Summary. We consider a high dimensional regression model with a possible change point due to a covariate threshold and develop the lasso estimator of regression coefficients as well as the threshold parameter. Our lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the l 1 -estimation loss for regression coefficients. Since the lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold effect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a factor that is nearly n 1 even when the number of regressors can be much larger than the sample size n. We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data.

Knowledge of the variation of crustal thickness is essential in many applications, such as forward dynamic modelling, numerical heat flow calculations, seismologic applications and geohistory reconstructions. We present a 3-D model of the Moho undulations over the entire Tibetan plateau derived from gravity inversion. The gravity field has been obtained by using the Gravity Recovery and Climate Experiment (GRACE) potential field development which has been integrated with terrestrial data, and is presently the best available in the studied area. For the effective use of the global geopotential model that has no height information of observation stations, upward continuation is applied. The Moho model is characterized by a sequence of troughs and ridges with a semi-regular pattern, which could reflect the continent-continent collision between the Indian and Eurasian plates. The three deep Moho belts (troughs) and shallow Moho belts (ridges) between them are clearly found to have an E-W directional trend parallel to the border of the plateau and tectonic lines, while variation of the directionality is observed in central to southeast Tibet. To describe the distinctive shape of the Moho troughs beneath Tibet, we introduce the term, 'Moho ranges'. The most interesting aspects of the Moho ranges are (1) that they run in parallel with the border and tectonic sutures of the plateau, (2) that the distances between ranges are found at regular distances of about 330 km except in northeast Tibet and (3) that the splitting of the ranges into two branches is found as the distance between them is increasing. From our study, we conclude that the distinctive undulations of the Tibetan Moho have been formed by buckling in a compressional environment, superimposed on the regional increase in crustal thickness. According to our analysis, the GRACE satellite-only data turns out to have good enough resolution for being used to determine the very deep Moho beneath Tibet. Our Moho model is the first one that covers the entire plateau

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LRtype test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function. The article provides an alternative, novel method that can be used to establish the asymptotic null distribution, even when the usual quadratic approximation is intractable. We illustrate the usefulness of our approach in the examples of the maximum score estimation, maximum likelihood estimation, quantile regression, and maximum rank correlation estimation. We establish consistency and local power properties of the test. We provide some simulation results and also an empirical application to tipping in racial segregation. This article has supplementary materials online. Terms of use: Documents in