Related papers: Linear Regression for Power Law Distribution Fitti…

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…

Multiple matrix sampling is a survey methodology technique that randomly chooses a relatively small subset of items to be presented to survey respondents for the purpose of reducing respondent burden. The data produced are missing…

This paper proposes a new linear power flow model for distribution system with accurate voltage magnitude estimates. The new model can be seen as a generalization of LinDistFlow model to multiphase distribution system with generic network…

In this paper, a novel linear formulation for power system state estimation that simultaneously treats conventional and synchrophasor measurements is proposed. A linear circuit model for conventional measurements is introduced to enable a…

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…

The adaptive LASSO has been used for consistent variable selection in place of LASSO in the linear regression model. In this article, we propose a modified LARS algorithm to combine adaptive LASSO with some biased estimators, namely the…

We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and…

Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…

This paper considers sparse linear discriminant analysis of high-dimensional data. In contrast to the existing methods which are based on separate estimation of the precision matrix $\O$ and the difference $\de$ of the mean vectors, we…

This paper deals with improvement of linear quantile regression, when there are a few distinct values of the covariates but many replicates. On can improve asymptotic efficiency of the estimated regression coefficients by using suitable…

Power laws and power laws with exponential cut-off are two distinct families of distributions on the positive real half-line. In the present paper, we propose a unified treatment of both families by building a family of distributions that…

Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent $\alpha$ using the…

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of…

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…

In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…