Bootstrap Tests of Stochastic Dominance with Asymptotic Similarity on the Boundary

We propose a new method of testing stochastic dominance which improves on existing tests based on bootstrap or subsampling. Our test requires estimation of the contact sets between the marginal distributions. Our tests have asymptotic sizes that are exactly equal to the nominal level uniformly over the boundary points of the null hypothesis and are therefore valid over the whole null hypothesis. We also allow the prospects to be indexed by infinite as well as finite dimensional unknown parameters, so that the variables may be residuals from nonparametric and semiparametric models. Our simulation results show that our tests are indeed more powerful than the existing subsampling and recentered bootstrap.Set estimation, Size of test, Unbiasedness, Similarity, Bootstrap, Subsampling

Kernel Methods for Small Sample and Asymptotic Tail Inference for Dependent, Heterogeneous Data

This paper considers tail shape inference techniques robust to substantial degrees of serial dependence and heterogeneity. We detail a new kernel estimator of the asymptotic variance and the exact small sample mean-squared-error, and a simple representation of the bias of the B. Hill (1975) tail index estimator for dependent, heterogeneous data. Under mild assumptions regarding the tail fractile sequence, memory and heterogeneity, choosing the sample fractile by non-parametrically minimizing the mean-squared-error leads to a consistent and asymptotically normal estimator. A broad simulation study demonstrates the merits of the resulting minimum MSE estimator for autoregressive and GARCH data. We analyze the distribution of a standardiz ed Hill-estimator in order to asses the accuracy of the kernel e stimator of the asymptotic variance, and the distribution of the minimum MSE estimator. Finally, we apply the estimators to a small study of the tail shape of equity markets returns.Hill estimator; regular variation; extremal near epoch dependence; kernel estimator; mean-square-error.

Testing for linearity in scalar-on-function regression with responses missing at random

We construct a goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing At Random (MAR). For that, we extend an existing testing procedure for the case where all responses have been observed to the case where the responses are MAR. The testing procedure gives rise to a statistic based on a marked empirical process indexed by the randomly projected functional covariate. The test statistic depends on a suitable estimator of the functional slope of the FLMSR when the sample has MAR responses, so several estimators are proposed and compared. With any of them, the test statistic is relatively easy to compute and its distribution under the null hypothesis is simple to calibrate based on a wild bootstrap procedure. The behavior of the resulting testing procedure as a function of the estimators of the functional slope of the FLMSR is illustrated by means of several Monte Carlo experiments. Additionally, the testing procedure is applied to a real data set to check whether the linear hypothesis holds.Comment: 21 pages, 6 figures, 4 table