Related papers: Fitting an Equation to Data Impartially
We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted least-squares fitting is only appropriate when there…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
We propose an estimation approach to analyse correlated functional data which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation…
In partially linear additive models the response variable is modelled with a linear component on a subset of covariates and an additive component in which the rest of the covariates enter to the model as a sum of univariate unknown…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…
In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…
Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each…
The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with…
In regression analysis of multivariate data, it is tacitly assumed that response and predictor variables in each observed response-predictor pair correspond to the same entity or unit. In this paper, we consider the situation of "permuted…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
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…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…