The neural networks (NN) remain as black boxes, albeit their quite successful stories everywhere. It is mainly because they provide only the complex structure of the underlying network with a huge validation data set whenever their serendipities reveal themselves. In this paper, we propose the statistical NN learning model related to the concept of universal Turing computer for regression predictive

An efficient market is often related to the market liquidity in a certain sense. In this paper, the autoregressive conditional duration (ACD) model is used for modeling and analyzing the market liquidity based on high-frequency financial data, which takes the volume duration as its measure index. Considering the high peak and heavy tail of high-frequency financial data, the self-weighted quantile regression

In this paper, we consider some objective priors for the ratio of variabilities in a bivariate normal distribution. We develop the first and second order matching priors and reference priors. We obtain that the second order matching prior matches the alternative coverage probabilities up to the same order. It is also an HPD matching priors. It turns out that the derived reference priors do not satisfy

We propose a new technique for consistent estimation of the number and locations of the change-points in the structure of an irregularly spaced time series. The core of the segmentation procedure is the ensemble binary segmentation method (EBS), a technique in which a large number of multiple change-point detection tasks using the binary segmentation method are applied on sub-samples of the data of

There is no closed form maximum likelihood estimator (MLE) for some distributions. This might cause some problems in real-time processing. Using an extension of Box–Cox transformation, we develop a closed-form estimator for the family of distributions. If such closed-form estimators exist, they have the invariance property like MLE and are equal in distribution with respect to the transformation. Specifically

A correction to this paper has been published: https://doi.org/10.1007/s42952-021-00116-6

In this study, we review a recent progress regarding the change point test for integer-valued time series models, specifically concentrating on the CUSUM test for integer-valued autoregressive (INAR) and generalized autoregressive conditional heteroscedastic (INGARCH) models. Because time series often experience changes in underlying models, the change point test has been a fundamental issue in time

This paper presents a generalization of the bagging procedure by using smoothed bootstrap with bagging, a procedure we call generalized bagging. Our generalized bagging method unifies input and output smearing, in the sense that noise is added to both the input and the output, so that input smearing and output smearing become special cases of generalized bagging. We discuss the choice of optimal smoothing

A large amount of online social network data such as Facebook or Twitter are extensively generated by the growth of social network platforms in recent years. Development of a network time series model and its statistical inference are as important as the rapid progress on the social network technology and evolution. In this work we consider a network vector autoregression for the large-scale social

Doubly truncated data arise when an individual is potentially observed only if its failure-time lies within a certain interval, unique to that individual. In this paper, we consider the pseudo-observations approach for estimating regression coefficients when data is subject to double truncation. The pseudo-observations generated from the nonparametric maximum likelihood estimates (NPMLE) of the survival

In this paper we discuss a general way of improving the bias properties of nonparametric kernel regression estimators. The procedure involves choosing a parametric model and constructing a semiparametric estimator that consists of a parametric component and a nonparametric adjustment, where the parametric component is picked from the parametric model in such a way that the resulting estimator has the

In terms of statistical process control (SPC), the probability distributions of the quality characteristics are critical in detecting changes in the process and product quality in manufacturing processes. Non-normally distributed output variables explained by input variables are common in real industries. The observation-based Shewhart control chart as well as the deviance residual-based Shewhart control

This paper describes a moments estimator for a standard state-space model with coefficients generated by a random walk. The method calculates the conditional expectations of the coefficients, given the observations. A penalized least squares estimation is linked to the GLS (Aitken) estimates of the corresponding linear model with time-invariant parameters. The estimates are moments estimates. They

Clustering is an important statistical tool for the analysis of unsupervised data. Spectral clustering and stochastic block models, based on networks and graphs, are well established and widely used for community detection among many clustering algorithms. In this paper we review and discuss important statistical issues in spectral clustering and stochastic block models.

In this paper, we provide some general results for the usual stochastic ordering of the extreme order statistics arising from two sets of random variables with different marginal distributions and different underlying Archimedean copulas structure. Application to some general models as marginal distributions which are including the well-known semiparametric family of distributions in statistics, is

In this paper, we consider statistical inference for a heteroscedastic semiparametric varying-coefficient partially linear model with measurement errors in the nonparametric component when exact linear restriction on the parametric component is assumed to hold. Two types of weighted bias-corrected restricted estimators of the parametric and nonparametric components are proposed based on a bias-corrected

High-dimensional Poisson reduced-rank models have been considered for statistical inference on low-dimensional locations of the individuals based on the observations of high-dimensional count vectors. In this study, we assume sparsity on a so-called loading matrix to enhance its interpretability. The sparsity assumption leads to the use of \(L_1\) penalty, for the estimation of the loading. We provide

Researchers want to know whether the change in an explanatory variable X affects the change in a response variable Y (i.e., X causes Y). In practice, there can be two causal paths from X to Y, the path through a mediating variable M (indirect effect) and the path not through M (direct effect). The parameter estimation and hypothesis testing can be performed by a regression-based mediation model. It

In this paper, we introduced a new two-component nonparametric mixture model with a stochastic dominance constraint, a model arising naturally from many genetic studies. For this model, we proposed and studied two estimations. The first one is based on cumulative distribution functions with use of the stochastic dominance inequality, while the second one is a maximum likelihood estimation of the multinomial

High dimensional data sets against the small sample size is essential for most of the sciences. The variable selection contributes to a better prediction of real-life phenomena. A multivariate approach called partial least squares (PLS) has the potential to model the high dimensional data, where the sample size is usually smaller than the number of variables. Truncation for variables selection in PLS

