We show that the number of segregating sites is a sufficient statistic for the scaled mutation parameter (theta) in the limit as the number of sites tends to infinity and there is free recombination between sites. We assume that the mutation parameter at each site tends to zero such than the total mutation parameter (theta) is constant in the limit. Our results show that Watterson's estimator i...

A sufficient statistic is a significant concept in statistics, which means a probability variable that has sufficient information required for an inference task. We investigate the roles of sufficient statistics and related quantities in stochastic thermodynamics. Specifically, we prove that for general continuous-time bipartite networks, the existence of a sufficient statistic implies that an ...

Nowadays, Hidden Markov models are extensively utilized for modeling stochastic processes. These models help researchers establish and implement the desired theoretical foundations using Markov algorithms such as Forward one. however, Using Stability hypothesis and the mean statistic for determining the values of Markov functions on unstable statistical data set has led to a significant reducti...

In a previous study (1998), how to evaluate whether adaptive testing data used for online calibration sufficiently fit the item response model used by C. Glas was studied. Three approaches were suggested, based on a Lagrange multiplier (LM) statistic, a Wald statistic, and a cumulative sum (CUMSUM) statistic respectively. For all these methods, the asymptotic variance of the parameter estimates...

We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The data are assumed to be generated by a true MLP model and the estimation of the parameters of the MLP is done by maximizing the likelihood of the model. When the number of hidden units of the true model is known, the asymptotic distribution of the likelihood ratio (LR) statistic i...

in some quality control applications, the quality of a process or a product is described by the relationship between a response variable and one or more explanatory variables, called a profile. moreover, in most practical applications, the qualitative characteristic of a product/service is vague, uncertain and linguistic and cannot be precisely stated. the purpose of this paper is to propose a ...

The paper focuses on the asymptotic comparison of maximum likelihood estimators and uniformly minimum variance unbiased (with respect to quadratic loss) for one-parameter truncation families where a sufficient statistic is either or sample. Easily verifiable conditions are formulated under which those results valid.