Authors:Xiaohui Liu; Qihua Wang; Yi Liu Pages: 249 - 269 Abstract: Abstract In this paper, a jackknife empirical likelihood based approach is developed to test whether the underlying distribution is equal to a specified one. The limiting distribution of the proposed testing statistic is derived under some mild conditions. It turns out that the proposed test is consistent and easy to be implemented. Some simulation studies are conducted to evaluate the finite sample behaviors by comparing the proposed method with the existing one. A real data example is also analyzed to illustrate the proposed test approach. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0550-9 Issue No:Vol. 69, No. 2 (2017)

Authors:Ao Yuan; Mihai Giurcanu; George Luta; Ming T. Tan Pages: 271 - 302 Abstract: Abstract For incomplete data models, the classical U-statistic estimator of a functional parameter of the underlying distribution cannot be computed directly since the data are not fully observed. To estimate such a functional parameter, we propose a U-statistic using a substitution estimator of the conditional kernel given the observed data. This kernel estimator is obtained by substituting the non-parametric maximum likelihood estimator for the underlying distribution function in the expression of the conditional kernel. We study the asymptotic properties of the proposed U-statistic for several incomplete data models, and in a simulation study, we assess the finite sample performance of the Mann–Whitney U-statistic with conditional kernel in the current status model. The analysis of a real-world data set illustrates the application of the proposed methods in practice. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0537-6 Issue No:Vol. 69, No. 2 (2017)

Authors:Jean-François Coeurjolly Pages: 303 - 331 Abstract: Abstract This paper is concerned with a robust estimator of the intensity of a stationary spatial point process. The estimator corresponds to the median of a jittered sample of the number of points, computed from a tessellation of the observation domain. We show that this median-based estimator satisfies a Bahadur representation from which we deduce its consistency and asymptotic normality under mild assumptions on the spatial point process. Through a simulation study, we compare the new estimator, in particular, with the standard one counting the mean number of points per unit volume. The empirical study confirms the asymptotic properties established in the theoretical part and shows that the median-based estimator is more robust to outliers than standard procedures. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0536-7 Issue No:Vol. 69, No. 2 (2017)

Authors:Andrew M. Raim; Nagaraj K. Neerchal; Jorge G. Morel Pages: 333 - 364 Abstract: Abstract A simple closed form of the Fisher information matrix (FIM) usually cannot be obtained under a finite mixture. Several authors have considered a block-diagonal FIM approximation for binomial and multinomial finite mixtures, used in scoring and in demonstrating relative efficiency of proposed estimators. Raim et al. (Stat Methodol 18:115–130, 2014a) noted that this approximation coincides with the complete data FIM of the observed data and latent mixing process jointly. It can, therefore, be formulated for a wide variety of missing data problems. Multinomial mixtures feature a number of trials, which, when taken to infinity, result in the FIM and approximation becoming arbitrarily close. This work considers a clustered sampling scheme which allows the convergence result to be extended significantly to the class of exponential family finite mixtures. A series of examples demonstrate the convergence result and suggest that it can be further generalized. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0542-9 Issue No:Vol. 69, No. 2 (2017)

Authors:Jiang Hu; Zhidong Bai; Chen Wang; Wei Wang Pages: 365 - 387 Abstract: Abstract In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problems in multivariate statistical analysis and there have been various tests proposed in the literature. Motivated by Bai and Saranadasa (Stat Sin 6:311–329, 1996) and Chen and Qin (Ann Stat 38:808–835, 2010), we introduce a test statistic and derive the asymptotic distributions under the null and the alternative hypothesis. In addition, it is compared with a test statistic recently proposed by Srivastava and Kubokawa (J Multivar Anal 115:204–216, 2013). It is shown that our test statistic performs better especially in the large dimensional case. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0543-8 Issue No:Vol. 69, No. 2 (2017)

Authors:Giacomo Aletti; Matteo Ruffini Pages: 389 - 416 Abstract: Abstract In this paper, we study periodical stochastic processes, and we define the conditions that are needed by a model to be a good noise model on the circumference. The classes of processes that fit the required conditions are studied together with their expansion in random Fourier series to provide results about their path regularity. Finally, we discuss a simple and flexible parametric model with prescribed regularity that is used in applications, and we prove the asymptotic properties of the maximum likelihood estimates of model parameters. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0546-5 Issue No:Vol. 69, No. 2 (2017)

Authors:Paweł Marcin Kozyra; Tomasz Rychlik Pages: 417 - 428 Abstract: Abstract For classic i.i.d. samples with an arbitrary nondegenerate and finite variance distribution, Papadatos (1995, Annals of the Institute of Statistical Mathematics, 47, 185–193) presented sharp lower and upper bounds on the variances of order statistics, expressed in population variance units. We provide here analogous results for spacings. Also, we describe the parent distributions which attain the bounds. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0545-6 Issue No:Vol. 69, No. 2 (2017)

