Authors:C. F. Jeff Wu Pages: 249 - 268 Abstract: Interactions and effect aliasing are among the fundamental concepts in experimental design. In this paper, some new insights and approaches are provided on these subjects. In the literature, the “de-aliasing” of aliased effects is deemed to be impossible. We argue that this “impossibility” can indeed be resolved by employing a new approach which consists of reparametrization of effects and exploitation of effect non-orthogonality. This approach is successfully applied to three classes of designs: regular and nonregular two-level fractional factorial designs, and three-level fractional factorial designs. For reparametrization, the notion of conditional main effects (cme’s) is employed for two-level regular designs, while the linear-quadratic system is used for three-level designs. For nonregular two-level designs, reparametrization is not needed because the partial aliasing of their effects already induces non-orthogonality. The approach can be extended to general observational data by using a new bi-level variable selection technique based on the cme’s. A historical recollection is given on how these ideas were discovered. PubDate: 2018-04-01 DOI: 10.1007/s10463-018-0646-0 Issue No:Vol. 70, No. 2 (2018)
Authors:Yi Liu; Qihua Wang Pages: 283 - 301 Abstract: In this paper, the conditional distance correlation (CDC) is used as a measure of correlation to develop a conditional feature screening procedure given some significant variables for ultrahigh-dimensional data. The proposed procedure is model free and is called conditional distance correlation-sure independence screening (CDC-SIS for short). That is, we do not specify any model structure between the response and the predictors, which is appealing in some practical problems of ultrahigh-dimensional data analysis. The sure screening property of the CDC-SIS is proved and a simulation study was conducted to evaluate the finite sample performances. Real data analysis is used to illustrate the proposed method. The results indicate that CDC-SIS performs well. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0597-2 Issue No:Vol. 70, No. 2 (2018)
Authors:Chen Chen; Hosam Mahmoud Pages: 303 - 321 Abstract: We study poissonized triangular (reducible) urns on two colors, which we take to be white and blue. We analyze the number of white and blue balls after a certain period of time has elapsed. We show that for balanced processes in this class, a different scaling is needed for each color to produce nontrivial limits, contrary to the distributions in the usual irreducible urns which only require the same scaling for both colors. The limit distributions (of the scaled variables) underlying triangular urns are Gamma. The technique we use couples partial differential equations with the method of moments applied in a bootstrapped manner to produce exact and asymptotic moments. For the dominant color, we get exact moments, while relaxing the balance condition. The exact moments include alternating signs and Stirling numbers of the second kind. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0594-5 Issue No:Vol. 70, No. 2 (2018)
Authors:Kangning Wang Pages: 323 - 351 Abstract: Spatial semiparametric varying coefficient models are a useful extension of spatial linear model. Nevertheless, how to conduct variable selection for it has not been well investigated. In this paper, by basis spline approximation together with a general M-type loss function to treat mean, median, quantile and robust mean regressions in one setting, we propose a novel partially adaptive group \(L_{r} (r\ge 1)\) penalized M-type estimator, which can select variables and estimate coefficients simultaneously. Under mild conditions, the selection consistency and oracle property in estimation are established. The new method has several distinctive features: (1) it achieves robustness against outliers and heavy-tail distributions; (2) it is more flexible to accommodate heterogeneity and allows the set of relevant variables to vary across quantiles; (3) it can keep balance between efficiency and robustness. Simulation studies and real data analysis are included to illustrate our approach. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0589-2 Issue No:Vol. 70, No. 2 (2018)
Authors:Uttam Bandyopadhyay; Atanu Biswas Pages: 353 - 371 Abstract: In this paper, we obtain fixed-width confidence interval for covariate-adjusted response-adaptive designs. Specifically, we consider logistic regression model and the normal regression model for binary and continuous responses, respectively, both in the situations for presence and absence of treatment–covariate interactions. Simulation study and real-data analysis are carried out. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0596-3 Issue No:Vol. 70, No. 2 (2018)
