We propose a new test for the parametric form of the volatility function in continuous time diffusion models of the type dXt = a(t,Xt)dt + σ(t,Xt)dWt. Our approach involves a range-based estimation of the integrated volatility and the integrated quarticity, which are used to construct the test statistic. Under rather weak assumptions on the drift and volatility we prove weak convergence of the ...

We describe a test statistic for unbinned goodness-of-fit of data in one dimension. The statistic is based on the two-dimensional Random Walk. The rejection power of this test is explored both for simple and compound hypotheses and, for the examples explored, it is found to be comparable to that for the χ test. We discuss briefly how it may be possible to extend this test to multi-dimensional d...

1. Answer the following questions (briefly explain your answers) a) What is a "test statistic" in the context of Hypothesis testing? A test statistic is the "score" one calculates from the data. Usefull test statistics follow known, well defined distributions under the null, and possibly known distribution(s) under the alternative hypothesis. The test consists of seeing how likely it is, that t...

We consider the non-nested testing prqblem of non-parametric regressions. We show that, when the regression functions are unknown under both the null and the alternative hypotheses, an extension of the J-test procedure of Davidson and Mackinnon (1981) will lead to a test statistic with well defined asymptotic properties. The derivation of the test statistic involves double kernel estimation. Mo...

The distribution of running time could be anything at all. We didnt even say whether it is continuous or discrete. Even so, the null hypothesis does induce a probability distribution on the test statistic without any other information. Specifically, it implies that the samples are indistinguishable and exchangeable. Our test statistic is a mean of 6 values (algorithm B running times) minus the ...

Data collected from response adaptive designs are dependent. Traditional statistical methods need to be justified for the use in response adaptive designs. This paper generalizes the Rao’s score test to response adaptive designs and introduces a generalized score statistic. Simulation is conducted to compare the statistical powers of the Wald, the score, the generalized score and the likelihood...

We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a...

When working with multilook fully polarimetric synthetic aperture radar (SAR) data, an appropriate way of representing the backscattered signal consists of the so-called covariance matrix. For each pixel, this is a 3 3 Hermitian positive definite matrix that follows a complex Wishart distribution. Based on this distribution, a test statistic for equality of two such matrices and an associated a...

This paper presents a test of independence that can be applied to the estimated residuals of any time series model that can be transformed into a model driven by independent and identically distributed errors. The rst order asymptotic distribution of the test statistic is independent of estimation error provided that the parameters of the model under test can be estimated p n{consistently. Beca...

In this paper, the definition of the Toeplitz autocorrelation matrix is used to derive a kernel-based portmanteau test statistic for ARMA models. Under the null hypothesis of no serial correlation, the distribution of the test statistic is approximated by a standard normal using the kernel-based normalized spectral density estimator, without having to specify any alternative model. Unlike most ...