Related papers: A Note on Cohen's d From a Partitioned Linear Regr…
The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's $d$. A recently proposed generalized estimator allows conditioning on further independent variables…
The Frisch--Waugh--Lovell Theorem states the equivalence of the coefficients from the full and partial regressions. I further show the equivalence between various standard errors. Applying the new result to stratified experiments reveals…
In this paper, I discuss three aspects of the Frisch-Waugh-Lovell theorem. First, I show that the theorem holds for linear instrumental variables estimation of a multiple regression model that is either exactly or overidentified. I show…
This paper traces the historical and analytical development of what is known in the econometrics literature as the Frisch-Waugh-Lovell theorem. This theorem demonstrates that the coefficients on any subset of covariates in a multiple…
The residualization procedure has been applied in many different fields to estimate models with multicollinearity. However, there exists a lack of understanding of this methodology and some authors discourage its use. This paper aims to…
We present a fast and memory efficient algorithm for the estimation of generalized linear models with an additive separable k-way error component. The brute force approach uses dummy variables to account for the unobserved heterogeneity,…
In the context of generalized measurement theory, the Gleason-Busch theorem assures the unique form of the associated probability function. Recently, in Flatt et al. Phys. Rev. A 96, 062125 (2017), the case of subsequent measurements has…
Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…
Linear regression is widely used to model relationships between responses and predictors. In modern applications, one encounters data where the responses are non-Euclidean random objects situated in a metric space, paired with Euclidean…
The random vector of frequencies in a generalized urn model is viewed as conditionally independent random variables, given their sum. Such a representation is exploited to derive Edgeworth expansions for a sum of functions of such…
This paper characterizes the values of partial regression coefficients, defined as projection coefficients onto the space spanned by explanatory variables, for random variables generated by linear structural equation models using graphical…
We consider a diffusion process on $\mathbb R^n$ and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the…
Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However (partially) linear models for example, which would deliver these, may fit poorly to the data. On the other hand, an…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance,…
We propose and develop the thesis that the quantum theoretical description of experiments emerges from the desire to organize experimental data such that the description of the system under scrutiny and the one used to acquire the data are…
A prescription is presented for a new and practical correlation coefficient, $\phi_K$, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of $\phi_K$ form an advantage over…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description…
The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value…