Annals of the Institute of Statistical Mathematics最新文献

We consider relative model comparison for the parametric coefficients of an ergodic Lévy driven model observed at high-frequency. Our asymptotics is based on the fully explicit two-stage Gaussian quasi-likelihood function (GQLF) of the Euler-approximation type. For selections of the scale and drift coefficients, we propose explicit Gaussian quasi-AIC and Gaussian quasi-BIC statistics through the stepwise inference procedure, and prove their asymptotic properties. In particular, we show that the mixed-rates structure of the joint GQLF, which does not emerge in the case of diffusions, gives rise to the non-standard forms of the regularization terms in the selection of the scale coefficient, quantitatively clarifying the relation between estimation precision and sampling frequency. Also shown is that the stepwise strategies are essential for both the tractable forms of the regularization terms and the derivation of the asymptotic properties of the Gaussian quasi-information criteria. Numerical experiments are given to illustrate our theoretical findings.

We derive limiting distributions of symmetrized estimators of scatter. Instead of considering all (n(n-1)/2) pairs of the n observations, we only use nd suitably chosen pairs, where (d ge 1) is substantially smaller than n. It turns out that the resulting estimators are asymptotically equivalent to the original one whenever (d = d(n) rightarrow infty) at arbitrarily slow speed. We also investigate the asymptotic properties for arbitrary fixed d. These considerations and numerical examples indicate that for practical purposes, moderate fixed values of d between 10 and 20 yield already estimators which are computationally feasible and rather close to the original ones.

This work is concerned with testing the marginal linear effects of high-dimensional predictors in quantile regression. We introduce a novel test that is constructed using maxima of pairwise quantile correlations, which permit consistent assessment of the marginal linear effects. The proposed testing procedure is computationally efficient with the aid of a simple multiplier bootstrap method and does not involve any need to select tuning parameters, apart from the number of bootstrap replications. Other distinguishing features of the new procedure are that it imposes no structural assumptions on the unknown dependence structures of the predictor vector and allows the dimension of the predictor vector to be exponentially larger than sample size. To broaden the applicability, we further extend the preceding analysis to the censored response case. The effectiveness of our proposed approach in the finite samples is illustrated through simulation studies.

The estimation of treatment effects on the response variable is often a primary goal in empirical investigations in disciplines such as medicine, economics and marketing. Typically, the investigator would select one model from a multitude of models and estimate the treatment effects based on this single winning model. In this paper, we consider an alternative model averaging approach, where estimates of treatment effects are obtained from not one single model but a weighted ensemble of models. We develop a weight choice method based on a minimisation of the approximate risk under squared error loss of the model average estimator of the conditional treatment effects. We prove that the model average estimator resulting from this criterion has an optimal asymptotic property. The results of a simulation study show that the proposed approach is superior to various existing model selection and averaging methods in a large region of the parameter space in finite samples. The proposed method is applied to a data set on HIV treatment.

Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules, which are statistically principled tools for the comparative evaluation of predictive performance, to the point process setting, and place both new and existing methodology in this framework. With reference to earthquake likelihood model testing, we demonstrate that extant techniques apply in much broader contexts than previously thought. In particular, the Poisson log-likelihood can be used for theoretically principled comparative forecast evaluation in terms of cell expectations. We illustrate the approach in a simulation study and in a comparative evaluation of operational earthquake forecasts for Italy.

We propose novel goodness-of-fit tests for the Weibull distribution with unknown parameters. These tests are based on an alternative characterizing representation of the Laplace transform related to the density approach in the context of Stein’s method. Asymptotic theory of the tests is derived, including the limit null distribution, the behaviour under contiguous alternatives, the validity of the parametric bootstrap procedure, and consistency of the tests against a large class of alternatives. A Monte Carlo simulation study shows the competitiveness of the new procedure. Finally, the procedure is applied to real data examples taken from the materials science.

Estimation of compiler causal treatment effects has been discussed by many authors under different situations but only limited literature exists for interval-censored failure time data, which often occur in many areas such as longitudinal or periodical follow-up studies. Particularly it does not seem to exist a method that can deal with informative interval censoring, which can happen naturally and make the analysis much more challenging. Also, it has been shown that when the informative censoring exists, the analysis without taking it into account would yield biased or misleading results. To address this, we propose an estimated sieve maximum likelihood approach with the use of instrumental variables. The asymptotic properties of the resulting estimators of regression parameters are established, and a simulation study is performed and suggests that it works well. Finally, it is applied to a set of real data that motivated this study.

In this paper, we consider variable selection for a class of semiparametric spatial autoregressive models based on exponential squared loss (ESL). Using the orthogonal projection technique, we propose a novel orthogonality-based variable selection procedure that enables simultaneous model selection and parameter estimation, and identifies the significance of spatial effects. Under appropriate conditions, we show that the proposed procedure is consistent and the resulting estimator has oracle properties. Furthermore, some simulation studies and an analysis of the Boston housing price data are also carried out to examine the finite-sample performance of the proposed method.

Imputation is a popular technique for handling missing data. We address a nonparametric imputation using the regularized M-estimation techniques in the reproducing kernel Hilbert space. Specifically, we first use kernel ridge regression to develop imputation for handling item nonresponse. Although this nonparametric approach is potentially promising for imputation, its statistical properties are not investigated in the literature. Under some conditions on the order of the tuning parameter, we first establish the root-n consistency of the kernel ridge regression imputation estimator and show that it achieves the lower bound of the semiparametric asymptotic variance. A nonparametric propensity score estimator using the reproducing kernel Hilbert space is also developed by the linear expression of the projection estimator. We show that the resulting propensity score estimator is asymptotically equivalent to the kernel ridge regression imputation estimator. Results from a limited simulation study are also presented to confirm our theory. The proposed method is applied to analyze air pollution data measured in Beijing, China.