Confidence Bands for Convex Median Curves using Sign-Tests

Suppose that one observes pairs (x1,Y1), (x2,Y2), ..., (xn,Yn), where x1 < x2 < ... < xn are fixed numbers while Y1, Y2, ..., Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex or concave function f. We present a confidence band for this regression function f using suitable multiscale sign tests. While the exact computation of this band seems to require O(n4) steps, good approximations can be obtained in O(n2) steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size n tends to infinity.

M-Functionals of Multivariate Scatter

This survey provides a self-contained account of M-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying M-functionals and discuss their weak continuity and differentiability. This is done in a rather general framework with matrix-valued random variables. By doing so we reveal a connection between Tyler's (1987) M-functional of scatter and the estimation of proportional covariance matrices. Moreover, this general framework allows us to treat a new class of scatter estimators, based on symmetrizations of arbitrary order. Finally these results are applied to M-estimation of multivariate location and scatter via multivariate t-distributions.

Confidence Bands for Isotonic Median Curves using Sign-Tests

Suppose that one observes independent random variables (X1, Y1), (X2, Y2), …, (Xn, Yn) in R2 with unknown distributions, except that Median(Yi | Xi = M(x) for some unknown isotonic function M. We describe an explicit algorithm for the computation of confidence bands for the median function M whose running time is of order O(n2). The bands rely on multiscale sign tests and are shown to have desirable asymptotic properties.

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.

Performance of a new, 3D-monitor based random-dot stereotest for children under 4 years of age

BACKGROUND: The aim of this study was to determine the performance of a new, 3D-monitor based, objective stereotest in children under the age of four. METHODS: Random-dot circles (diameter 10 cm, crossed, disparity of 0.34 degrees) randomly changing their position were presented on an 3D-monitor while eye movements were monitored by infrared photo-oculography. If > or = 3 consecutive stimuli were seen, a positive response was assumed. One hundred thirty-four normal children aged 2 months to 4 years (average 17+/-15.3 months) were examined. RESULTS: Below the age of 12 months, we were not able to obtain a response to the 3D stimulus. For older children the following rates of positive responses were found: 12-18 months 25%, 18-24 months 10%, 24-30 months 16%, 30-36 months 57%, 36-42 months 100%, and 42-48 months 91%. Multiple linear logistic regression showed a significant influence on stimulus recognition of the explanatory variables age (p<0.00001) and child cooperation (p<0.001), but not of gender (p>0.1). CONCLUSIONS: This 3D-monitor based stereotest allows an objective measurement of random-dot stereopsis in younger children. It might open new ways to screen children for visual abnormalities and to study the development of stereovision. However, the current experimental setting does not allow determining random-dot stereopsis in children younger than 12 months.

The effects of cardiac output and pulmonary arterial hypertension on volumetric capnography derived-variables during normoxia and hypoxia

The aim of this study was to test the effect of cardiac output (CO) and pulmonary artery hypertension (PHT) on volumetric capnography (VCap) derived-variables. Nine pigs were mechanically ventilated using fixed ventilatory settings. Two steps of PHT were induced by IV infusion of a thromboxane analogue: PHT25 [mean pulmonary arterial pressure (MPAP) of 25 mmHg] and PHT40 (MPAP of 40 mmHg). CO was increased by 50 % from baseline (COup) with an infusion of dobutamine ≥5 μg kg(-1) min(-1) and decreased by 40 % from baseline (COdown) infusing sodium nitroglycerine ≥30 μg kg(-1) min(-1) plus esmolol 500 μg kg(-1) min(-1). Another state of PHT and COdown was induced by severe hypoxemia (FiO2 0.07). Invasive hemodynamic data and VCap were recorded and compared before and after each step using a mixed random effects model. Compared to baseline, the normalized slope of phase III (SnIII) increased by 32 % in PHT25 and by 22 % in PHT40. SnIII decreased non-significantly by 4 % with COdown. A combination of PHT and COdown associated with severe hypoxemia increased SnIII by 28 % compared to baseline. The elimination of CO2 per breath decreased by 7 % in PHT40 and by 12 % in COdown but increased only slightly with COup. Dead space variables did not change significantly along the protocol. At constant ventilation and body metabolism, pulmonary artery hypertension and decreases in CO had the biggest effects on the SnIII of the volumetric capnogram and on the elimination of CO2.