Adaptive Test of Conditional Moment Inequalities

In this paper, I construct a new test of conditional moment inequalities, which is based on studentized kernel estimates of moment functions with many different values of the bandwidth parameter. The test automatically adapts to the unknown smoothness of moment functions and has uniformly correct asymptotic size. The test has high power in a large class of models with conditional moment inequalities. Some existing tests have nontrivial power against n^{-1/2}-local alternatives in a certain class of these models whereas my method only allows for nontrivial testing against (n/\log n)^{-1/2}-local alternatives in this class. There exist, however, other classes of models with conditional moment inequalities where the mentioned tests have much lower power in comparison with the test developed in this paper

Rapid learning of visual ensembles

open3siWe recently demonstrated that observers are capable of encoding not only summary statistics, such as mean and variance of stimulus ensembles, but also the shape of the ensembles. Here, for the first time, we show the learning dynamics of this process, investigate the possible priors for the distribution shape, and demonstrate that observers are able to learn more complex distributions, such as bimodal ones. We used speeding and slowing of response times between trials (intertrial priming) in visual search for an oddly oriented line to assess internal models of distractor distributions. Experiment 1 demonstrates that two repetitions are sufficient for enabling learning of the shape of uniform distractor distributions. In Experiment 2, we compared Gaussian and uniform distractor distributions, finding that following only two repetitions Gaussian distributions are represented differently than uniform ones. Experiment 3 further showed that when distractor distributions are bimodal (with a 30° distance between two uniform intervals), observers initially treat them as uniform, and only with further repetitions do they begin to treat the distributions as bimodal. In sum, observers do not have strong initial priors for distribution shapes and quickly learn simple ones but have the ability to adjust their representations to more complex feature distributions as information accumulates with further repetitions of the same distractor distribution.openChetverikov, Andrey; Campana, Gianluca; Kristjánsson, ÁrniChetverikov, Andrey; Campana, Gianluca; Kristjánsson, Árn

Comparison and anti-concentration bounds for maxima of Gaussian random vectors

Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories. Here we give explicit comparisons of expectations of smooth functions and distribution functions of maxima of Gaussian random vectors without any restriction on the covariance matrices. We also establish an anti-concentration inequality for the maximum of a Gaussian random vector, which derives a useful upper bound on the L\'{e}vy concentration function for the Gaussian maximum. The bound is dimension-free and applies to vectors with arbitrary covariance matrices. This anti-concentration inequality plays a crucial role in establishing bounds on the Kolmogorov distance between maxima of Gaussian random vectors. These results have immediate applications in mathematical statistics. As an example of application, we establish a conditional multiplier central limit theorem for maxima of sums of independent random vectors where the dimension of the vectors is possibly much larger than the sample size.Comment: 22 pages; discussions and references update

Inference on causal and structural parameters using many moment inequalities

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters, a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly enter the market. We consider the test statistic given by the maximum of $p$ Studentized (or $t$-type) inequality-specific statistics, and analyze various ways to compute critical values for the test statistic. Specifically, we consider critical values based upon (i) the union bound combined with a moderate deviation inequality for self-normalized sums, (ii) the multiplier and empirical bootstraps, and (iii) two-step and three-step variants of (i) and (ii) by incorporating the selection of uninformative inequalities that are far from being binding and a novel selection of weakly informative inequalities that are potentially binding but do not provide first order information. We prove validity of these methods, showing that under mild conditions, they lead to tests with the error in size decreasing polynomially in $n$ while allowing for $p$ being much larger than $n$, indeed $p$ can be of order $\exp (n^{c})$ for some $c > 0$. Importantly, all these results hold without any restriction on the correlation structure between $p$ Studentized statistics, and also hold uniformly with respect to suitably large classes of underlying distributions. Moreover, in the online supplement, we show validity of a test based on the block multiplier bootstrap in the case of dependent data under some general mixing conditions.Comment: This paper was previously circulated under the title "Testing many moment inequalities

Original Effective, Safe Technique of Obtaining Platelet Rich Plasma by Centrifugation of the Blood Plasma in Modified Syringe Containers

The aim: to develop, substantiate an effective and safe technology for producing PRP (platelet rich plasma). To quantify the substrate based on the recommended centrifugation protocols.Materials and methods: the effectiveness of the original harvesting protocol was evaluated by quantifying the number of platelets. The proposed technique is formed basing on the basic principles of double centrifugation of whole blood in test tubes with anticoagulant, separation with the release of a plasma layer with a high content of platelets.The centrifuging mode for quantifying the effectiveness of the substrate was selected according to recommendations based on a study confirming maximum efficiency (160g×10min + 250g×15min).For quantitative evaluation, blood was collected from 10 healthy volunteers (7 men, 3 women) with an average age of 26.0±2.6, and centrifuged in standard mode. Quantitative evaluation of platelets of whole blood and the obtained PRP substrate was carried out with a semi-automatic analyzer.Results: the proposed technique is based on the use as a container for centrifuging a syringe with a LuerLock design, which is hermetically sealed with a congruent plug, adapted by the external size of the centrifuge rotor bowl. Phase selection after centrifugation was performed by aspiration of the syringe contents after centrifugation is performed through a three-way valve. The substrate was obtained by repeated centrifugation of the contents, which allows obtaining a variable volume and platelet concentration in PRP. The amount of platelets (PLT) of whole blood is 227.0±57.0 thousand per ml. PLT PRP 945.0±279.0 thousand per ml.Conclusions: the proposed method of separation of whole blood with the release of the platelet rich plasma demonstrates high efficiency, which corresponds to the level of increasing the number of platelets in reducing the volume at the level of the best ready-made solutions.The equipment is economical and does not require highly specialized equipment and consumables. The proposed technique provides a wide choice to the performer in the received volume of the substrate