Sequential Probability Ratio Test (SPRT) has been widely used to detect process anomalies. The purpose of this paper is to present a practical procedure on the basis of SPRT, which recognizes if the mean of a latent Gaussian process Yt significantly deviates from presumed value, via an observable signal resulting from Yt. An equation for estimating the unknown nuisance parameter of the process ...

Composite likelihood may be useful for approximating likelihood based inference when the full likelihood is too complex to deal with. Stemming from a misspecified model, inference based on composite likelihood requires suitable corrections. Here we focus on the composite likelihood ratio statistic for a multidimensional parameter of interest, and we propose a parameterization invariant adjustme...

We have developed a new test against spurious long memory based on the invariance of long memory parameter to aggregation. By using the local Whittle estimator, the statistic takes the supremum among combinations of paired aggregated series. Simulations show that the test performs good in finite sample sizes, and is able to distinguish long memory from spurious processes with excellent power. M...

The poweRlaw package provides code to fit heavy tailed distributions, including discrete and continuous power-law distributions. The fitting procedure follows the method detailed in Clauset et al.1. The parameter 1 A. Clauset, C.R. Shalizi, and M.E.J. Newman. Power-law distributions in empirical data. SIAM review, 51(4):661– 703, 2009 values are obtained by maximising the likelihood. The cut-of...

An example of a regular statistical experiment is constructed where an insufficient statistic preserves the Fisher information contained in the data. The data are a pair (∆, X) where ∆ is a binary random variable and, given∆,X has a density f(x−θ|∆) depending on a location parameter θ. The phenomenon is based on the fact that f(x|∆) smoothly vanishes at one point; it can be eliminated by adding...

Application of the Johnson bivariate S(B) distribution, or alternatively the S(BB) distribution, is presented here as a tool for the analysis of concentration data and in particular for characterizing the relationship between exposures and biomarkers. Methods for fitting the marginal S(B) distributions are enhanced by maximizing the Shapiro-Wilk W statistic. The subsequent goodness of fit for t...

Various authors claim to have found evidence of stochastic long memory behavior in futures’ contract returns using the Hurst statistic. This paper reexamines futures’ returns for evidence of persistent behavior using a biased-corrected version of the Hurst statistic and an estimate of the long-memory parameter based on the process spectrum. Results based on these new methods provide no evidence...

We construct a continuous, strictly increasing, and bounded function T which maps Lebesgue almost the entire real line onto an algebraically independent set of real numbers. It follows that P n i=1 T (X i) is a uniformly continuous one-dimensional suucient statistic for every IID{model P n = fP n : P 2 Pg such that each P 2 P has a Lebesgue density. It also follows that the one{parameter expone...

We discuss Rissanen’s scheme of ‘complete coding’ in which a two-part data code is further shortened by conditioning the second part not only on the estimates, but also on the fact that these estimates were preferred to any others. We show that the scheme does not lead to improved estimates of parameters. The resulting message lengths may validly be employed to select among competing model clas...