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

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

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’

The additive hazards model is one of the most popular regression models for analyzing failure time data, especially when one is interested in the excess risk or risk difference. Although a couple of methods have been developed in the literature for regression analysis of interval-censored data, a general type of failure time data, they may be complicated or inefficient. Corresponding to this, we present

This paper presents a general methodology for nonparametric estimation of a function s related to a nonnegative real random variable X, under a constraint of type \(s(0)=c\). When a projection estimator of the target function is available, we explain how to modify it in order to obtain an estimator which satisfies the constraint. We extend risk bounds from the initial to the new estimator, and propose

In this article, we consider a new robust estimation procedure for the partial functional linear model (PFLM) with the slope function approximated by spline basis functions. This robust estimation procedure applies a modified Huber’s function with tail function replaced by the exponential squared loss (ESL) to achieve robustness against outliers. A data-driven procedure is presented for selecting the

This paper investigates estimation of semiparametric varying-coefficient spatial autoregressive models in which the dependent variable is missing at random. An inverse propensity score weighted sieve two-stage least squares (S-2SLS) estimation with imputation is proposed. The proposed estimators are shown to be consistent, no matter the initial value is taken as the naive S-2SLS estimate or the naive

Non-inferiority (NI) trials have gained recognition as an effective tool with which to search for substitutes for a standard treatment that is associated with certain undesirable features, such as adverse side-effects, an exorbitant cost, or an extremely complicated therapeutic regimen. Statistical methods have been developed for NI studies with multiple experimental treatments. However, experimental

The original version of this article unfortunately contained a mistake.

We, in this paper, apply the smoothed and maximum empirical likelihood (EL) methods to construct the confidence intervals of the conditional quantile difference with left-truncated data. In particular, we prove the smoothed empirical log-likelihood ratio of the conditional quantile difference is asymptotically chi-squared when the observations with multivariate covariates form a stationary \(\alpha\)-mixing

In this paper, we consider two estimators, a hard thresholding wavelet estimator and a block thresholding wavelet estimator, for the regression function in heteroscedastic nonparametric model with negatively super-additive dependent (NSD) errors. The random design distribution is known or unknown, and the corresponding adaptive properties of these estimators are investigated over Besov spaces, for

We propose an adaptive design for variable selection in Bayesian modeling process. First randomly select some models to evaluate (e.g. by posterior model probability). Using these models, we predict the performance of all models in the candidate pool, based on which more models are selected and evaluated, in which models with good predicted performance or large prediction variances have high probabilities

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