The sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is well-known; however, the evaluation of its performance is a very difficult problem. In this paper it is shown that the distribution of the sufficient statistic can be approximated by the distribution of a Poisson-driven shot-noise random variable, which can be readily computed.

In logistic regression models, we consider the deviance statistic (the log likelihood ratio statistic) D as a goodness-of-fit test statistic. In this paper, we show the derivation of an expression of asymptotic expansion for the distribution of D under a null hypothesis. Using the continuous term of the expression, we obtain Bartlett-type transformed statistic D̃ that improves the speed of conve...

The von Mises distribution is often useful for modelling circular data problems. We consider a model for which von Mises data is contaminated with a certain proportion of points uniformly distributed around the circle. Maximum likelihood estimation is used to produce parameter estimates for this mixture model. Computational issues involved with obtaining the maximum likelihood estimates for the...

The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as function of the orientation two vectors; one representing optimal signal-to-noise ratio, and other maximised or F-statistic. Analytic marginalisation over angle between vectors yields marginalised which Further analytic explored using different choices prior. Monte-Carlo simulations show that ratios had i...

Relations are derived that can be used to infer parameters in situations where theoretical predictions can be compared to experimental data only indirectly via Monte Carlo simulation. We consider least square and likelihood ratio fits. Parameter changes in the fitting procedures are performed by reweighting Monte Carlo events. Formulas for goodness-of-fit tests based on the w2 and the likelihoo...

We apply the modified likelihood ratio test to two binomial mixture models arising in genetic linkage analysis. The limiting distribution of the test statistic for both models is shown to be a mixture of chi-squared distributions. A consideration of random family sizes for both models gives similar results. We also explore the power properties under local alternatives. Simulation studies show t...

If you seem to be able to do data assimilation with uncertain static parameters then you are probably not working in environmental science. In this field, applications are often characterized by sensitive dependence on initial conditions and attracting sets in the state-space, which, taken together, can be a major challenge to numerical methods, leading to very peaky likelihood functions. Inher...

A testing problem of homogeneity in gamma mixture models is studied. It is found that there is a proportion of the penalized likelihood ratio test statistic that degenerates to zero. The limiting distribution of this statistic is found to be the chi-bar-square distributions. The degeneration is due to the negative-definiteness of a complicated random matrix, depending on the shape parameter und...

We continue our recent work on finite-sample, i.e., non-asymptotic, inference with two-step, monotone incomplete data from Nd(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. Under the assumption that Σ is block-diagonal when partitioned according to the two-step pattern, we derive the distributions of the diagonal blocks of b Σ and of the estimated regression matrix,...

This paper proposes a modified quasi-likelihood test of Markov regime switching models. Despite its popularity in economics and finance, there are few papers that develop tests for regime switching models. Recently, Cho and White (2007) derive the asymptotic distribution of the quasi-likelihood ratio (QLR) statistic of Markov regime switching models with a scalar parameter. The asymptotic distr...