Nonparametric Independence Screening in Sparse Ultra-High Dimensional Varying Coefficient Models

The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection arrives. In this paper, we propose and investigate marginal nonparametric screening methods to screen variables in ultra-high dimensional sparse varying-coefficient models. The proposed nonparametric independence screening (NIS) selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable. The sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order, and the dimensionality reduction of NIS is quantified. To enhance practical utility and the finite sample performance, two data-driven iterative NIS methods are proposed for selecting thresholding parameters and variables: conditional permutation and greedy methods, resulting in Conditional-INIS and Greedy-INIS. The effectiveness and flexibility of the proposed methods are further illustrated by simulation studies and real data applications

Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group selection. Nonconvex penalties such as SCAD and MCP have been proposed and shown to have several advantages over the lasso; these penalties may also be extended to the group selection problem, giving rise to group SCAD and group MCP methods. Here, we describe algorithms for fitting these models stably and efficiently. In addition, we present simulation results and real data examples comparing and contrasting the statistical properties of these methods

Inference regarding multiple structural changes in linear models estimated via two stage least squares

In this paper, we extend Bai and Perron’s (1998, Econometrica, p.47-78) framework for multiple break testing to linear models estimated via Two Stage Least Squares (2SLS). Within our framework, the break points are estimated simultaneously with the regression parameters via minimization of the residual sum of squares on the second step of the 2SLS estimation. We establish the consistency of the resulting estimated break point fractions. We show that various F-statistics for structural instability based on the 2SLS estimator have the same limiting distribution as the analogous statistics for OLS considered by Bai and Perron (1998). This allows us to extend Bai and Perron’s (1998) sequential procedure for selecting the number of break points to the 2SLS setting. Our methods also allow for structural instability in the reduced form that has been identified a priori using data-based methods. As an empirical illustration, our methods are used to assess the stability of the New Keynesian Phillips curve.unknown break points; structural change; instrumental variables; endogenous regressors; structural stability tests; new Keynesian Phillips curve

How good are dynamic factor models at forecasting output and inflation? A meta-analytic approach

This paper surveys existing factor forecast applications for real economic activity and inflation by means of a meta-analysis and contributes to the current debate on the determinants of the forecast performance of large-scale dynamic factor models relative to other models. We find that, on average, factor forecasts are slightly better than other models' forecasts. In particular, factor models tend to outperform small-scale models, whereas they perform slightly worse than alternative methods which are also able to exploit large datasets. Our results further suggest that factor forecasts are better for US than for UK macroeconomic variables, and that they are better for US than for euro-area output; however, there are no significant differences between the relative factor forecast performance for US and euro-area inflation. There is also some evidence that factor models are better suited to predict output at shorter forecast horizons than at longer horizons. These findings all relate to the forecasting environment (which cannot be influenced by the forecasters). Among the variables capturing the forecasting design (which can, by contrast, be influenced by the forecasters), the size of the dataset from which factors are extracted seems to positively affect the relative factor forecast performance. There is some evidence that quarterly data lend themselves better to factor forecasts than monthly data. Rolling forecasts are preferable to recursive forecasts. The factor estimation technique seems to matter as well. Other potential determinants - namely whether forecasters rely on a balanced or an unbalanced panel, whether restrictions implied by the factor structure are imposed in the forecasting equation or not and whether an iterated or a direct multi-step forecast is made - are found to be rather irrelevant. Moreover, we find no evidence that pre-selecting the variables to be included in the panel from which factors are extracted helped to improve factor forecasts in the past. --Factor models,forecasting,meta-analysis