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Abstract: Abstract In the linear regression model with possibly autoregressive errors, we construct a family of nonparametric tests for significance of regression, under a nuisance autoregression of model errors. The tests avoid an estimation of nuisance parameters, in contrast to the tests proposed in the literature. A simulation study illustrate their good performance. PubDate: 2022-08-03
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Abstract: Abstract Strong orthogonal arrays (SOAs) have received more and more attention recently since they enjoy more desirable space-filling properties than ordinary orthogonal arrays. Among them, the SOAs of strength \(2+\) are the most advisable as they satisfy the same two-dimensional space-filling property as SOAs of strength 3 while having more columns for given run sizes. In addition, column-orthogonality is also a desirable property for designs of computer experiments. Existing column-orthogonal SOAs of strength \(2+\) have limited columns. In this paper, we propose a new class of space-filling designs, called group SOAs of strength \(2+\) , and provide construction methods for such designs. The proposed designs can accommodate more columns than column-orthogonal SOAs of strength \(2+\) for given run sizes while satisfying similar stratifications and retaining a high proportion of column-orthogonal columns. Orthogonal arrays and difference schemes play important roles in the construction. The construction procedures are easy to implement and a large amount of group SOAs with \(s^2\) levels are constructed where \(s \ge 2\) is a prime power. In addition, the run sizes of the constructed designs are s times the ones of the orthogonal arrays used in the construction procedure. Thus they are relatively flexible. PubDate: 2022-08-01
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Abstract: Abstract Uniform designs have been widely used in physical and computer experiments due to their robust performances. The level permutation method can efficiently construct uniform designs with both lower discrepancy and less aberration. However, the related existing literature has mostly discussed uniform fixed-level designs, the construction of uniform mixed-level designs has been quite few studied. In this paper, a novel level permutation method for constructing uniform mixed-level designs is proposed. Our main idea is to perform level permutations on a new class of designs, called minimum average discrepancy designs, rather than generalized minimum aberration designs as in the fixed-level case. Several theoretical results on the design optimality and construction are obtained. Numerical results suggest the good performance of the resulting designs under various popular discrepancies. PubDate: 2022-08-01
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Abstract: Abstract Fan et al. (Ann Stat 47(6):3009–3031, 2019) constructed a distributed principal component analysis (PCA) algorithm to reduce the communication cost between multiple servers significantly. However, their algorithm’s guarantee is only for sub-Gaussian data. Spurred by this deficiency, this paper enhances the effectiveness of their distributed PCA algorithm by utilizing robust covariance matrix estimators of Minsker (Ann Stat 46(6A):2871–2903, 2018) and Ke et al. (Stat Sci 34(3):454–471, 2019) to tame heavy-tailed data. The theoretical results demonstrate that when the sampling distribution is symmetric innovation with the bounded fourth moment or asymmetric with the finite 6th moment, the statistical error rate of the final estimator produced by the robust algorithm is similar to that of sub-Gaussian tails. Extensive numerical trials support the theoretical analysis and indicate that our algorithm is robust to heavy-tailed data and outliers. PubDate: 2022-08-01
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Abstract: Abstract We prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous functions defined on [0, 1] which satisfy some suitable conditions. In this way we generalize some recent results by Giuliano et al. (J Statist Plann Inference 157–158:77–89, 2015) which concern the empirical cumulative entropies defined in Di Crescenzo et al. (J Statist Plann Inference 139:4072–4087, 2009a). PubDate: 2022-08-01
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Abstract: Abstract The purpose of the paper is to provide a general method based on conditional quantile curves to predict record values from preceding records. The predictions are based on conditional median (or median regression) curves. Moreover, conditional quantiles curves are used to provide confidence bands for these predictions. The method is based on the recently introduced concept of multivariate distorted distributions that are used instead of copulas to represent the dependence structure. This concept allows us to compute the conditional quantile curves in a simple way. The theoretical findings are illustrated with a non-parametric model (standard uniform), two parametric models (exponential and Pareto), and a non-parametric procedure for the general case. A real data set and a simulated case study in reliability are analysed. PubDate: 2022-08-01