Authors:Christopher Partlett; Prakash Patil Pages: 429 - 460 Abstract: Abstract In this paper, we show that some of the most commonly used tests of symmetry do not have power which is reflective of the size of asymmetry. This is because the primary rationale for the test statistics that are proposed in the literature to test for symmetry is to detect the departure from symmetry, rather than the quantification of the asymmetry. As a result, tests of symmetry based upon these statistics do not necessarily generate power that is representative of the departure from the null hypothesis of symmetry. Recent research has produced new measures of asymmetry, which have been shown to do an admirable job of quantifying the amount of asymmetry. We propose several new tests based upon one such measure. We derive the asymptotic distribution of the test statistics and analyse the performance of these proposed tests through the use of a simulation study. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0547-4 Issue No:Vol. 69, No. 2 (2017)

Authors:Vygantas Paulauskas; Marijus Vaičiulis Pages: 461 - 487 Abstract: Abstract In the paper, we propose a new class of functions which is used to construct tail index estimators. Functions from this new class are non-monotone in general, but they are the product of two monotone functions: the power function and the logarithmic function, which play essential role in the classical Hill estimator. The newly introduced generalized moment ratio estimator and generalized Hill estimator have a better asymptotic performance compared with the corresponding classical estimators over the whole range of the parameters that appear in the second-order regular variation condition. Asymptotic normality of the introduced estimators is proved, and comparison (using asymptotic mean square error) with other estimators of the tail index is provided. Some preliminary simulation results are presented. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0548-3 Issue No:Vol. 69, No. 2 (2017)

Authors:Yong Kong Pages: 489 - 495 Abstract: Abstract Distributions of runs of length at least k (Type II runs) and overlapping runs of length k (Type III runs) are derived in a unified way using a new generating function approach. A new and more compact formula is obtained for the probability mass function of the Type III runs. PubDate: 2017-04-01 DOI: 10.1007/s10463-015-0549-2 Issue No:Vol. 69, No. 2 (2017)

Authors:Jingjing Wu; Rohana J. Karunamuni Abstract: Abstract In this paper, we investigate a hypothesis testing problem in regular semiparametric models using the Hellinger distance approach. Specifically, given a sample from a semiparametric family of \(\nu \) -densities of the form \(\{f_{\theta ,\eta }:\theta \in \Theta ,\eta \in \Gamma \},\) we consider the problem of testing a null hypothesis \(H_{0}:\theta \in \Theta _{0}\) against an alternative hypothesis \(H_{1}:\theta \in \Theta _{1},\) where \(\eta \) is a nuisance parameter (possibly of infinite dimensional), \(\nu \) is a \(\sigma \) -finite measure, \(\Theta \) is a bounded open subset of \(\mathbb {R}^{p}\) , and \(\Gamma \) is a subset of some Banach or Hilbert space. We employ the Hellinger distance to construct a test statistic. The proposed method results in an explicit form of the test statistic. We show that the proposed test is asymptotically optimal (i.e., locally uniformly most powerful) and has some desirable robustness properties, such as resistance to deviations from the postulated model and in the presence of outliers. PubDate: 2017-03-11 DOI: 10.1007/s10463-017-0608-y

Authors:Soutir Bandyopadhyay; Arnab Maity Abstract: Abstract The varying coefficient models (VCMs) are extremely important tools in the statistical literature and are widely used in many subject areas for data modeling and exploration. In linear VCMs, typically the errors are assumed to be independent. However, in many situations, especially in spatial or spatiotemporal settings, this is not a viable assumption. In this article, we consider nonparametric VCMs with a general dependent error structure which allows for both spatially autoregressive and spatial moving average models as special cases. We investigate asymptotic properties of local polynomial estimators of the model components. Specifically, we show that the estimates of the unknown functions and their derivatives are consistent and asymptotically normally distributed. We show that the rate of convergence and the asymptotic covariance matrix depend on the error dependence structure and we derive the explicit formula for the convergence results. PubDate: 2017-03-11 DOI: 10.1007/s10463-017-0607-z

Authors:Buddhananda Banerjee; Satyaki Mazumder Abstract: Abstract An existence of change point in a sequence of temporally ordered functional data demands more attention in its statistical analysis to make a better use of it. Introducing a dynamic estimator of covariance kernel, we propose a new methodology for testing an existence of change in the mean of temporally ordered functional data. Though a similar estimator is used for the covariance in finite dimension, we introduce it for the independent and weakly dependent functional data in this context for the first time. From this viewpoint, the proposed estimator of covariance kernel is more natural one when the sequence of functional data may possess a change point. We prove that the proposed test statistics are asymptotically pivotal under the null hypothesis and consistent under the alternative. It is shown that our testing procedures outperform the existing ones in terms of power and provide satisfactory results when applied to real data. PubDate: 2017-03-09 DOI: 10.1007/s10463-017-0606-0

