Annals of the Institute of Statistical Mathematics最新文献

We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory, assuming that the number of clusters tends to infinity with the sample size. However, when the number of clusters is fixed, classical asymptotic theory developed under a divergent number of clusters is no longer valid and can lead to erroneous conclusions. In this paper, we establish the asymptotic properties of the ML estimators of random-effects parameters under a general setting, which can be applied to conduct valid statistical inference with fixed numbers of clusters. Our asymptotic theorems allow both fixed effects and random effects to be misspecified, and the dimensions of both effects to go to infinity with the sample size.

For ( 1le i le r), let (F_i) be the cumulative incidence function (CIF) corresponding to the ith risk in an r-competing risks model. We assume a discrete or a grouped time framework and obtain the maximum likelihood estimators (m.l.e.) of these CIFs under the restriction that (F_i(t)/F_{i+1}(t)) is nondecreasing, (1 le i le r-1.) We also derive the likelihood ratio tests for testing for and against this restriction and obtain their asymptotic distributions. The theory developed here can also be used to investigate the association between a failure time and a discretized or ordinal mark variable that is observed only at the time of failure. To illustrate the applicability of our results, we give examples in the competing risks and the mark variable settings.

For the class of Gauss–Markov processes we study the problem of asymptotic equivalence of the nonparametric regression model with errors given by the increments of the process and the continuous time model, where a whole path of a sum of a deterministic signal and the Gauss–Markov process can be observed. We derive sufficient conditions which imply asymptotic equivalence of the two models. We verify these conditions for the special cases of Sobolev ellipsoids and Hölder classes with smoothness index (>1/2) under mild assumptions on the Gauss–Markov process. To give a counterexample, we show that asymptotic equivalence fails to hold for the special case of Brownian bridge. Our findings demonstrate that the well-known asymptotic equivalence of the Gaussian white noise model and the nonparametric regression model with i.i.d. standard normal errors (see Brown and Low (Ann Stat 24:2384–2398, 1996)) can be extended to a setup with general Gauss–Markov noises.

Feature selection for the high-dimensional Cox proportional hazards model (Cox model) is very important in many microarray genetic studies. In this paper, we propose a sequential feature selection procedure for this model. We define a novel partial profile score to assess the impact of unselected features conditional on the current model, significant features are thereby added into the model sequentially, and the Extended Bayesian Information Criteria (EBIC) is adopted as a stopping rule. Under mild conditions, we show that this procedure is selection consistent. Extensive simulation studies and two real data applications are conducted to demonstrate the advantage of our proposed procedure over several representative approaches.

This paper proposes a blockwise network autoregressive (BWNAR) model by grouping nodes in the network into nonoverlapping blocks to adapt networks with blockwise structures. Before modeling, we employ the pseudo likelihood ratio criterion (pseudo-LR) together with the standard spectral clustering approach and a binary segmentation method developed by Ma et al. (Journal of Machine Learning Research, 22, 1–63, 2021) to estimate the number of blocks and their memberships, respectively. Then, we acquire the consistency and asymptotic normality of the estimator of influence parameters by the quasi-maximum likelihood estimation method without imposing any distribution assumptions. In addition, a novel likelihood ratio test statistic is proposed to verify the heterogeneity of the influencing parameters. The performance and usefulness of the model are assessed through simulations and an empirical example of the detection of fraud in financial transactions, respectively.

The research is about a systematic investigation on the following issues. First, we construct different outcome regression-based estimators for conditional average treatment effect under, respectively, true, parametric, nonparametric and semiparametric dimension reduction structure. Second, according to the corresponding asymptotic variance functions when supposing the models are correctly specified, we answer the following questions: what is the asymptotic efficiency ranking about the four estimators in general? how is the efficiency related to the affiliation of the given covariates in the set of arguments of the regression functions? what do the roles of bandwidth and kernel function selections play for the estimation efficiency; and in which scenarios should the estimator under semiparametric dimension reduction regression structure be used in practice? Meanwhile, the results show that any outcome regression-based estimation should be asymptotically more efficient than any inverse probability weighting-based estimation. Several simulation studies are conducted to examine the finite sample performances of these estimators, and a real dataset is analyzed for illustration.

Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of a posteriori probability, the rate of convergence is shown which is independent of the dimension of the image. This proves that in image classification, it is possible to circumvent the curse of dimensionality by convolutional neural networks. Furthermore, the obtained result gives an indication why convolutional neural networks are able to outperform the standard feedforward neural networks in image classification. Our classifiers are compared with various other classification methods using simulated data. Furthermore, the performance of our estimates is also tested on real images.

Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment rules. When a new edge is created, with probability (pin (0,1)), it follows the PA rule. Otherwise, this new edge is added between two uniformly chosen nodes. Such mixture makes the in- and out-degrees of a fixed node grow at a slower rate, compared to the pure PA case, thus leading to lighter distributional tails. For estimation and inference, we develop two numerical methods which are applied to both synthetic and real network data. We see that with extra flexibility given by the parameter p, the hybrid random network provides a better fit to real-world scenarios, where lighter tails from in- and out-degrees are observed.

In this paper we study generalized semi-Markov high dimension regression models in continuous time, observed at fixed discrete time moments. The generalized semi-Markov process has dependent jumps and, therefore, it is an extension of the semi-Markov regression introduced in Barbu et al. (Stat Inference Stoch Process 22:187–231, 2019a). For such models we consider estimation problems in nonparametric setting. To this end, we develop model selection procedures for which sharp non-asymptotic oracle inequalities for the robust risks are obtained. Moreover, we give constructive sufficient conditions which provide through the obtained oracle inequalities the adaptive robust efficiency property in the minimax sense. It should be noted also that, for these results, we do not use neither sparse conditions nor the parameter dimension in the model. As examples, regression models constructed through spherical symmetric noise impulses and truncated fractional Poisson processes are considered. Numerical Monte-Carlo simulations confirming the theoretical results are given in the supplementary materials.