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Abstract: Abstract Li et al. (Comm Statist Theory Methods 49: 924–941, 2020) introduced the concept of inverse Yates-order (IYO) designs, and obtained most of two-level IYO designs have general minimum lower-order confounding (GMC) property. For this reason, the paper extends two-level IYO designs to three-level cases. We first propose the definition of \(3^{n-m}\) IYO design \(D_q(n)\) from the saturated design \(H_q\) with three levels. Then, the formulas of lower-order confounding are obtained according to the factor number of \(3^{n-m}\) IYO design: (i) \(q<n<3^{q-1}\) , and (ii) \(3^{q-1}\le n\le (N-1)/2\) , where \(N=3^{n-m}\) . Under case (ii), we obtain the explicit expressions of lower-order confounding for four structure types of IYO designs. Some examples are given to illustrate the theoretical results. Compared with GMC designs, three-level IYO designs with 27- and 81-run are tabulated to show that some of them have GMC property through lower-order confounding. PubDate: 2022-07-28
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Abstract: Abstract We focus on estimating daily integrated volatility (IV) by realized measures based on intraday returns following a discrete-time stochastic model with a pronounced intraday periodicity (IP). We demonstrate that neglecting the IP-impact on realized estimators may lead to invalid statistical inference concerning IV for a common finite number of intraday returns. For a given IP functional form, we analytically derive robust IP-correction factors for realized measures of IV as well as their asymptotic distributions. We show both in Monte Carlo simulations and empirically that the proposed bias corrections are the robust way to account for IP by computing realized estimators. PubDate: 2022-07-16
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Abstract: Abstract The \(\gamma \) -divergence is well-known for having strong robustness against heavy contamination. By virtue of this property, many applications via the \(\gamma \) -divergence have been proposed. There are two types of \(\gamma \) -divergence for the regression problem, in which the base measures are handled differently. In this study, these two \(\gamma \) -divergences are compared, and a large difference is found between them under heterogeneous contamination, where the outlier ratio depends on the explanatory variable. One \(\gamma \) -divergence has the strong robustness even under heterogeneous contamination. The other does not have in general; however, it has under homogeneous contamination, where the outlier ratio does not depend on the explanatory variable, or when the parametric model of the response variable belongs to a location-scale family in which the scale does not depend on the explanatory variables. Hung et al. (Biometrics 74(1):145–154, 2018) discussed the strong robustness in a logistic regression model with an additional assumption that the tuning parameter \(\gamma \) is sufficiently large. The results obtained in this study hold for any parametric model without such an additional assumption. PubDate: 2022-07-01
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Abstract: Abstract In this paper, the problem of testing the hypothesis of linear combination of k-sample means of high-dimensional data is investigated under a low-dimensional factor model. We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of independent chi-squared distribution of 1 degree of freedom under the null hypothesis and mild conditions. We provide numerical studies on both sizes and powers to illustrate performance of the proposed test. PubDate: 2022-07-01 DOI: 10.1007/s00184-021-00841-2
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Abstract: Abstract This paper deals with the nonparametric estimation of the expectile regression when the observations are spatially correlated and are of a functional nature. The main findings of this work is the establishment of the almost complete convergence for the proposed estimator under some general mixing conditions. The performance of the proposed estimator is examined by using simulated data. Finally, the studied model is used to evaluate the air quality indicators in northeast China. PubDate: 2022-07-01 DOI: 10.1007/s00184-021-00846-x
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Abstract: Abstract In the present paper the metric of distance is adapted to a sequence of binary trials and the concept of r-weak runs is introduced and defined. The new structure gives rise to new families of binomial-type distributions, which are studied in the case of independent but not necessarily identically distributed binary trials. It is highlighted how the new theoretical results can be profitably applied to various fields, such as Agriculture, Finance and Reliability Engineering. PubDate: 2022-07-01 DOI: 10.1007/s00184-021-00842-1
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Abstract: Abstract When the levels of some factors in an experiment are difficult to be changed or controlled, fractional factorial split-plot (FFSP) designs are commonly used in which the factors are classified as the whole plot (WP) and sub-plot (SP) factors. Mixed-level designs are used in practice when the levels of the factors are not equal to each other. This paper considers the mixed-level FFSP designs with the WP factors being more important than the SP factors. It proposes the combined minimum aberration criterion of type WP (WP-MA \(^{c}\) ) for mixed-level FFSP designs. Some optimal mixed-level FFSP designs are constructed under the WP-MA \(^{c}\) criterion. PubDate: 2022-07-01 DOI: 10.1007/s00184-021-00838-x
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Abstract: Abstract A large number of existing high-dimensional panel data analyses are established based on normal or nearly normal distribution assumptions, which may be not robust to severe departures of normality. Since the observed data may not follow the normal distribution in some specific applications, it is necessary to design robust tests to departures of normality. On this ground, we propose a rank-based score test for testing slope homogeneity in high-dimensional panel data regressions, where robust tests to departures of normality are still rare. Both theoretical and numerical results demonstrate the advantage of the proposed test in robustness to departures of normality. PubDate: 2022-07-01 DOI: 10.1007/s00184-021-00845-y