Authors:Mihai Giurcanu; Brett Presnell Abstract: Abstract We study the standard-bootstrap, the centered-bootstrap, and the empirical-likelihood bootstrap tests of hypotheses used in conjunction with generalized method of moments inference in correctly specified and misspecified moment condition models. We show that, under correct specification, the standard-bootstrap estimator of the null distribution of the J-test converges in distribution to a random distribution, verifying its inconsistency, while the centered and the empirical-likelihood bootstrap estimators are consistent. We provide higher-order expansions of the size distortions of the analytic and the bootstrap tests. We show that the standard-bootstrap parameter-tests are consistent under misspecification, while the centered-bootstrap parameter-tests are inconsistent. We propose a general bootstrap methodology which is highly accurate under correct specification and consistent under misspecification. In a simulation study, we explore the finite sample behavior of the analytic and the bootstrap tests for a panel data model and we apply our methodology on a real-world data set. PubDate: 2017-03-07 DOI: 10.1007/s10463-017-0604-2

Authors:M. Razmkhah; S. Simriz Abstract: Abstract Suppose that the failure times of the units placed on a life-testing experiment are independent but nonidentically distributed random variables. Under progressively type II censoring scheme, distributional properties of the proposed random variables are presented and some inferences are made. Assuming that the random variables come from a proportional hazard rate model, the formulas are simplified and also the amount of Fisher information about the common parameters of this family is calculated. The results are also extended to a fixed covariates model. The performance of the proposed procedure is investigated via a real data set. Some numerical computations are also presented to study the effect of the proportionality rates in view of the Fisher information criterion. Finally, some concluding remarks are stated. PubDate: 2017-02-28 DOI: 10.1007/s10463-017-0598-9

Authors:Xiangshun Kong; Mingyao Ai; Kwok Leung Tsui Abstract: Abstract Sliced Latin hypercube designs are popularly adopted for computer experiments with qualitative factors. Previous constructions require the sizes of different slices to be identical. Here we construct sliced designs with flexible sizes of slices. Besides achieving desirable one-dimensional uniformity, flexible sliced designs (FSDs) constructed in this paper accommodate arbitrary sizes for different slices and cover ordinary sliced Latin hypercube designs as special cases. The sampling properties of FSDs are derived and a central limit theorem is established. It shows that any linear combination of the sample means from different models on slices follows an asymptotic normal distribution. Some simulations compare FSDs with other sliced designs in collective evaluations of multiple computer models. PubDate: 2017-02-25 DOI: 10.1007/s10463-017-0603-3

Authors:Qingguo Tang; R. J. Karunamuni Abstract: Abstract Finite mixture regression (FMR) models are frequently used in statistical modeling, often with many covariates with low significance. Variable selection techniques can be employed to identify the covariates with little influence on the response. The problem of variable selection in FMR models is studied here. Penalized likelihood-based approaches are sensitive to data contamination, and their efficiency may be significantly reduced when the model is slightly misspecified. We propose a new robust variable selection procedure for FMR models. The proposed method is based on minimum-distance techniques, which seem to have some automatic robustness to model misspecification. We show that the proposed estimator has the variable selection consistency and oracle property. The finite-sample breakdown point of the estimator is established to demonstrate its robustness. We examine small-sample and robustness properties of the estimator using a Monte Carlo study. We also analyze a real data set. PubDate: 2017-02-25 DOI: 10.1007/s10463-017-0602-4

Authors:Konstantin Eckle; Nicolai Bissantz; Holger Dette; Katharina Proksch; Sabrina Einecke Abstract: Abstract In this paper, we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a significance test for a mode at a specific point is constructed. Moreover, we develop multiscale methods for identifying regions of monotonicity and a general procedure for detecting the modes of a multivariate density. It is shown that the latter method localizes the modes with an effectively optimal rate. The theoretical results are illustrated by means of a simulation study and a data example. The new method is applied to and motivated by the determination and verification of the position of high-energy sources from X-ray observations by the Swift satellite which is important for a multiwavelength analysis of objects such as Active Galactic Nuclei. PubDate: 2017-02-24 DOI: 10.1007/s10463-017-0605-1

Authors:Weihua Zhao; Jianbo Li; Heng Lian Abstract: Abstract We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset. PubDate: 2017-02-20 DOI: 10.1007/s10463-017-0599-8

Authors:Péter Kevei Abstract: Abstract High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process \((Y_{n\varDelta })_{n \in {\mathbb {Z}}}\) as \(\varDelta \downarrow 0\) , where \((Y_t)_{t \in {\mathbb {R}}}\) is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the univariate results to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive \(\varDelta \) . However, the results established here provide a useful and insightful approximation when \(\varDelta \) is very small. PubDate: 2017-02-20 DOI: 10.1007/s10463-017-0601-5