Communications in Mathematics and Statistics最新文献

Conditional quantile regression provides a useful statistical tool for modeling and inferring the relationship between the response and covariates in the heterogeneous data. In this paper, we develop a novel testing procedure for the ultrahigh-dimensional partially linear quantile regression model to investigate the significance of ultrahigh-dimensional interested covariates in the presence of ultrahigh-dimensional nuisance covariates. The proposed test statistic is an (L_2)-type statistic. We estimate the nonparametric component by some flexible machine learners to handle the complexity and ultrahigh dimensionality of considered models. We establish the asymptotic normality of the proposed test statistic under the null and local alternative hypotheses. A screening-based testing procedure is further provided to make our test more powerful in practice under the ultrahigh-dimensional regime. We evaluate the finite-sample performance of the proposed method via extensive simulation studies. A real application to a breast cancer dataset is presented to illustrate the proposed method.

The optimal stopping problem for pricing Russian options in finance requires taking the supremum of the discounted reward function over all finite stopping times. We assume the logarithm of the asset price is a spectrally negative Markov additive process with finitely many regimes. The reward function is given by the exponential of the running supremum of the price process. Previous work on Russian optimal stopping problem suggests that the optimal stopping time would be an upcrossing time of the drawdown at a certain level for each regime. We derive explicit formulas for identifying the stopping levels and computing the corresponding value functions through a recursive algorithm. A numerical is provided for finding these stopping levels and their value functions.

The spectrum of the normalized Laplacian matrix of a graph provides a lot of structural information of the graph, and it has applications in numerous areas and in different guises. In this paper, we completely characterize all connected graphs of order (nge 25) with some normalized Laplacian eigenvalue (rho in big (0,,frac{n-1}{n-2}big )) having multiplicity (n{-4}).

For a one-dimensional simple symmetric random walk ((S_n)), an edge x (between points (x-1) and x) is called a favorite edge at time n if its local time at n achieves the maximum among all edges. In this paper, we show that with probability 1 three favorite edges occurs infinitely often. Our work is inspired by Tóth and Werner (Comb Probab Comput 6:359–369, 1997), and Ding and Shen (Ann Probab 46:2545–2561, 2018), disproves a conjecture mentioned in Remark 1 on page 368 of Tóth and Werner (1997).

Equivalence assessment via various indices such as relative risk has been widely studied in a matched-pair design with discrete or continuous endpoints over the past years. But existing studies mainly focus on the fully observed or missing at random endpoints. Nonignorable missing endpoints are commonly encountered in a matched-pair design. To this end, this paper proposes several novel methods to assess equivalence of two diagnostics via the difference between two correlated areas under ROC curves (AUCs) in a matched-pair design with nonignorable missing endpoints. An exponential tilting model is utilized to specify the nonignorable missing endpoint mechanism. Three nonparametric approaches and three semiparametric approaches are developed to estimate the difference between two correlated AUCs based on the kernel-regression imputation, inverse probability weighted (IPW), and augmented IPW methods. Under some regularity conditions, we show the consistency and asymptotic normality of the proposed estimators. Simulation studies are conducted to study the performance of the proposed estimators. Empirical results show that the proposed methods outperform the complete-case method. An example from clinical studies is illustrated by the proposed methodologies.

Let (sigma ={sigma _{i} mid iin I}) be some partition of the set of all primes and G a finite group. A subgroup A of G is (sigma )-permutable in G provided G is (sigma )-full; that is, G has a Hall (sigma _{i})-subgroup for all (iin I) and A permutes with all such Hall subgroups H of G; that is, (AH=HA). Answering the Question 6.4 in Skiba (Probl Phys Math Tech 42(21):89–96, 2014), we get a description of finite (sigma )-full groups G in which (sigma )-permutability is a transitive relation.

The combined use of two drugs is a major treatment approach for complex diseases such as cancer and HIV due to its potential for efficacy at lower, less toxic doses and the need to reduce developmental time and cost. Experimental designs have been proposed in the literature to test whether there are synergistic or antagonistic actions between the combined drugs. The existing designs for synergy testing are primarily one-dimensional (1D), allocating the doses of one drug while keeping the dose of another, the mixing proportion, or the total dose of the two drugs fixed. This paper considers two-dimensional (2D) designs in which the doses of two drugs can be varied simultaneously over the entire dose region. Based on the premise that prior information about the single-drug experiments is already available, we propose a succinct dose-response model that encompasses a wide class of potential synergistic/antagonistic actions deviated from additivity. We show that the uniform design measure over the 2D dose region is optimal under the proposed model in the sense that it maximizes the minimum power in the F-test to detect drug synergy. Methods for sample size calculation and design generation for our 2D optimal design are given. We illustrate the use of the proposed design and demonstrate its advantages over the 1D optimal design via a combination study of two anticancer drugs.

Model averaging has been considered to be a powerful tool for model-based prediction in the past decades. However, its application in ultra-high dimensional multi-categorical data is faced with challenges arising from the model uncertainty and heterogeneity. In this article, a novel two-step model averaging method is proposed for multi-categorical response when the number of covariates is ultra-high. First, a class of adaptive multinomial logistic regression candidate models are constructed where different covariates for each category are allowed to accommodate heterogeneity. Second, the optimal model weights is chosen by applying the Kullback–Leibler loss plus a penalty term. We show that the proposed model averaging estimator is asymptotically optimal by achieving the minimum Kullback–Leibler loss among all possible averaging estimators. Empirical evidences from simulation studies and a real data example demonstrate that the proposed model averaging method has superior performance to the state-of-the-art approaches.

In this paper, we present new variants of both the de Casteljau subdivision algorithm for curves and Doo–Sabin subdivision algorithm for surfaces. Our subdivision schemes are built on nonlinear weighted averaging rules which are induced by monotonic functions. These averaging rules are used instead of midpoint averaging rule in the mentioned well-known subdivision algorithms. The analysis shows that the smoothness of the subdivision schemes for curves is inherited from the smoothness of the function which induces the averaging rule used in the refinement of the schemes. The results show that with our subdivision schemes, both convex surfaces and concave surfaces can be generated by the same scheme. This happens by only interchanging the weights of two adjacent points when computing the edge points in the subdivision refinement. This is an advantage since a designer can adjust the limit shape according to his interests.