Authors:Heidar Eyjolfsson; Dag Tjøstheim Pages: 373 - 393 Abstract: In this paper, we discuss a class of mean-reverting, and self-exciting continuous-time jump processes. We give a short overview, with references, of the development of such processes, discuss maximum likelihood estimation, and put them into context with processes that have been proposed recently. More specifically, we introduce a class of SDE-governed intensity processes with varying jump intensity. We study Markovian aspects of this process, and analyse its stability properties. Finally, we consider parameter estimation of our model class with daily quotes of UK electricity prices over a specific period. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0591-8 Issue No:Vol. 70, No. 2 (2018)
Authors:Jin-Jian Hsieh; Hong-Rui Wang Pages: 395 - 419 Abstract: In this paper, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. The estimation of quantile regression parameters for the non-terminal event is complicated. We cannot make inference on the non-terminal event without extra assumptions. Thus, we handle this problem by assuming that the joint distribution of the terminal event and the non-terminal event follows a parametric copula model with unspecified marginal distributions. We use the stochastic property of the martingale method to estimate the quantile regression parameters under semi-competing risks data. We also prove the large sample properties of the proposed estimator, and introduce a model diagnostic approach to check model adequacy. From simulation results, it shows that the proposed estimator performs well. For illustration, we apply our proposed approach to analyze a real data. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0593-6 Issue No:Vol. 70, No. 2 (2018)
Authors:Hidetoshi Shimodaira; Haruyoshi Maeda Pages: 421 - 438 Abstract: We derive an information criterion to select a parametric model of complete-data distribution when only incomplete or partially observed data are available. Compared with AIC, our new criterion has an additional penalty term for missing data, which is expressed by the Fisher information matrices of complete data and incomplete data. We prove that our criterion is an asymptotically unbiased estimator of complete-data divergence, namely the expected Kullback–Leibler divergence between the true distribution and the estimated distribution for complete data, whereas AIC is that for the incomplete data. The additional penalty term of our criterion for missing data turns out to be only half the value of that in previously proposed information criteria PDIO and AICcd. The difference in the penalty term is attributed to the fact that our criterion is derived under a weaker assumption. A simulation study with the weaker assumption shows that our criterion is unbiased while the other two criteria are biased. In addition, we review the geometrical view of alternating minimizations of the EM algorithm. This geometrical view plays an important role in deriving our new criterion. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0592-7 Issue No:Vol. 70, No. 2 (2018)
Authors:Michael Kohler; Adam Krzyżak; Reinhard Tent; Harro Walk Pages: 439 - 465 Abstract: Nonparametric estimation of a quantile of a random variable m(X) is considered, where \(m: \mathbb {R}^d\rightarrow \mathbb {R}\) is a function which is costly to compute and X is a \(\mathbb {R}^d\) -valued random variable with a given density. An importance sampling quantile estimate of m(X), which is based on a suitable estimate \(m_n\) of m, is defined, and it is shown that this estimate achieves a rate of convergence of order \(\log ^{1.5}(n)/n\) . The finite sample size behavior of the estimate is illustrated by simulated data. PubDate: 2018-04-01 DOI: 10.1007/s10463-016-0595-4 Issue No:Vol. 70, No. 2 (2018)
Authors:Péter Kevei Pages: 467 - 487 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: 2018-04-01 DOI: 10.1007/s10463-017-0601-5 Issue No:Vol. 70, No. 2 (2018)
Authors:Han-Ying Liang; Elias Ould Saïd Pages: 155 - 189 Abstract: Based on empirical likelihood method, we construct new weighted estimators of conditional density and conditional survival functions when the interest random variable is subject to random left-truncation; further, we define a plug-in weighted estimator of the conditional hazard rate. Under strong mixing assumptions, we derive asymptotic normality of the proposed estimators which permit to built a confidence interval for the conditional hazard rate. The finite sample behavior of the estimators is investigated via simulations too. PubDate: 2018-02-01 DOI: 10.1007/s10463-016-0587-4 Issue No:Vol. 70, No. 1 (2018)
Authors:Huijun Guo; Youming Liu Abstract: This paper studies multivariate wavelet regression estimators with errors-in-variables under strong mixing data. We firstly prove the strong consistency for non-oscillating and Fourier-oscillating noises. Then, a convergence rate is provided for non-oscillating noises, when an estimated function has some smoothness. Finally, the consistency and convergence rate are discussed for a practical wavelet estimator. PubDate: 2018-02-27 DOI: 10.1007/s10463-018-0653-1
