Related papers: Assessing symmetry of financial returns series
Asymmetric statistical errors arise for experimental results obtained by Maximum Likelihood estimation, in cases where the number of results is finite and the log likelihood function is not a symmetric parabola. This note discusses how…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
Energy distance is a statistical distance between the distributions of random variables, which characterizes the equality of the distributions. Utilizing the energy distance, we develop a nonparametric test for the diagonal symmetry, which…
The recent empirical work of Amaya et al. (2015) has pointed out that the realized skewness, which is the sample skewness of intraday high-frequency returns of a financial asset, serves as forecasting future returns in the cross-section.…
In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…
This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model…
Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical…
Let $\rho$ be a general law--invariant convex risk measure, for instance the average value at risk, and let $X$ be a financial loss, that is, a real random variable. In practice, either the true distribution $\mu$ of $X$ is unknown, or the…
The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal…
In order to investigate the origin of large price fluctuations, we analyze stock price changes of ten frequently traded NASDAQ stocks in the year 2002. Though the influence of the trading frequency on the aggregate return in a certain time…
This paper develops a statistical framework for goodness-of-fit testing of volatility functions in McKean-Vlasov stochastic differential equations, which describe large systems of interacting particles with distribution-dependent dynamics.…
We study the empirical measure of the output of the t-distributed stochastic neighbour embedding algorithm when the initial data is given by n independent, identically distributed inputs. We prove that under certain assumptions on the…
Most existing methods for testing equality of means of functional data from multiple populations rely on assumptions of equal covariance and/or Gaussianity. In this work we provide a new testing method based on a statistic that is…
We consider a stationary linear $AR(p)$ model with zero mean. The autoregression parameters as well as the distribution function (d.f.) $G(x)$ of innovations are unknown. We consider two situations. In the first situation the observations…
In this article, we propose a one-sample test to check whether the support of the unknown distribution generating the data is homologically equivalent to the support of some specified distribution or not OR using the corresponding…
Often it is not easy to choose between estimators, based on the estimated MSE and bias using simulation studies. Normality in small samples and a variance of the estimator, which is correct and easy to calculate using a single sample, give…
Ratios of sample percentiles or of quantiles based on a single sample are often published for skewed income data to illustrate aspects of income inequality, but distribution-free confidence intervals for such ratios are to our knowledge not…
In this paper we deal with the problem of testing for the quality of $k$ probability distributions. We introduce a generalization of the maximum mean discrepancy that permits to characterize the null hypothesis. Then, an estimator of it is…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…