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Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many…
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we…
We consider finite mixtures of generalized linear models with binary output. We prove that cross moment (between the output and the regression variables) until order 3 are sufficient to identify all parameters of the model. We propose a…
Detecting changes in asset co-movements is of much importance to financial practitioners, with numerous risk management benefits arising from the timely detection of breakdowns in historical correlations. In this article, we propose a…
Reduced-rank regressions are powerful tools used to identify co-movements within economic time series. However, this task becomes challenging when we observe matrix-valued time series, where each dimension may have a different co-movement…
We design a system for risk-analyzing and pricing portfolios of non-performing consumer credit loans. The rapid development of credit lending business for consumers heightens the need for trading portfolios formed by overdue loans as a…
The main goal of this paper is an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal CAPM model we built a general sampling model suitable in…
This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To…
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…
In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…
A regression method for proportional, or fractional, data with mixed effects is outlined, designed for analysis of datasets in which the outcomes have substantial weight at the bounds. In such cases a normal approximation is particularly…
This paper presents in detail the originally developed Quadratic Point Estimate Method (QPEM), aimed at efficiently and accurately computing the first four output moments of probabilistic distributions, using 2n^2+1 sample (or sigma)…
Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…
Betas are possibly the most frequently applied tool to analyze how securities relate to the market. While in very widespread use, betas only express dynamics derived from second moment statistics. Financial returns data often deviate from…
In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true…