Related papers: Stepwise Choice of Covariates in High Dimensional …
Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$…
In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian…
Given data $y$ and $k$ covariates $x$ the problem is to decide which covariates to include when approximating $y$ by a linear function of the covariates. The decision is based on replacing subsets of the covariates by i.i.d. normal random…
We consider the problem of variable selection in linear models when $p$, the number of potential regressors, may exceed (and perhaps substantially) the sample size $n$ (which is possibly small).
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…
In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian…
The dual problem of testing the predictive significance of a particular covariate, and identification of the set of relevant covariates is common in applied research and methodological investigations. To study this problem in the context of…
This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform…
It is argued that all model based approaches to the selection of covariates in linear regression have failed. This applies to frequentist approaches based on P-values and to Bayesian approaches although for different reasons. In the first…
This paper considers multiple regression procedures for analyzing the relationship between a response variable and a vector of covariates in a nonparametric setting where both tuning parameters and the number of covariates need to be…
For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…
The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…
Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint.…
Variable selection is a procedure to attain the truly important predictors from inputs. Complex nonlinear dependencies and strong coupling pose great challenges for variable selection in high-dimensional data. In addition, real-world…
Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…
While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the…
In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…