Accurate inference on a scalar interest parameter in the presence of a nuisance parameter may be obtained using an adjusted version of the signed root likelihood ratio statistic, in particular BarndorffNielsen’s R∗ statistic. The adjustment made by this statistic may be decomposed into a sum of two terms, interpreted as correcting respectively for the possible effect of nuisance parameters and ...

This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the leastsquares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process ...

A simulation-based approach is proposed for approximating a Bayesian analysis. Parameters and data are simulated from a Bayesian model and inference about a parameter is performed by exploring the set of simulated parameter values conditional on a set of values of a simulated statistic. The approach is used to learn about parameters of a streaky model on the basis of a statistic used to measure...

Consider a semiparametric model indexed by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. In many applications, pseudolikelihood provides a convenient way to infer the parameter of interest, where the nuisance parameter is replaced by a consistent estimator. The purpose of this paper is to establish the asymptotic behaviour of the pseudolikelihood ratio statis...

This paper investigates the asymptotic properties of the likelihood ratio statistic for testing homogeneity in normal mixture models in the presence of a structural parameter. The asymptotic null distributions of the ordinary likelihood ratio statistic and the modified likelihood ratio statistic are the same, having the probability density function(pdf) (1/2)g1(x)+(1/2)g2(x) where g1(x) and g2(...

We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitud...

For the parameter estimation problem, we know nothing about the parameter but the observations from such a distribution. Therefore, the observations X1, · · · , Xn is our first hand of information source about the parameter, that is to say, all the available information about the parameter is contained in the observations. However, we know that the estimators we obtained are always functions of...

The NIST Statistical Test Suite has 15 tests. The principal strategy of the NIST Statistical Test Suite is to judge statistical randomness property of random bit generating algorithms. Based on 300 to 500 different keys, the algorithm generates a series of even number of different long random sequences of n bits, n varying between 13 and 15 lacs, each of which is tested by the 15 tests. Each te...