Related papers: Combining Empirical Likelihood and Robust Estimati…

A literature search shows that robust regression techniques are rarely used in applied econometrics. We list several misconceptions about robustness which lead to this situation. We show that most data sets are not normal, least squares…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

Restricted maximum likelihood (REML) estimation is a widely accepted and frequently used method for fitting linear mixed models, with its principal advantage being that it produces less biased estimates of the variance components. However,…

Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function,…

Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often…

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable…

The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…

There is often a scarcity of training data for machine learning (ML) classification and regression models in industrial production, especially for time-consuming or sparsely run manufacturing processes. A majority of the limited…

Unlike parametric regression, machine learning (ML) methods do not generally require precise knowledge of the true data generating mechanisms. As such, numerous authors have advocated for ML methods to estimate causal effects.…

Parameter estimation with the maximum $L_q$-likelihood estimator (ML$q$E) is an alternative to the maximum likelihood estimator (MLE) that considers the $q$-th power of the likelihood values for some $q<1$. In this method, extreme values…

We have developed a new regression technique, the maximum likelihood (ML)-based method and its variant, the KS-test based method, designed to obtain unbiased regression results from typical astronomical data. A normalizing flow model is…

Randomized experiments are the gold standard for causal inference, and justify simple comparisons across treatment groups. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This…

The Extreme Learning Machine (ELM) is a growing statistical technique widely applied to regression problems. In essence, ELMs are single-layer neural networks where the hidden layer weights are randomly sampled from a specific distribution,…

Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that…

Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often…

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…

The tracking method based on the extreme learning machine (ELM) is efficient and effective. ELM randomly generates input weights and biases in the hidden layer, and then calculates and computes the output weights by reducing the iterative…

Traditional likelihood based methods for parameter estimation get highly affected when the given data is contaminated by outliers even in a small proportion. In this paper, we consider a robust parameter estimation method, namely the…

There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…

In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. In many situations, the…