Annals of the Institute of Statistical Mathematics最新文献

Exploring more accurate estimates of financial value at risk (VaR) has always been an important issue in applied statistics. To this end either quantile or expectile regression methods are widely employed at present, but an accumulating body of research indicates that (L^{p}) quantile regression outweighs both quantile and expectile regression in many aspects. In view of this, the paper extends (L^{p}) quantile regression to a general classical nonlinear conditional autoregressive model and proposes a new model called the conditional (L^{p}) quantile nonlinear autoregressive regression model (CAR-(L^{p})-quantile model for short). Limit theorems for regression estimators are proved in mild conditions, and algorithms are provided for obtaining parameter estimates and the optimal value of p. Simulation study of estimation’s quality is given. Then, a CLVaR method calculating VaR based on the CAR-(L^{p})-quantile model is elaborated. Finally, a real data analysis is conducted to illustrate virtues of our proposed methods.

The IHK program is a general framework in asymptotic decision theory, introduced by Ibragimov and Hasminskii and extended to semimartingales by Kutoyants. The quasi-likelihood analysis (QLA) asserts that a polynomial type large deviation inequality is always valid if the quasi-likelihood random field is asymptotically quadratic and if a key index reflecting the identifiability is non-degenerate. As a result, following the IHK program, the QLA gives a way to inference for various nonlinear stochastic processes. This paper provides a reformed and simplified version of the QLA and improves accessibility to the theory. As an example of the advantages of the scheme, the user can obtain asymptotic properties of the quasi-Bayesian estimator by only verifying non-degeneracy of the key index.

We introduce a new type of influence function, the asymptotic expected sensitivity function, which is often equivalent to but mathematically more tractable than the traditional one based on the Gâteaux derivative. To illustrate, we study the robustness of some important measures of association, including Spearman’s rank correlation and Kendall’s concordance measure, and the recently developed Chatterjee’s correlation.

We derive asymptotic properties of penalized estimators for singular models for which identifiability may break and the true parameter values can lie on the boundary of the parameter space. Selection consistency of the estimators is also validated. The problem that the true values lie on the boundary is solved by our previous results applicable to singular models, besides, penalized estimation and non-ergodic statistics. To overcome non-identifiability, we consider a suitable penalty such as the non-convex Bridge and the adaptive Lasso that stabilize the asymptotic behavior of the estimator and shrink inactive parameters. Then the estimator converges to one of the most parsimonious values among all the true values. The oracle property can also be obtained even if likelihood ratio tests for model selection are labor intensive due to singularity of models. Examples are: a superposition of parametric proportional hazard models and a counting process having intensity with multicollinear covariates.

This work discusses a model of a partially observed linear system that depends on some unknown parameters. An approximation of the unobserved component is proposed, which involves three steps. First, a method of moment estimator of unknown parameters is constructed, and second, this estimator is used to define the one-step MLE-process. Finally, the last estimator is substituted into the equations of the Kalman filter. The solution of obtained equations provides us with the desired approximation (adaptive Kalman filter). The asymptotic properties of all the mentioned estimators and both maximum likelihood and Bayesian estimators of the unknown parameters are detailed. The asymptotic efficiency of adaptive filtering is discussed.

Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the explicit form of the integral term can be derived only for specific densities, such as normal and exponential densities. While we may perform a numerical integration for each iteration of the optimization algorithms, the computational complexity has hindered the practical application of DPD-based estimation to more general parametric densities. To address the issue, this study introduces a stochastic approach to minimize DPD for general parametric density models. The proposed approach can also be employed to minimize other density power-based (gamma)-divergences, by leveraging unnormalized models. We provide R package for implementation of the proposed approach in https://github.com/oknakfm/sgdpd.

Up to now, almost all existing methods for joint modeling survival data and longitudinal data rely on parametric/semiparametric assumptions on longitudinal covariate process, and the resulting inferences critically depend on the validity of these assumptions that are difficult to verify in practice. The kernel method-based procedures rely on choices of kernel function and bandwidth, and none of the existing methods provides estimate for the baseline distribution in proportional hazards model. This article proposes a proportional hazards model for joint modeling right censored survival data and intensive longitudinal data taking into account of within-subject historic change patterns. Without any parametric/semiparametric assumptions or use of kernel method, we derive empirical likelihood-based maximum likelihood estimators and partial likelihood estimators for the regression parameter and the baseline distribution function. We develop stable computing algorithms and present some simulation results. Analyses of real dataset are conducted for smoking cessation data and liver disease data.

The tail conditional allocation plays an important role in a number of areas, including economics, finance, insurance, and management. Fixed-margin confidence intervals and the assessment of their coverage probabilities are of much interest. In this paper, we offer a convenient way to achieve these goals via resampling. The theoretical part of the paper, which is technically demanding, is rigorously established under minimal conditions to facilitate the widest practical use. A simulation-based study and an analysis of real data illustrate the performance of the developed methodology.

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the parameter space or where even identifiability fails. For that, we propose a more general local approximation of the parameter space (at the true value) than previous studies. This estimation theory is comprehensive in that it can handle penalized estimation as well as quasi-maximum likelihood estimation (in the ergodic or non-ergodic statistics) under such non-regular models. In penalized estimation, depending on the boundary constraint, even the concave Bridge estimator does not necessarily give selection consistency. Therefore, we describe some sufficient condition for selection consistency, precisely evaluating the balance between the boundary constraint and the form of the penalty. An example is penalized MLE of variance components of random effects in linear mixed models.