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Abstract: Abstract For a finite mixture of skew normal distributions, the maximum likelihood estimator is not well-defined because of the unboundedness of the likelihood function when scale parameters go to zero and the divergency of the skewness parameter estimates. To overcome these two problems simultaneously, we propose constrained maximum likelihood estimators under constraints on both the scale parameters and the skewness parameters. The proposed estimators are consistent and asymptotically efficient under relaxed constraints on the scale and skewness parameters. Numerical simulations show that in finite sample cases the proposed estimators outperform the ordinary maximum likelihood estimators. Two real datasets are used to illustrate the success of the proposed approach. PubDate: 2022-06-30
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Abstract: Abstract In this paper, we focus on partially linear varying coefficient quantile regression with observations missing at random, which allows the responses or responses and covariates simultaneously missing. By means of empirical likelihood method, we construct posterior distributions of the parameter in the model, and investigate their large sample properties under fixed prior. Meanwhile, we use a Bayesian hierarchical model based on empirical likelihood, spike and slab Gaussian priors to discuss variable selection. By using MCMC algorithm, finite sample performance of the proposed methods is investigated via simulations, and real data analysis is discussed too. PubDate: 2022-06-18
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Abstract: Abstract Composite quantile regression (CQR) estimator is a robust and efficient alternative to the M-estimator and ordinary quantile regression estimator in linear models. In order to construct sparse CQR estimation in the presence of distributed data, we propose a penalized communication-efficient surrogate loss function that is computationally superior to the original global loss function. The proposed method only needs the worker machines to compute the gradient based on local data without a penalty and the central machine to solve a regular estimation problem. We prove that the estimation errors based on the proposed method match the estimation error bound of the centralized method by analyzing the entire data set simultaneously. A modified alternating direction method of multipliers algorithm is developed to efficiently obtain the sparse CQR estimator. The performance of the proposed estimator is studied through simulation, and an application to a real data set is also presented. PubDate: 2022-06-16
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Abstract: Abstract The von Mises–Fisher distribution is one of the most widely used probability distributions to describe directional data. Finite mixtures of von Mises–Fisher distributions have found numerous applications. However, the likelihood function for the finite mixture of von Mises–Fisher distributions is unbounded and consequently the maximum likelihood estimation is not well defined. To address the problem of likelihood degeneracy, we consider a penalized maximum likelihood approach whereby a penalty function is incorporated. We prove strong consistency of the resulting estimator. An Expectation–Maximization algorithm for the penalized likelihood function is developed and experiments are performed to examine its performance. PubDate: 2022-06-15
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Abstract: Abstract In the early stage of exploring a complex system, a preliminary experiment is used to capture the key characteristics of the model. Symmetrical global sensitivity analysis (SGSA) is one such experiment that explores the symmetrical structure of model by decomposing the model into independent symmetric functions. However, the existing experimental plans for SGSA rely on deterministic computational models that produce unique values of outputs when executed for specific values of inputs. In this paper, the problem of designing experiments for non-parametric SGSA is considered. Here the phrase “non-parametric” refers to model outputs containing random errors. The main result in the paper shows that a symmetrical design with certain constraints achieves A-optimum for the estimation of each output element function, and guarantees the superiority of the SGSA result. The statistical properties of non-parametric SGSA based on the optimal designs are further discussed, showing that the non-influential sensitivity indices can be estimated with low bias and volatility. Two explicit structures of the optimal designs are obtained. The optimality of the derived design is validated by simulation in the end. PubDate: 2022-06-10
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Abstract: Abstract In this paper, we consider a coherent system composed of components whose lifetimes are independent and identically discretely distributed random variables. We study several aging and stochastic properties of the conditional residual lifetime of the system under the condition that some of its components have failed by time t. Moreover, we compare the conditional residual lifetimes of two coherent systems by using various stochastic orders. PubDate: 2022-06-08
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