Authors:Ensiyeh Nezakati; Mostafa Razmkhah; Firoozeh Haghighi Abstract: A k-out-of-n:F system with both of soft and hard failures is considered such that its components degrade through internal and external factors. A linear model is considered for degradation path of each component. Reliability function of the system is derived and the effect of varying the parameters are studied on reliability function for some systems. Moreover, the effect of calibration on reliability and maximum working time of such a system is investigated. The optimal number of calibrations is also determined for some special cases. PubDate: 2018-02-26 DOI: 10.1007/s10463-018-0650-4
Authors:Piotr Graczyk; Hideyuki Ishi; Salha Mamane Abstract: Let G be the graph corresponding to the graphical model of nearest neighbor interaction in a Gaussian character. We study Natural Exponential Families (NEF) of Wishart distributions on convex cones \(Q_G\) and \(P_G\) , where \(P_G\) is the cone of tridiagonal positive definite real symmetric matrices, and \(Q_G\) is the dual cone of \(P_G\) . The Wishart NEF that we construct include Wishart distributions considered earlier for models based on decomposable(chordal) graphs. Our approach is, however, different and allows us to study the basic objects of Wishart NEF on the cones \(Q_G\) and \(P_G\) . We determine Riesz measures generating Wishart exponential families on \(Q_G\) and \(P_G\) , and we give the quadratic construction of these Riesz measures and exponential families. The mean, inverse-mean, covariance and variance functions, as well as moments of higher order, are studied and their explicit formulas are given. PubDate: 2018-02-23 DOI: 10.1007/s10463-018-0647-z
Authors:Lina Liao; Cheolwoo Park; Hosik Choi Abstract: This paper concerns the study of the entire conditional distribution of a response given predictors in a heterogeneous regression setting. A common approach to address heterogeneous data is quantile regression, which utilizes the minimization of the \(L_1\) norm. As an alternative to quantile regression, we consider expectile regression, which relies on the minimization of the asymmetric \(L_2\) norm and detects heteroscedasticity effectively. We assume that only a small set of predictors is relevant to the response and develop penalized expectile regression with SCAD and adaptive LASSO penalties. With properly chosen tuning parameters, we show that the proposed estimators display oracle properties. A numerical study using simulated and real examples demonstrates the competitive performance of the proposed penalized expectile regression, and its combined use with penalized quantile regression would be helpful and recommended for practitioners. PubDate: 2018-02-19 DOI: 10.1007/s10463-018-0645-1
Authors:Debajit Chatterjee; Uttam Bandyopadhyay Abstract: In the spirit of Bross (Biometrics 14:18–38, 1958), this paper considers ridit reliability functionals to develop test procedures for the equality of \(K(>2)\) treatment effects in nonparametric analysis of covariance (ANCOVA) model with d covariates based on two different methods. The procedures are asymptotically distribution free and are not based on the assumption that the distribution functions (d.f.’s) of the response variable and the associated covariates are continuous. By means of simulation study, the proposed methods are compared with the methods provided by Tsangari and Akritas (J Multivar Anal 88:298–319, 2004) and Bathke and Brunner (Recent advances and trends in nonparametric statistics, Elsevier, Amsterdam, 2003) under ANCOVA in terms of type I error rate and power. PubDate: 2018-02-06 DOI: 10.1007/s10463-017-0643-8
Authors:Sigeo Aki Abstract: Let k be a positive integer. Some exact distributions of the waiting time random variables for k consecutive repetitions of a pattern are derived in a sequence of independent identically distributed trials. It is proved that the number of equations of conditional probability generating functions for deriving the distribution can be reduced to less than or equal to the length of the basic pattern to be repeated consecutively. By using the result, various properties of the distributions of usual runs are extended to those of consecutive repetitions of a pattern. These results include some properties of the geometric distribution of order k and those of the waiting time distributions of the \((k_1,k_2)\) -events. Further, the probability generating function of the number of non-overlapping occurrences of k consecutive repetitions of a pattern can be written in an explicit form with k as a parameter. Some recurrence relations, which are useful for evaluating the probability mass functions, are also given. PubDate: 2018-02-06 DOI: 10.1007/s10463-018-0644-2
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