Related papers: Model-free Study of Ordinary Least Squares Linear …
Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating links between these variables and partial sums of the…
Random forest (RF) is one of the most popular methods for estimating regression functions. The local nature of the RF algorithm, based on intra-node means and variances, is ideal when errors are i.i.d. For dependent error processes like…
The cost of both generalized least squares (GLS) and Gibbs sampling in a crossed random effects model can easily grow faster than $N^{3/2}$ for $N$ observations. Ghosh et al. (2020) develop a backfitting algorithm that reduces the cost to…
Ordinal regression is aimed at predicting an ordinal class label. In this paper, we consider its semi-supervised formulation, in which we have unlabeled data along with ordinal-labeled data to train an ordinal regressor. There are several…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
We study an $\ell_{1}$-regularized generalized least-squares (GLS) estimator for high-dimensional regressions with autocorrelated errors. Specifically, we consider the case where errors are assumed to follow an autoregressive process,…
It is well known that in the presence of heteroscedasticity ordinary least squares estimator is not efficient. I propose a generalized automatic least squares estimator (GALS) that makes partial correction of heteroscedasticity based on a…
We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. In a statistical context in which such functions measure loss, this says that the least favourable…
We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…
Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the…
Many econometrics textbooks imply that under mean independence of the regressors and the error term, the OLS parameters have a causal interpretation. We show that even when this assumption is satisfied, OLS might identify a pseudo-parameter…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for…
The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population…
Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization…
An iteratively reweighted least squares (IRLS) method is proposed for estimating polyserial and polychoric correlation coefficients in this paper. It iteratively calculates the slopes in a series of weighted linear regression models fitting…
Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…
It has recently been discovered that the conclusions of many highly influential econometrics studies can be overturned by removing a very small fraction of their samples (often less than $0.5\%$). These conclusions are typically based on…
Freedman [Adv. in Appl. Math. 40 (2008) 180-193; Ann. Appl. Stat. 2 (2008) 176-196] critiqued ordinary least squares regression adjustment of estimated treatment effects in randomized experiments, using Neyman's model for randomization…