Evaluating hedge fund performance: a stochastic dominance approach

We introduce a general and flexible framework for hedge fund performance evaluation and asset allocation: stochastic dominance (SD) theory. Our approach utilizes statistical tests for stochastic dominance to compare the returns of hedge funds. We form hedge fund portfolios by using SD criteria and examine the out-of-sample performance of these hedge fund portfolios. Compared to performance of portfolios of randomly selected hedge funds and mean-variance e¢ cient hedge funds, our results show that fund selection method based on SD criteria greatly improves the performance of hedge fund portfolio

Convexity and a sum-product type estimate

In this paper we further study the relationship between convexity and additive growth, building on the work of Schoen and Shkredov (\cite{SS}) to get some improvements to earlier results of Elekes, Nathanson and Ruzsa (\cite{ENR}). In particular, we show that for any finite set $A\subset{\mathbb{R}}$ and any strictly convex or concave function $f$, $$|A+f(A)|\gg{\frac{|A|^{24/19}}{(\log|A|)^{2/19}}}$$ and $$\max\{|A-A|,\ |f(A)+f(A)|\}\gg{\frac{|A|^{14/11}}{(\log|A|)^{2/11}}}.$$ For the latter of these inequalities, we go on to consider the consequences for a sum-product type problem

Isochores Merit the Prefix 'Iso'

The isochore concept in human genome sequence was challenged in an analysis by the International Human Genome Sequencing Consortium (IHGSC). We argue here that a statement in IGHSC analysis concerning the existence of isochore is incorrect, because it had applied an inappropriate statistical test. To test the existence of isochores should be equivalent to a test of homogeneity of windowed GC%. The statistical test applied in the IHGSC's analysis, the binomial test, is however a test of a sequence being random on the base level. For testing the existence of isochore, or homogeneity in GC%, we propose to use another statistical test: the analysis of variance (ANOVA). It can be shown that DNA sequences that are rejected by binomial test may not be rejected by the ANOVA test.Comment: 14 pages (including 1 figure), submitte

Local Linear Fitting Under Near Epoch Dependence: Uniform consistency with Convergence Rates

Local linear fitting is a popular nonparametric method in statistical and econometric modelling. Lu and Linton (2007) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modelling.α-mixing, local linear fitting, near epoch dependence, convergence rates, uniform consistency

Visual7W: Grounded Question Answering in Images

We have seen great progress in basic perceptual tasks such as object recognition and detection. However, AI models still fail to match humans in high-level vision tasks due to the lack of capacities for deeper reasoning. Recently the new task of visual question answering (QA) has been proposed to evaluate a model's capacity for deep image understanding. Previous works have established a loose, global association between QA sentences and images. However, many questions and answers, in practice, relate to local regions in the images. We establish a semantic link between textual descriptions and image regions by object-level grounding. It enables a new type of QA with visual answers, in addition to textual answers used in previous work. We study the visual QA tasks in a grounded setting with a large collection of 7W multiple-choice QA pairs. Furthermore, we evaluate human performance and several baseline models on the QA tasks. Finally, we propose a novel LSTM model with spatial attention to tackle the 7W QA tasks.Comment: CVPR 201

An improved sum-product estimate for general finite fields

This paper improves on a sum-product estimate obtained by Katz and Shen for subsets of a finite field whose order is not prime