Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite sample inference on the parameters given an adaptive lasso model for some fixed value of the shrinkage parameter. Central in this study is the test of the hypothesis that a given adaptive lasso parameter equals zero, which therefore tests for a false positive. To this end we construct a simple testing procedure and show, theoretically and empirically through extensive Monte Carlo simulations, that the adaptive lasso combines efficient parameter estimation, variable selection, and valid finite sample inference in one step. Moreover, we analytically derive a bias correction factor that is able to significantly improve the empirical coverage of the test on the active variables. Finally, we apply the introduced testing procedure to investigate the relation between the short rate dynamics and the economy, thereby providing a statistical foundation (from a model choice perspective) to the classic Taylor rule monetary policy model

Robustness of Bootstrap in Instrumental Variable Regression

This paper studies robustness of bootstrap inference methods for instrumental variable regression models. In particular, we compare the uniform weight and implied probability bootstrap approximations for parameter hypothesis test statistics by applying the breakdown point theory, which focuses on behaviors of the bootstrap quantiles when outliers take arbitrarily large values. The implied probabilities are derived from an information theoretic projection from the empirical distribution to a set of distributions satisfying orthogonality conditions for instruments. Our breakdown point analysis considers separately the effects of outliers in dependent variables, endogenous regressors, and instruments, and clarifies the situations where the implied probability bootstrap can be more robust than the uniform weight bootstrap against outliers. Effects of tail trimming introduced by Hill and Renault (2010) are also analyzed. Several simulation studies illustrate our theoretical findings.Bootstrap, Breakdown point, Instrumental variable regression

On Bartlett Correctability of Empirical Likelihood in Generalized Power Divergence Family

Baggerly (1998) showed that empirical likelihood is the only member in the Cressie-Read power divergence family to be Bartlett correctable. This paper strengthens Baggerly's result by showing that in a generalized class of the power divergence family, which includes the Cressie-Read family and other nonparametric likelihood such as Schennach's (2005, 2007) exponentially tilted empirical likelihood, empirical likelihood is still the only member to be Bartlett correctable. Bartlett correction, Empirical likelihood, Cressie-Read power divergence family

Breakdown Point Theory for Implied Probability Bootstrap

This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when outliers take arbitrarily large values, and derive the breakdown points for those bootstrap quantiles. The breakdown point properties characterize the situation where the implied probability bootstrap is more robust than the uniform weight bootstrap against outliers. Simulation studies illustrate our theoretical findings.Bootstrap, Breakdown point, GMM

On Bartlett Correctability of Empirical Likelihood in Generalized Power Divergence Family

Baggerly (1998) showed that empirical likelihood is the only member in the Cressie-Read power divergence family to be Bartlett correctable. This paper strengthens Baggerly’s result by showing that in a generalized class of the power divergence family, which includes the Cressie-Read family and other nonparametric likelihood such as Schennach’s (2005, 2007) exponentially tilted empirical likelihood, empirical likelihood is still the only member to be Bartlett correctable

Breakdown Point Theory for Implied Probability Bootstrap

This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when outliers take arbitrarily large values, and derive the breakdown points for those bootstrap quantiles. The breakdown point properties characterize the situation where the implied probability bootstrap is more robust than the uniform weight bootstrap against outliers. Simulation studies illustrate our theoretical findings

Robustness of Bootstrap in Instrumental Variable Regression

This paper studies robustness of bootstrap inference methods for instrumental variable regression models. In particular, we compare the uniform weight and implied probability bootstrap approximations for parameter hypothesis test statistics by applying the breakdown point theory, which focuses on behaviors of the bootstrap quantiles when outliers take arbitrarily large values. The implied probabilities are derived from an information theoretic projection from the empirical distribution to a set of distributions satisfying orthogonality conditions for instruments. Our breakdown point analysis considers separately the effects of outliers in dependent variables, endogenous regressors, and instruments, and clarifies the situations where the implied probability bootstrap can be more robust than the uniform weight bootstrap against outliers. Effects of tail trimming introduced by Hill and Renault (2010) are also analyzed. Several simulation studies illustrate our theoretical findings

Relative error accurate statistic based on nonparametric likelihood

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p-value of the TET statistic can provide an accurate approximation to the p-value of an infeasible saddlepoint statistic, which admits a Lugannani–Rice style adjustment with relative errors of order n −1 both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- and overidentified moment condition models. A limitation of our analysis is that the theoretical approximation results are exclusively for the infeasible saddlepoint statistic, and closeness of the p-values for the infeasible statistic to the ones for the feasible TET statistic is only numerically assessed

Empirical likelihood for high frequency data

This paper introduces empirical likelihood methods for interval estimation and hypothesis testing on volatility measures in some high frequency data environments. We propose a modified empirical likelihood statistic that is asymptotically pivotal under infill asymptotics, where the number of high frequency observations in a fixed time interval increases to infinity. The proposed statistic is extended to be robust to the presence of jumps and microstructure noise. We also provide an empirical likelihood-based test to detect the presence of jumps. Furthermore, we study higher-order properties of a general family of nonparametric likelihood statistics and show that a particular statistic admits a Bartlett correction: a higher-order refinement to achieve better coverage or size properties. Simulation and a real data example illustrate the usefulness of our approach

Multidimensional Participation in Hybrid Wireless Communities

Wireless communities have been long considered an interesting approach to provide mobile Internet, but the key issue is whether they are able to attract and retain a critical mass of active members. It is therefore crucial to understand what motivates and dissuades people from joining and participating in them, especially with the development of mainstream 3G technologies, in order to evaluate their potential development. This paper analyzes motivations and barriers influencing participation in a large wireless community – Fon – based on a survey of 268 members. Two distinct forms of participation driven by different motivations emerge: a ‘participation by sharing’ driven by idealistic motivation and a ‘social participation’ driven by social motives and technical interest. Utilitarian motivations do not play a major role for active participation despite being crucial in attracting members to the community. Accordingly, the way hybrid wireless communities are currently designed (hardly offering occasions for a social usage experience, experimentation and with decreasing utilitarian benefits due the development of 3G technologies) is casting serious doubts about a possible potential development above the status of a niche complement to the dominant cellular technologies