Annals of the Institute of Statistical Mathematics最新文献

This paper derives several formulae for the probability that a Wiener process, which has a stochastic drift and random variance, crosses a one-sided stochastic boundary within a finite time interval. A non-explicit formula is first obtained by the Girsanov theorem when considering an equivalent probability measure in which the boundary is constant and equal to its starting value. A more explicit formula is then achieved by decomposing the Radon–Nikodym derivative inverse. This decomposition expresses it as the product of a random variable, which is measurable with respect to the Wiener process’s final value, and an independent random variable. We also provide an explicit formula based on a strong theoretical assumption. To apply the Girsanov theorem, we assume that the difference between the drift increment and the boundary increment, divided by the standard deviation, is absolutely continuous. Additionally, we assume that its derivative satisfies Novikov’s condition.

This paper provides a novel perspective on feature screening in the analysis of high-dimensional right-censored large-p-large-N survival data. The research introduces a distributed feature screening method known as Aggregated Distance Correlation Screening (ADCS). The proposed screening framework involves expressing the distance correlation measure as a function of multiple component parameters, each of which can be estimated in a distributed manner using a natural U-statistic from data segments. By aggregating the component estimates, a final correlation estimate is obtained, facilitating feature screening. Importantly, this approach does not necessitate any specific model specification for responses or predictors and is effective with heavy-tailed data. The study establishes the consistency of the proposed aggregated correlation estimator (widetilde{omega }_{j}) under mild conditions and demonstrates the sure screening property of the ADCS. Empirical results from both simulated and real datasets confirm the efficacy and practicality of the ADCS approach proposed in this paper.

Statistical inference for high-dimensional parameters (HDPs) can leverage their intrinsic correlations, as spatially or temporally close parameters tend to have similar values. This is why nonlinear mixed-effects models (NMMs) are commonly used for HDPs. Conversely, in many practical applications, the random effects (REs) in NMMs are correlated HDPs that should remain constant during repeated sampling for frequentist inference. In both scenarios, the inference should be conditional on REs, instead of marginal inference by integrating out REs. We summarize recent theory of conditional inference for NMM, and then propose a bias-corrected RE predictor and confidence interval (CI). We also extend this methodology to accommodate the case where some REs are not associated with data. Simulation studies indicate our new approach leads to substantial improvement in the conditional coverage rate of RE CIs, including CIs for smooth functions in generalized additive models, compared to the existing method based on marginal inference.

Propensity score weighting is widely used to correct the selection bias in the sample with missing data. The propensity score function is often developed using a model for the response probability, which completely ignores the outcome regression model. In this paper, we explore an alternative approach by developing smoothed propensity score weights that provide a more efficient estimation by removing unnecessary auxiliary variables in the propensity score model. The smoothed propensity score function is obtained by applying the information projection of the original propensity score function to the space that satisfies the moment conditions on the balancing scores obtained from the outcome regression model. By including the covariates for the outcome regression models only in the density ratio model, we can achieve an efficiency gain. Penalized regression is used to identify important covariates. Some limited simulation studies are presented to compare with the existing methods.

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.