Search results for "Cross-sectional regression"
showing 3 items of 3 documents
Selection of the Best Subset of Variables in Regression and Time Series Models
2009
The problem of variable selection is one of the most pervasive model selection problems in statistical applications. Often referred to as the problem of subset selection, it arises when one wants to model the relationship between a variable of interest and a subset of potential explanatory variables or predictors, but there is uncertainty about which subset to use. Several papers have dealt with various aspects of the problem but it appears that the typical regression user has not benefited appreciably. One reason for the lack of resolution of the problem is the fact that it is has not been well defined. Indeed, it is apparent that there is not a single problem, but rather several problems …
Exploring regression structure with graphics
1993
We investigate the extent to which it may be possible to carry out a regression analysis using graphics alone, an idea that we refer to asgraphical regression. The limitations of this idea are explored. It is shown that graphical regression is theoretically possible with essentially no constraints on the conditional distribution of the response given the predictors, but with some conditions on marginal distribution of the predictors. Dimension reduction subspaces and added variable plots play a central role in the development. The possibility of useful methodology is explored through two examples.
On the ambiguous consequences of omitting variables
2015
This paper studies what happens when we move from a short regression to a long regression (or vice versa), when the long regression is shorter than the data-generation process. In the special case where the long regression equals the data-generation process, the least-squares estimators have smaller bias (in fact zero bias) but larger variances in the long regression than in the short regression. But if the long regression is also misspecified, the bias may not be smaller. We provide bias and mean squared error comparisons and study the dependence of the differences on the misspecification parameter.