4,418 research outputs found
A Kolmogorov-Smirnov test for the molecular clock on Bayesian ensembles of phylogenies
Divergence date estimates are central to understand evolutionary processes
and depend, in the case of molecular phylogenies, on tests of molecular clocks.
Here we propose two non-parametric tests of strict and relaxed molecular clocks
built upon a framework that uses the empirical cumulative distribution (ECD) of
branch lengths obtained from an ensemble of Bayesian trees and well known
non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS)
goodness-of-fit test. In the strict clock case, the method consists in using
the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny
is clock-like, in other words, if it follows a Poisson law. The ECD is computed
from the discretized branch lengths and the parameter of the expected
Poisson distribution is calculated as the average branch length over the
ensemble of trees. To compensate for the auto-correlation in the ensemble of
trees and pseudo-replication we take advantage of thinning and effective sample
size, two features provided by Bayesian inference MCMC samplers. Finally, it is
observed that tree topologies with very long or very short branches lead to
Poisson mixtures and in this case we propose the use of the two-sample KS test
with samples from two continuous branch length distributions, one obtained from
an ensemble of clock-constrained trees and the other from an ensemble of
unconstrained trees. Moreover, in this second form the test can also be applied
to test for relaxed clock models. The use of a statistically equivalent
ensemble of phylogenies to obtain the branch lengths ECD, instead of one
consensus tree, yields considerable reduction of the effects of small sample
size and provides again of power.Comment: 14 pages, 9 figures, 8 tables. Minor revision, additin of a new
example and new title. Software:
https://github.com/FernandoMarcon/PKS_Test.gi
Commercial real estate return distributions: a review of literature and empirical evidence
This paper review the literature on the distribution of commercial real estate returns. There is growing evidence that the assumption of normality in returns is not safe. Distributions are found to be peaked, fat-tailed and, tentatively, skewed. There is some evidence of compound distributions and non-linearity. Public traded real estate assets (such as property company or REIT shares) behave in a fashion more similar to other common stocks. However, as in equity markets, it would be unwise to assume normality uncritically. Empirical evidence for UK real estate markets is obtained by applying distribution fitting routines to IPD Monthly Index data for the aggregate index and selected sub-sectors. It is clear that normality is rejected in most cases. It is often argued that observed differences in real estate returns are a measurement issue resulting from appraiser behaviour. However, unsmoothing the series does not assist in modelling returns. A large proportion of returns are close to zero. This would be characteristic of a thinly-traded market where new information arrives infrequently. Analysis of quarterly data suggests that, over longer trading periods, return distributions may conform more closely to those found in other asset markets. These results have implications for the formulation and implementation of a multi-asset portfolio allocation strategy
Exact goodness-of-fit tests for censored dats
The statistic introduced in Fortiana and Grané (2003) is modified so that it can be used to test
the goodness-of-fit of a censored sample, when the distribution function is fully specified. Exact
and asymptotic distributions of three modified versions of this statistic are obtained and exact
critical values are given for different sample sizes. Empirical power studies show the good
performance of these statistics in detecting symmetrical alternatives
Statistical tests for whether a given set of independent, identically distributed draws does not come from a specified probability density
We discuss several tests for whether a given set of independent and
identically distributed (i.i.d.) draws does not come from a specified
probability density function. The most commonly used are Kolmogorov-Smirnov
tests, particularly Kuiper's variant, which focus on discrepancies between the
cumulative distribution function for the specified probability density and the
empirical cumulative distribution function for the given set of i.i.d. draws.
Unfortunately, variations in the probability density function often get
smoothed over in the cumulative distribution function, making it difficult to
detect discrepancies in regions where the probability density is small in
comparison with its values in surrounding regions. We discuss tests without
this deficiency, complementing the classical methods. The tests of the present
paper are based on the plain fact that it is unlikely to draw a random number
whose probability is small, provided that the draw is taken from the same
distribution used in calculating the probability (thus, if we draw a random
number whose probability is small, then we can be confident that we did not
draw the number from the same distribution used in calculating the
probability).Comment: 18 pages, 5 figures, 6 table
Asymptotic properties of a goodness-of-fit test based on maximum correlations
We study the efficiency properties of the goodness-of-fit test based on the Qn statistic
introduced in Fortiana and Grané (2003) using the concepts of Bahadur asymptotic relative
efficiency and Bahadur asymptotic optimality. We compare the test based on this statistic with
those based on the Kolmogorov-Smirnov, the Cramér-von Mises and the Anderson-Darling
statistics. We also describe the distribution families for which the test based on Qn is
asymptotically optimal in the Bahadur sense and, as an application, we use this test to detect the
presence of hidden periodicities in a stationary time series
Verification tools for probabilistic forecasts of continuous hydrological variables
In the present paper we describe some methods for verifying and evaluating probabilistic forecasts of hydrological variables. We propose an extension to continuous-valued variables of a verification method originated in the meteorological literature for the analysis of binary variables, and based on the use of a suitable cost-loss function to evaluate the quality of the forecasts. We find that this procedure is useful and reliable when it is complemented with other verification tools, borrowed from the economic literature, which are addressed to verify the statistical correctness of the probabilistic forecast. We illustrate our findings with a detailed application to the evaluation of probabilistic and deterministic forecasts of hourly discharge value
Two-dimensional Kolmogorov-type Goodness-of-fit Tests Based on Characterizations and their Asymptotic Efficiencies
In this paper new two-dimensional goodness of fit tests are proposed. They
are of supremum-type and are based on different types of characterizations. For
the first time a characterization based on independence of two statistics is
used for goodness-of-fit testing. The asymptotics of the statistics is studied
and Bahadur efficiencies of the tests against some close alternatives are
calculated. In the process a theorem on large deviations of Kolmogorov-type
statistics has been extended to the multidimensional case
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