相关论文: Higher-order asymptotic normality of approximation…

We examine the normal approximation of the modified likelihood root, an inferential tool from higher-order asymptotic theory, for the linear exponential and location-scale family. We show that the $r^\star$ statistic can be thought of as a…

We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…

A variety of estimators for the parameters of the Generalized Pareto distribution, the approximating distribution for excesses over a high threshold, have been proposed, always assuming the underlying data to be independent. We recently…

Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes,…

Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence…

This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237--264]. This new necessary and sufficient condition extends…

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…

The present manuscript studies signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked…

We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…

When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…

We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…

We study asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In…

Inference about a scalar parameter of interest typically relies on the asymptotic normality of common likelihood pivots, such as the signed likelihood root, the score and Wald statistics. Nevertheless, the resulting inferential procedures…

Suppose $\{\widehat\theta_n\colon n\ge1\}$ is a strongly consistent sequence of estimators for a parameter $\theta$, where $\widehat\theta_n$ is based on the first $n$ observations. Consider $Q_\varepsilon$, the number of times…

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…

Statistical models incorporating change points are common in practice, especially in the area of biomedicine. This approach is appealing in that a specific parameter is introduced to account for the abrupt change in the response variable…

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…