Annals of the Institute of Statistical Mathematics最新文献

For two-sided hypothesis testing in location families, the classical optimality criterion is the one leading to uniformly most powerful unbiased (UMPU) tests. Such optimal tests, however, are constructed in exponential models only. We argue that if the base distribution is symmetric, then it is natural to consider uniformly most powerful symmetric (UMPS) tests, that is, tests that are uniformly most powerful in the class of level-(alpha ) tests whose power function is symmetric. For single-observation models, we provide a condition ensuring existence of UMPS tests and give their explicit form. When this condition is not met, UMPS tests may fail to exist and we provide a weaker condition under which there exist UMP tests in the class of level-(alpha ) tests whose power function is symmetric and U-shaped. In the multi-observation case, we obtain results in exponential models that also allow for non-location families.

The purpose of this paper is to investigate the multivariate frequency polygon as a density estimator for stationary random fields indexed by multidimensional lattice points space. Optimal cell widths that asymptotically minimize integrated mean square error (IMSE) are derived. Under weak conditions, the IMSE of frequency polygons achieves the same rate of convergence to zero as that of kernel estimators. The frequency polygon can also attain the optimal uniform rate of convergence and the almost sure convergence under general conditions. Finally, a result of (L^1) convergence is given. Frequency polygons thus appear to be very good density estimators with respect to the criteria of IMSE, of uniform convergence, of almost sure convergence and of (L^1) convergence. We apply our results to simulated data and real data.

An old problem in multivariate statistics is that linear Gaussian models are often unidentifiable. In factor analysis, an orthogonal rotation of the factors is unidentifiable, while in linear regression, the direction of effect cannot be identified. For such linear models, non-Gaussianity of the (latent) variables has been shown to provide identifiability. In the case of factor analysis, this leads to independent component analysis, while in the case of the direction of effect, non-Gaussian versions of structural equation modeling solve the problem. More recently, we have shown how even general nonparametric nonlinear versions of such models can be estimated. Non-Gaussianity is not enough in this case, but assuming we have time series, or that the distributions are suitably modulated by observed auxiliary variables, the models are identifiable. This paper reviews the identifiability theory for the linear and nonlinear cases, considering both factor analytic and structural equation models.

The nonparametric regression model with correlated errors is a powerful tool for time series forecasting. We are interested in the estimation of such a model, where the errors follow an autoregressive and moving average (ARMA) process, and the covariates can also be correlated. Instead of estimating the constituent parts of the model in a sequential fashion, we propose a spline-based method to estimate the mean function and the parameters of the ARMA process jointly. We establish the desirable asymptotic properties of the proposed approach under mild regularity conditions. Extensive simulation studies demonstrate that our proposed method performs well and generates strong evidence supporting the established theoretical results. Our method provides a new addition to the arsenal of tools for analyzing serially correlated data. We further illustrate the practical usefulness of our method by modeling and forecasting the weekly natural gas scraping data for the state of Iowa.

This paper deals with a projection least squares estimator of the drift function of a jump diffusion process X computed from multiple independent copies of X observed on [0, T]. Risk bounds are established on this estimator and on an associated adaptive estimator. Finally, some numerical experiments are provided.

In this paper, we compare two regression curves by measuring their difference by the area between the two curves, represented by their (L^1)-distance. We develop asymptotic confidence intervals for this measure and statistical tests to investigate the similarity/equivalence of the two curves. Bootstrap methodology specifically designed for equivalence testing is developed to obtain procedures with good finite sample properties and its consistency is rigorously proved. The finite sample properties are investigated by means of a small simulation study.