Entropy-based Test Research Articles

The impact of fat-tailed distributions on some leading unit roots tests

There is substantial evidence that many time series associated with financial and insurance claim data are fat-tailed, with a (much) higher probability of " outliers' compared with the normal distribution. However, standard tests, or variants of them, for the presence of unit roots assume a normal distribution for the innovations driving the series. Application of the former to the latter therefore involves an inconsistency. We assess the impact of this inconsistency and provide information on its impact on inference when innovations are drawn from the Cauchy and sequence of t(v) distributions. A simple prediction that fat tails will uniformly lead to over-sizing of standard tests (because the fatness in the tail translates to the test distribution) turns out to be incorrect: we find that some tests are over-sized but some are under-sized. We also consider size retention and the power of the Dickey-Fuller pivotal and normalized bias test statistics and weighted symmetric versions of these tests. To make the unit root testing procedure feasible, we develop an entropy-based test for some fat-tailed distributions and apply it to share prices from the FTSE100.

An entropy-based test for goodness of fit of the von mises distribution

The maximum entropy characterization of the von Mises distribution on the circle is exploited to derive a consistent goodness of fit test for the von Mises distribution. Monte Carlo simulation results are tabulated giving critical values of the test statistic for various sample sizes and values of the concentration parameter. A power analysis is presented for various alternative hypotheses, comparing this entropy statistic to two other competing goodness of fit statistics. The entropy statistic is shown to compare favorably and may be more attractive, especially considering its ease of computation.

An approximate entropy test for randomness

We develop an entropy-based test for randomness of binary time series of finite length. The test uses the frequencies of contiguous blocks of different lengths. A simple condition ib the block lengths and the length of the time series enables one to estimate the entropy rate for the data, and this information is used to develop a statistic to test the hypothesis of randomness. This static measures the deviation of the estimated entropy of the observed data from the theoretical maximum under the randomness hypothesis. This test offers a real alternative to the conventional runs test. Critical percentage points, based on simulations, are provided for testing the hypothesis of randomness. Power calculations using dependent data show that the proposed test has higher power against the runs test for short series, and it is similar to the runs test for long series. The test is applied to two published data sets that wree investigated by others with respect to their randomness.

Entropy-based goodness-of-fit test for exponentiality

A goodness of fit test for exponentiality based on the entropy is proposed. This test is ronsistent against very broad family of alternatives. An approximate formulae for calculating critical values of the test is given. A simulation study of the test power shows that the entropy-based test seems to be a competitive tool for testing exponentiality.

Comparative noninformativities of quantum priors based on monotone metrics

We consider a number of prior probability distributions of particular interest, all being defined on the three-dimensional convex set of two-level quantum systems. Each distribution is — following recent work of Petz and Sudar — taken to be proportional to the volume element of a monotone metric on that Riemannian manifold. We apply and entropy-based test (a variant of one recently developed by Clarke) to determine which of two priors is more noninformative in nature. This involves converting them to posterior probability distributions based on some set of hypothesized outcomes of measurements of the quantum system in question. It is, then, ascertained whether or not the relative entropy (Kullback-Leibler statistic) between a pair of priors increases or decreases when one of them is exchanged with its corresponding posterior. The findings lead us to assert that the maximal monotone metric yields the most noninformative prior distribution and the minimal monotone (that is, the Bures) metric, the least. Our conclusions both agree and disagree, in certain respects, with ones recently reached by Hall, who relied upon a less specific test criterion than our entropy-based one.

On entropy-based goodness-of-fit tests

A general form of a goodness-of-fit test statistic for families of maximum entropy distributions is obtained. Particular cases of such families are normal, exponential, double-exponential, gamma and beta distributions. The proposed test is shown to be consistent against an appropriate class of alternatives. Simulation and Monte Carlo results are given for exponential and double exponential distributions. The proposed test compares favorably with other goodness-of-fit tests. This paper generalizes the work of Vasicek [7] regarding entropy-based test of normality and further work by Dudewicz and van der Meulen [1].

Entropy-Based Tests of Uniformity

Abstract The power properties of an entropy-based test are investigated when used for testing uniformity on [0, 1]. Percentage points and power against seven alternatives are reported. Compared with other tests of uniformity, the entropy-based test possesses good power properties for many alternatives. Some asymptotic null and alternative distributions are derived. For sample sizes up to 100 the table of percentage points provides a practical guide for using this test. A theory of entropy-based tests of distributional hypotheses other than uniformity is outlined.

Entropy-Based Tests of Uniformity

Abstract The power properties of an entropy-based test are investigated when used for testing uniformity on [0, 1]. Percentage points and power against seven alternatives are reported. Compared with other tests of uniformity, the entropy-based test possesses good power properties for many alternatives. Some asymptotic null and alternative distributions are derived. For sample sizes up to 100 the table of percentage points provides a practical guide for using this test. A theory of entropy-based tests of distributional hypotheses other than uniformity is outlined.