For square contingency tables with ordered categories, an index based on Kullback–Leibler information (or Shannon entropy) has been proposed in order to measure the degree of departure from global marginal homogeneity. Although there are two types of maximum global marginal inhomogeneity [i.e., whether (1) all observations concentrate in the lower-left triangle cells in the table, or whether (2) they

Estimation of the scale parameter of the scale mixture of a location–scale family under the scale-invariant loss function is considered. The technique of Strawderman (Ann Stat 2(1):190–198, 1974) is used to obtain a class of estimators improving upon the best affine equivariant estimator of the scale parameter under certain conditions. Further, integral expressions of risk difference approach of Kubokawa

Missing responses generally exist in educational and psychological assessments. The statistical inference will lead to serious deviation if the missing responses are not properly modeled in the framework of non-ignorable missing mechanism. In this current study, it is studied whether the different missing mechanism (ignorable missing and non-ignorable missing) models are appropriate to analyze the

Level permutations of factors can improve space-filling properties of designs, and the properties of the three-level Triple designs constructed by tripling method are related to original designs. In this paper, a new strategy for tripling is provided for constructing three-level uniform designs. By considering all possible level permutations of factors, the relationship is built between the average

We propose new closed-form estimators for two-parameter weighted Lindley (WL) distribution. These new estimators are derived from likelihood equations of power transformed WL distribution. They behave very similarly to maximum likelihood estimators (MLEs) and achieve consistency and asymptotic normality. Numerical results show that, unlike existing closed-form estimators, the new estimators are uniformly

An omitted covariate in the regression function leads to hidden or unobserved heterogeneity in generalized linear models (GLMs). Using this fact, we develop two novel goodness-of-fit tests for gamma GLMs. The first is a score test to check the existence of hidden heterogeneity and the second is a Hausman-type specification test to detect the difference between two estimators for the dispersion parameter

We develop two new approximate confidence interval methods for estimating a population proportion using balanced ranked-set sampling (RSS). Unlike existing RSS-based methods, the new methods control the coverage probability well not just under perfect rankings, but also under imperfect rankings. One method uses a Wilson-type interval, and the other is based on making a mid-P adjustment to a Clopper–Pearson-type

This paper proposes tests for the null of sphericity and identity matrix for nonparametric time-varying coefficient panel data models with fixed effects. Firstly, based on the local linear smoothing technique, the estimators of the unknown coefficient functions and model residuals are obtained. Secondly, proper test statistics are proposed aiming at tests for sphericity or identity matrix with a large

We are motivated by our laboratory experiment on the flocking behavior of termites. To test for the existence of flocking behavior, we revisit the problem to test uniform samples (with the samples uniformly distributed) on the circle. Unlike most existing works, we assume that the samples are exchangeably dependent. We consider the class of normalized infinitely divisible distributions for the spacings

The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for data sets that exhibit a dynamic structure they seem fit poorly. In this work, we develop a two-level dynamic heteroscedastic hierarchical model and suggest some empirical estimators for the association hyper-parameters. Moreover, we derive the risk properties of the estimators. Our proposed

We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally \(\beta \)-Hölder class with an exponentially decreasing tail, which does not need to be sub-Gaussian. We obtain posterior convergence rates of the regression coefficient and the error density, which are nearly optimal and adaptive

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

Methods to compare two samples of interval-valued data are discussed. In the interval-valued data, observations have the form of intervals and are often read as two-dimensional vector of lower and upper bounds. We consider four methods, two of which are the applications of existing methods for bivariate data, and the other two are based on the marginalization (univariate distributional representation)

This paper investigates the hypothesis test of the parametric component in partial functional linear quantile regression model in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. A quantile rank score test based on functional principal component analysis is developed. Under mild conditions, we establish the consistency

In this paper, we consider the statistical inferences for a class of partially linear models with high dimensional endogenous covariates, when high dimensional instrumental variables are also available. A regularized estimation procedure is proposed for identifying the optimal instrumental variables, and estimating covariate effects of the parametric and nonparametric components. Under some conditions

In this paper, we focus on the empirical likelihood inference for partially linear single-index errors-in-variables (EV) models when the data are right censored and the censoring indicator is missing at random (MAR). Two bias-corrected empirical log-likelihood ratio (BCELR) functions for the parameters by using regressing calibration and imputation methods are introduced. The limiting distributions

In many case–control genetic association studies, a secondary phenotype that may have common genetic factors with disease status can be identified. However, the secondary phenotype is observed only for case subjects but may be used as a surrogate marker for disease status. When information on the secondary phenotype is available only for a case group, due to cost and different data sources, fitting

The Birnbaum–Saunders (BS) distribution, introduced in 1969, is a popular univariate fatigue life distribution which has been widely used to model right-skewed lifetime and reliability data. In this paper, a new class of generalized multivariate BS distributions is proposed based on mean-variance mixture models to accommodate strongly skewed and heavy tailed multivariate lifetime data. Some special

We discuss jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) based inference for finding confidence intervals for probability weighted moment (PWM). We obtain the asymptotic distribution of the JEL ratio and AJEL ratio statistics. We compare the performance of the proposed confidence intervals with recently developed methods in terms of coverage probability and

Change point analysis has become an important research topic in many fields of applications. Several research work have been carried out to detect changes and its locations in time series data. In this paper, a nonparametric method based on the empirical likelihood is proposed to detect structural changes in the parameters of autoregressive (AR) models . Under certain conditions, the asymptotic null

Parameter change test has been an important issue in time series analysis. The problem has also been actively explored in the field of integer-valued time series, but the testing in the presence of outliers has not yet been extensively investigated. This study considers the problem of testing for parameter change in Poisson autoregressive models particularly when observations are contaminated by outliers