ترغب بنشر مسار تعليمي؟ اضغط هنا

High-dimensional instrumental variables regression and confidence sets -- v2/2012

139   0   0.0 ( 0 )
 نشر من قبل Eric Gautier
 تاريخ النشر 2018
  مجال البحث الاحصاء الرياضي
والبحث باللغة English
 تأليف Eric Gautier




اسأل ChatGPT حول البحث

This was a revision of arXiv:1105.2454v1 from 2012. It considers a variation on the STIV estimator where, instead of one conic constraint, there are as many conic constraints as moments (instruments) allowing to use more directly moderate deviations for self-normalized sums. The idea first appeared in formula (6.5) in arXiv:1105.2454v1 when some instruments can be endogenous. For reference and to avoid confusion with the STIV estimator, this estimator should be called C-STIV.



قيم البحث

اقرأ أيضاً

We consider a $l_1$-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension $d$ of the input variable $X$ is very large (sometimes depending on the number of observations). Estimation of a $bet a$-regular regression function $f$ cannot be faster than the slow rate $n^{-2beta/(2beta+d)}$. Hopefully, in some situations, $f$ depends only on a few numbers of the coordinates of $X$. In this paper, we construct two procedures. The first one selects, with high probability, these coordinates. Then, using this subset selection method, we run a local polynomial estimator (on the set of interesting coordinates) to estimate the regression function at the rate $n^{-2beta/(2beta+d^*)}$, where $d^*$, the real dimension of the problem (exact number of variables whom $f$ depends on), has replaced the dimension $d$ of the design. To achieve this result, we used a $l_1$ penalization method in this non-parametric setup.
We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to avoid non- vanishing biases in addition to handle the high dimensionality of the parameters. A recent growing literature has proposed various estimators that achieve good rates of convergence. Our main contribution complements this literature with the construction of simultaneous confidence regions for the parameters of interest in such high-dimensional linear models with error-in-variables. These confidence regions are based on the construction of moment conditions that have an additional orthogonal property with respect to nuisance parameters. We provide a construction that requires us to estimate an additional high-dimensional linear model with error-in-variables for each component of interest. We use a multiplier bootstrap to compute critical values for simultaneous confidence intervals for a subset $S$ of the components. We show its validity despite of possible model selection mistakes, and allowing for the cardinality of $S$ to be larger than the sample size. We apply and discuss the implications of our results to two examples and conduct Monte Carlo simulations to illustrate the performance of the proposed procedure.
We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence rates, an d show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the ``difficulty of which depends on eigenvalues of a certain integral operator which is determined by the joint density of endogenous and instrumental variables. We delineate the role played by problem difficulty in determining both the optimal convergence rate and the appropriate choice of smoothing parameter.
101 - Botond Szabo 2014
We consider the problem of constructing Bayesian based confidence sets for linear functionals in the inverse Gaussian white noise model. We work with a scale of Gaussian priors indexed by a regularity hyper-parameter and apply the data-driven (slight ly modified) marginal likelihood empirical Bayes method for the choice of this hyper-parameter. We show by theory and simulations that the credible sets constructed by this method have sub-optimal behaviour in general. However, by assuming self-similarity the credible sets have rate-adaptive size and optimal coverage. As an application of these results we construct $L_{infty}$-credible bands for the true functional parameter with adaptive size and optimal coverage under self-similarity constraint.
124 - Kun Zhou , Ker-Chau Li , 2019
The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level often happ ens after estimating the degree of smoothness. Similarly, for high-dimensional regression, oracle inequalities for sparse estimators could be utilized to construct sharp confidence sets. Yet the degree of sparsity itself is unknown and needs to be estimated, causing the honesty problem. To resolve this issue, we develop a novel method to construct honest confidence sets for sparse high-dimensional linear regression. The key idea in our construction is to separate signals into a strong and a weak group, and then construct confidence sets for each group separately. This is achieved by a projection and shrinkage approach, the latter implemented via Stein estimation and the associated Stein unbiased risk estimate. Our confidence set is honest over the full parameter space without any sparsity constraints, while its diameter adapts to the optimal rate of $n^{-1/4}$ when the true parameter is indeed sparse. Through extensive numerical comparisons, we demonstrate that our method outperforms other competitors with big margins for finite samples, including oracle methods built upon the true sparsity of the underlying model.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا