In this paper, we propose to use the empirical likelihood (EL) method to construct confidence regions for nonparametric regression models with spatial autoregressive errors. It is shown that the EL statistics for the related parameters asymptotically have chi-squared distributions, which are used to construct confidence regions for the parameters. Results from simulation study and real data analysis

The modal linear regression suggested by Yao and Li (Scand J Stat 41(3):656–671, 2014) models the conditional mode of a response Y given a vector of covariates \(\mathbf{z }\) as a linear function of \(\mathbf{z }\). To identify the conditional mode of Y given \(\mathbf{z }\), existing methods utilize a kernel density estimator to obtain the distribution of Y given \(\mathbf{z }\). Like other kernel-based

We propose a sparse vector heterogeneous autoregressive (VHAR) model for realized volatility forecasting. As a multivariate extension of a heterogeneous autoregressive model, a VHAR model can consider the dynamics of multinational stock volatilities in a compact manner. A sparse VHAR is estimated using adaptive lasso and some theoretical properties are provided. In practice, our sparse VHAR model can

We propose a definition of hub in complex networks by using the eigenvectors of the Laplacian matrix, and suggest a method of detecting hubs. The proposed definition provides a different concept from the classical measures such as the centrality or degree. Also, a method of determining the number of hubs is suggested using a scree plot. Illustrative examples based on artificial data sets and real data

This paper proposes a new method of detecting the gradual changes of time series when the changes in time series are mixed with seasonality. The key of the proposed method is to express the desired time-varying feature while removing the unwanted time-varying feature of seasonal effects through two-stage procedures. Asymptotic properties of the proposed methods are studied, and simulation results are

We congratulate the author for this interesting paper which introduces a novel method for the data segmentation problem that works well in a classical change point setting as well as in a frequent jump situation. Most notably, the paper introduces a new model selection step based on finding the ‘steepest drop to low levels’ (SDLL). Since the new model selection requires a complete (or at least relatively

We discuss Fryzlewicz’s paper that proposes WBS2.SDLL approach to detect possibly frequent changes in mean of a series. Our focus is on the potential issues related to the model misspecification. We present some numerical examples such as the self-exciting threshold autoregression and the unit root process, that can be confused as a frequent change-points model.

This article comments on the new version of wild binary segmentation in Fryzlewicz (Ann Stat 42(6):2243–2281, 2014).

In this discussion, we compare the choice of seeded intervals and that of random intervals for change point segmentation from practical, statistical and computational perspectives. Furthermore, we investigate a novel estimator of the noise level, which improves many existing model selection procedures (including the steepest drop to low levels), particularly for challenging frequent change point scenarios

Many existing procedures for detecting multiple change-points in data sequences fail in frequent-change-point scenarios. This article proposes a new change-point detection methodology designed to work well in both infrequent and frequent change-point settings. It is made up of two ingredients: one is “Wild Binary Segmentation 2” (WBS2), a recursive algorithm for producing what we call a ‘complete’

Let \(T>0,\alpha >\frac{1}{2}\). In the present paper we consider the \(\alpha \)-Brownian bridge defined as \(dX_t=-\alpha \frac{X_t}{T-t}dt+dW_t,\, 0\le t< T\), where W is a standard Brownian motion. We investigate the optimal rate of convergence to normality of the maximum likelihood estimator (MLE) for the parameter \( \alpha \) based on the continuous observation \(\{X_s,0\le s\le t\}\) as \(t\uparrow

A conventional regression model for functional data involves expressing a response variable in terms of the predictor function. Two assumptions, that (i) the predictor function and the error are independent and (ii) the relationship between the response variable and the predictor function takes functional linear model, are usually added to the model. Checking the validation of these two assumptions

Symmetric positive definite matrix data commonly appear in computer vision and medical imaging, such as diffusion tensor imaging. The aim of this paper is to develop a nonparametric estimation method for a symmetric positive definite matrix regression function given covariates. By obtaining a suitable parametrization based on the Cholesky decomposition, we make it possible to apply univariate smoothing

In this work, we introduce a local linear nonparametric estimation of the regression function of a censored scalar response random variable, given a functional random covariate. Under standard conditions, we establish the pointwise and the uniform almost-complete convergences, with rates, of the proposed estimator. Then, we carry out a simulation study and a real data analysis in order to compare the

In this paper, we consider rank estimation for partial functional linear regression models based on functional principal component analysis. The proposed rank-based method is robust to outliers in the errors and highly efficient under a wide range of error distributions. The asymptotic properties of the resulting estimators are established under some regularity conditions. A simulation study conducted

Large-scale data from various research fields are not only heterogeneous and sparse but also difficult to store on a single machine. Expectile regression is a popular alternative for modeling heterogeneous data. In this paper, we devise a distributed optimization approach to SCAD and adaptive LASSO penalized expectile regression, where the observations are randomly partitioned across multiple machines

We propose a new time varying correlation coefficient, which is a local correlation measure of a pair of time series. The time varying correlation coefficient is locally estimated using a nonparametric kernel method. Asymptotic normality of the estimated time varying correlation is established, which allows us to construct statistical methods of confidence interval and hypothesis tests. Finite sample

When data for a completely randomised design are categorical rather than continuous, the Cochran–Mantel–Haenszel suite of tests may be applied, albeit that there is only one stratum. In introductory design courses this design, and the randomised block design, are usually the first designs introduced. Using the completely randomised design instead of the randomised block design ignores blocks (strata)

Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process, in its simplest form, along with the Kullback–Leibler divergence is still an open problem. This is mainly attributed to the discreteness property of the Dirichlet

In this paper, we investigate the adequate check of the parametric Tobit model. A Cramér–Von Mises type test statistic is constructed, and its asymptotic properties under the null and alternative hypotheses are rigorously studied. The method is effective for the adequacy check of parametric regression models with a scalar or multivariate covariate. Furthermore, it avoids the nonparametric smoothing

The original version of this article unfortunately contained a mistake.

The reporting of effect sizes in social-scientific articles is becoming increasingly widespread and encouraged, particularly when research and experimental designs are involved. Two widely used experimental designs where the uniqueness of estimation can be guaranteed, the cell means and treatment effect models, are first introduced. Then, under those two experimental designs, it is proposed to explore

By introducing the notion of “empirical likelihood function of observing sums”, unequally-spaced time series data and longitudinal data generated from Lévy processes can be analyzed. Characteristic function is further incorporated to handle the situations where the density function of the increments is difficult to obtain. In the situations where both characteristic function and the density function

There is a considerable uncertainty in a hydrological projection, which arisen from the multiple stages composing the hydrological projection. Uncertainty decomposition analysis evaluates contribution of each stage to the total uncertainty in the hydrological projection. Some uncertainty decomposition methods have been proposed, but they still have some limitations: (1) they do not consider nonstationarity

Suppose that there are two populations which are mixed in proportions \(\lambda \) and \((1-\lambda )\), respectively, and an investigator wishes to classify an individual into one of these two populations based on a p-dimensional observation on the individual. This is the basic classification problem with applications in wide variety of fields. In practice, the optimal rule (Bayes rule) is not available

In biomedical research, multivariate functional data are frequently encountered. Majority of the existing approaches for functional data analysis focus on univariate functional data and the methodology for multivariate functional data is far less studied. Particularly, the problem of investigating covariate effects on multivariate functional data has received little attention. In this research, we

Stochastic frontier models have been considered as an alternative to deterministic frontier models in that they attribute the deviation of the output from the production frontier to both measurement error and inefficiency. However, such merit is often dimmed by strong assumptions on the distribution of the measurement error and the inefficiency such as the normal-half normal pair or the normal-exponential

Change-point models are generative models in which the underlying generative parameters change at different points in time. A Bayesian approach to the problem of hazard change with unknown multiple change-points is developed using informative priors for censored survival data. For the exponential distribution, piecewise constant hazard is considered with change-point estimation. The stochastic approximation

In order to analyze longitudinal ordinal data, researchers commonly use the cumulative logit random effects model. In these models, the random effects covariance matrix is used to account for both subject variation and serial correlation of repeated outcomes. However, the covariance matrix is assumed to be homoscedastic and restricted due to the high-dimensionality and positive-definiteness of the

Designing their experiments is the significant problem that experimenters face. Maximin distance designs, supersaturated designs, minimum aberration designs, uniform designs, minimum moment designs and orthogonal arrays are arguably the most exceedingly used designs for many real-life experiments. From different perspectives, several criteria have been proposed for constructing these designs for investigating

In this paper, we study the tests for sphericity and identity of covariance matrices in time-varying coefficient high-dimensional panel data models with fixed effects. In order to construct the effective test statistics and avoid the influence of the unknown fixed effects, we apply the difference method to eliminate the dependence of the residual sample, and further construct test statistics using

We obtain explicit formulae for the expected values \(E \{ \prod \nolimits _{i=1}^{3}g_i ( X_i ) \}\) of standard tri-variate Gaussian random vector \({\underline{X}}= \left( X_1, X_2 , X_3 \right) \) over the set \(g_i (x) \in \left\{ \delta (x), \mathrm {sgn}(x), |x|, x \right\} \) of nonlinear and linear functions. Based on the results, we also suggest corrections to long-known formulae for two

Allocating computation over multiple chains to reduce sampling time in MCMC is crucial in making MCMC more applicable in the state of the art models such as deep neural networks. One of the parallelization schemes for MCMC is partitioning the sample space to run different MCMC chains in each component of the partition (VanDerwerken and Schmidler in Parallel Markov chain Monte Carlo. arXiv:1312.7479

In this paper, we propose self-semi-supervised clustering, a new clustering method for large scale data with a massive null group. Self-semi-supervised clustering is a two-stage procedure: preselect a part of “null” group from the data in the first stage and apply semi-supervised clustering to the rest of the data in the second stage, allowing them to be assigned to the null group. We evaluate the

Model structural inference on semiparametric measurement error models have not been well developed in the existing literature, partially due to the difficulties in dealing with unobservable covariates. In this study, a framework for adaptive structure selection is developed in partially linear error-in-function models with error-prone covariates. Firstly, based on the profile-least-square estimators

Aalen’s additive hazards model plays a very important role in survival analysis. In this paper we are interested in the problem of estimating regression coefficients in the additive hazards model with censored length-biased data. Through both of the parametric invariance of the proportional likelihood ratio model and the unique structure of length-biased data, we propose a pairwise pseudo-likelihood

In applications, other than sample information, some prior information on parameters can be used to improve the estimation efficiency. In the framework of varying-coefficient partially linear models with the number of parametric and nonparametric components diverging, this paper proposes a restricted profile least-squares estimation for the parametric components after the varying coefficients are estimated

In the Bayesian framework, the marginal likelihood plays an important role in variable selection and model comparison. The marginal likelihood is the marginal density of the data after integrating out the parameters over the parameter space. However, this quantity is often analytically intractable due to the complexity of the model. In this paper, we first examine the properties of the inflated density

Rakotomamonjy (RO-CAI, pp 71–80, 2009) proposed an ROC-SVM that optimizes the receiver operating characteristic curve (ROC) particularly useful for unbalanced classification. In this article, we establish the piecewise linearity of the ROC-SVM solutions as a function of regularization parameter, and develop an efficient algorithm for computing the entire regularization paths of the ROC-SVM. Finally

In this work, we consider the identifiability assumption of Gaussian linear structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error variances are the same or known. Hence, this work proves the identifiability of Gaussian

This study examines an adaptive log-density estimation method with an \(\ell _1\)-type penalty. The proposed estimator is guaranteed to be a valid density in the sense that it is positive and integrates to one. The smoothness of the estimator is controlled in a data-adaptive way via \(\ell _1\) penalization. The advantages of the penalized log-density estimator are discussed with an emphasis on wavelet

We consider a Markov-modulated fluid flow model with server maintenance period. As soon as the fluid level reaches zero, the server begins a maintenance period of a random length. During the maintenance period, fluid arrives from outside depending on the state of the background Markov process and the level increases either vertically or linearly. This model can be applied to various real-world systems

In the present paper, we study the residual extropy using distribution function and quantile function approaches. We also investigate extropy in past lifetime in both approaches. Some characterizations and ageing properties of these extropy measures are proposed. Different stochastic orders based on the residual and past lifetime extropy are also presented.

The purpose of this paper is to derive the Fisher information matrix for the Flexible Generalized Skew-Normal distribution (FGSN). Initially we derive the score functions which lead to the maximum likelihood estimators. We then compute the information matrix and consider the special cases corresponding to the skew-normal distribution and the normal distribution. We provide an algorithm to generate

Matching priors in principle provide a possible compromise between frequentist and Bayesian and default priors for routine use in Bayesian inference in that posterior probability of the parameter also provides an interpretation as confidence statements. Here we introduce a matching prior for the ratio of two log-normal means which is nontrivial because the derivation of matching prior requires the

Entropy based dependence measures are used as an alternative to correlation for determining the lag dependency of time series models. In this study, we explore the properties of partial autoinformation function (PAIF) to identify the lag dependency of non-linear and non-Gaussian autoregressive models. Non-parametric estimators of autoinformation function (AIF) and PAIF are obtained and then studied

A new statistical test is proposed to distinguish between the distributions having logarithmically decaying upper tail from polynomially decaying upper tail. The empirical size and power of the proposed test are computed through simulation. The proposed test is applied to two real world data sets.

