Seminar for Statistics

Research Seminar


Time/Place: every Friday at 3.15 pm in the Main Building of ETH, HG G 19.1

Spring Semester 2015


Date Speaker Title Time Location
15-may-2015 (fri)
Anders Kock
Asymptotically Honest Confidence Regions for High Dimensional Parameters by the Desparsified Conservative Lasso 15:15-16:00 HG G 19.1
Abstract: In this paper we consider the conservative Lasso which we argue penalizes more correctly than the Lasso and show how it may be deparsified in the sense of van de Geer et al (2014) in order to construct asymptotically honest (uniform) confidence bands. In particular, we develop an oracle inequality for the conservative Lasso only assuming the existence of a certain number of moments. This is done by means of the Marcinkiewicz-Zygmund inequality which in our context provides sharper bounds than Nemirovski's inequality. We allow for heteroskedastic non-subgaussian error terms and covariates. Next, we desparsify the conservative Lasso estimator and derive the asymptotic distribution of tests involving an increasing number of parameters. As a stepping stone towards this, we also provide a feasible uniformly consistent estimator of the asymptotic covariance matrix of an increasing number of parameters which is robust against conditional heteroskedasticity. To our knowledge we are the first to do so. Next, we show that our confidence bands are honest over sparse high-dimensional sub vectors of the parameter space and that they contract at the optimal rate. All our results are valid in high-dimensional models. Our simulations reveal that the desparsified conservative Lasso estimates the parameters more precisely than the desparsified Lasso, has better size properties, and produces confidence bands with superior coverage rates.

Anders Kock (Aarhus University)

29-may-2015 (fri)
Anastasios Magdalinos
Robust Econometric Inference in Cointegrated Systems with Multiple Persistence Degrees 15:15-16:00 HG G 19.1
Abstract: A new econometric methodology of inference is developed in systems of cointegrating and predictive regressions with unknown and potentially multiple persistence degrees along equations. It is well known that conventional approaches to estimating cointegrating regressions fail to produce even asymptotically valid inference procedures when the regressors are nearly integrated, and substantial size distortions can occur in econometric testing. The new framework developed here enables a general approach to inference that resolves this difficulty and is robust to the persistence characteristics of the regressors, making it suitable for general practical application. Estimation of systems of time series with mixed I(0), I(1) and all intermediate near I(1) behavior is achieved by means of constructing mildly integrated "IVX" instruments by filtering the system regressors. A mixed Gaussian limit theory is established for the IVX estimator of the full system and a standard chi-squared limit theory is established for the corresponding IVX based Wald test statistic. This new IVX technique eliminates the endogeneity problems of conventional cointegration methods with near integrated regressors, accommodates the presence of stationary regressors and robustifies inference to uncertainty over the nature of the (potentially multiple) integration orders present in the system. The methods are easily implemented, widely applicable and help to alleviate practical concerns about the use of cointegration methodology.

Anastasios Magdalinos (University of Southampton))

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