics, so a practical control policy must be robust even for unknown noise. We aim to devise a test to evaluate the robustness of AQEM policies and assess the resource used by the po…
Proposes a method to identify elements in a skewness matrix for multivariate skew-elliptical distributions.
problem Label switching issue in Bayesian estimation of skewness matrix.
method Imposes a positive lower-triangular constraint and uses Bayesian sparse estimation with horseshoe prior.
result Successfully estimates the true structure of skewness dependency.
Bayesian framework predicts post-disruption travel times in metro networks.
problem Uncertainty in post-disruption travel times in metro networks.
method Bayesian spatiotemporal modeling framework capturing train interactions and non-Gaussian distributional characteristics.
result The proposed models consistently outperform baseline specifications in point prediction and uncertainty quantification.
New divergence measures improve KL approximation.
problem Improving KL divergence approximation without AC condition.
method Introduced α-geodesical skew divergence. result Properties of α-geodesical skew divergence studied.