We discuss a new kernel type estimator for density function \(f_X(x)\) with nonnegative support. Here, we use a type of gamma density as a kernel function and modify it with expansions of exponential and logarithmic functions. Our modified gamma kernel density estimator is not only free of the boundary bias, but the variance is also in smaller orders, which are \(O(n^{-1}h^{-1/4})\) in the interior

Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes at the cost of similar, long-winded algebraic steps being repeated and slowing down algorithmic development. We demonstrate how factor graph fragmentization can

In this paper, we study the weighted quantile average estimation technique for the parameter in additive partially linear models with missing covariates, which is proved to be an efficient method. The proposed method is based on optimally combining information over different quantiles via multiple quantile regression. We establish asymptotic normality of the weighted quantile average estimators when

Minimax lower bounds determine the complexity of given statistical problems by providing fundamental limit of any procedures. This paper gives a review on various aspects of obtaining minimax lower bounds focusing on a recent development. We first introduce classical methods, then more involved lower bound constructions such as testing two mixtures, two directional method, and global metric entropy

We consider block bootstrappings for panel mean change test of the squared CUSUM test of Horváth and Hušková (J Time Ser Anal 33:631–648, 2012): the circular block bootstrapping and stationary bootstrapping. First order asymptotic null validity of the test is proved under serial and/or cross-sectional correlation. Consistency of the test under an alternative hypothesis is also proved. A Monte-Carlo

In some sampling situations, the survey can result in an estimate of zero when it is known that the parameter being estimated is close to, but not equal to, zero. Examples include searching for rare animals or plants where the species is known to exist but all sample units failed to detect any activity. One way to deal with this is to ignore these zero estimates. Here we propose an estimator for sampling

Anderson (The Annals of Mathematical Statistics 30(3):676–687, 1959) studied the limiting distribution of the least square estimator for explosive AR(1) process under the independent and identically distributed (iid) condition on error i.e., \(X_t=\rho X_{t-1}+e_t\) where \(\rho >1\) and \(e_t\) is iid error with \(Ee=0\) and \(Ee^2<\infty \). This paper is mainly concerned about the limiting distribution

Support vector machines (SVM) is very efficient and popular tool for classification, however, its non-robustness to outliers is a critical drawback. In fact, SVM is more sensitive to outliers than other classifiers since the optimal separating hyperplane obtained by SVM is solely determined by support vectors. So far all the studies about outliers in SVM are done by trying to minimize the effect of

In this paper we consider the problem of estimating the support of a uniform distribution under symmetric additive errors. The maximum likelihood (ML) estimator is of our primary interest, but we also analyze the method of moments (MM) estimator, when it exists. Under some regularity conditions, the ML estimator is consistent and asymptotically efficient. Errors with Student’s t-distribution are shown

Multivariate longitudinal data is often encountered in the jobs of statisticians and practitioners. It is challenging to model the covariance matrix due to the complex structure of correlations among multiple responses. For this modeling task, several effective Cholesky decomposition based methods have been studied. However, direct interpretation of the covariation structure among multiple responses

This paper introduces a new class of distributions, named length-biased Weibull mixtures, in order to deal with heavy-tailed data encountered in quantitative risk modeling. As a generalization of the Erlang mixtures with common scale parameter, our proposed class possesses attractive modeling features such as flexibility to fit various distributional shapes and weak denseness in the class of distributions

We propose a fully Bayesian methodology for estimation of functions that have jump discontinuities. The proposed model is an extension of the LARK model, which enables functions to be represented by the small number of elements from an overcomplete system. In the proposed model, multiple kernels are used as the elements of an overcomplete system. Since these elements are composed of different types

We study the strong oracle property of concave penalized estimators in the high-dimensional linear regression model for a class of concave penalties that have infinite derivative at the origin. The class includes the bridge and log penalties as typical examples. It is known that infinite derivative of the penalty is not a problem for the weak oracle property but prevents the strong oracle property