相关论文: Double asymptotics for the chi-square statistic

For linear models with spatial errors, the empirical likelihood ratio statistics are constructed for the parameters of the models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

The G\"artner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distri-bution given any fixed initial point, which entails weak multiplicative…

The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…

We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi^2$-distance. The results are based on proper non-uniform estimates for…

An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous…

For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…

Let $\mathcal{P}_{\lambda}:=\mathcal{P}_{\lambda\kappa}$ denote a Poisson point process of intensity $\lambda\kappa$ on $[0,1]^d,d\geq2$, with $\kappa$ a bounded density on $[0,1]^d$ and $\lambda\in(0,\infty)$. Given a closed subset…

The generalised random graph contains $n$ vertices with positive i.i.d. weights. The probability of adding an edge between two vertices is increasing in their weights. We require the weight distribution to have finite second moments and…

The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in a specific model but is expected to be…

The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…

We prove the Simons-Johnson theorem for the sums $S_n$ of $m$-dependent random variables, with exponential weights and limiting compound Poisson distribution $\CP(s,\lambda)$. More precisely, we give sufficient conditions for…

Pearson's chi-square tests are among the most commonly applied statistical tools across a wide range of scientific disciplines, including medicine, engineering, biology, sociology, marketing and business. However, its usage in some areas is…

For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…

For $X_i(t), i=1,\ldots, n, t\in [0,T]$ centered Gaussian processes, the chi-square process $\sum_{i=1}^{n}X_i^2(t)$ appears naturally as limiting processes in various statistical models. In this paper, we are concerned with the exact tail…

In this paper we show that the conditional distribution of perturbed chi-quare risks can be approximated by certain distributions including the Gaussian ones. Our results are of interest for conditional extreme value models and multivariate…

In this paper, we prove a local limit theorem for the chi-square distribution with $r > 0$ degrees of freedom and noncentrality parameter $\lambda \geq 0$. We use it to develop refined normal approximations for the survival function. Our…

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

We study asymptotic probabilities of attaining the maximum in heterogeneous Gaussian samples. In the two-group setting, the first sample has variance $1$ and size $n_1$, while the second has variance $\sigma^2>1$ and size $n_2$. We…

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson…