In the small area estimation, the empirical best linear unbiased predictor (EBLUP) in the linear mixed model is useful because it gives a stable estimate for a mean of a small area. For measuring uncertainty of EBLUP, much of research is focused on second-order unbiased estimation of mean squared prediction errors in the univariate case. In this paper, we consider the multivariate Fay–Herriot model

We consider parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) from high frequency data which are observed in time and space. By using thinned data obtained from the high frequency data, adaptive estimators of the coefficient parameters including the volatility parameter are proposed. Moreover, we give some examples and simulation results of the

There is a growing interest in learning how the distribution of a response variable changes with a set of predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several formulations require computationally demanding algorithms for posterior inference. Motivated by this issue, we study a class of predictor-dependent infinite mixture models

We contemplate an experimental situation in a 2k-factorial experiment with acute resource crunch so that we need to conduct just a saturated design [SD] - with the understanding that precision of the estimates cannot be estimated from the data. It is known beforehand which effect(s)/interaction(s) are likely to be negligible. We examine the flexibility to the extent that an experimenter can make a

Let a be a finite signed measure on [−r,0] with r∈(0,∞). Consider a stochastic process (X(ϑ)(t))t∈[−r,∞) given by a linear stochastic delay differential equation dX(ϑ)(t)=ϑ∫[−r,0]X(ϑ)(t+u)a(du)dt+dW(t),t∈R+,where ϑ∈R is a parameter and (W(t))t∈R+ is a standard Wiener process. Consider a point ϑ∈R, where this model is unstable in the sense that it is locally asymptotically Brownian functional with certain

The matrix that transforms the response variable in a regression to its predicted value is commonly referred to as the hat matrix. The trace of the hat matrix is a standard metric for calculating degrees of freedom. The two prominent theoretical frameworks for studying hat matrices to calculate degrees of freedom in local polynomial regressions – ANOVA and non-ANOVA – abstract from both mixed data

We investigate predictive density estimation under the L2 Wasserstein loss for location families and location-scale families. We show that plug-in densities form a complete class and that the Bayesian predictive density is given by the plug-in density with the posterior mean of the location and scale parameters. We provide Bayesian predictive densities that dominate the best equivariant one in normal

The functional linear quantile regression model is widely used to characterize the relationship between a scalar response and a functional covariate. Most existing research results are based on a correct assumption that the response is related to the functional predictor through a linear model for given quantile levels. This paper focuses on investigating the adequacy check of the functional linear

We investigate asymptotically optimal multiple testing procedures for streams of sequential data in the context of prior information on the number of false null hypotheses (“signals”). We show that the “gap” and “gap-intersection” procedures, recently proposed and shown by Song and Fellouris (2017) to be asymptotically optimal for controlling type 1 and 2 familywise error rates (FWEs), are also asymptotically

We use the jackknife to bias correct the log-periodogram regression (LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias reduction is achieved without the usual increase in asymptotic variance, with the estimator viewed as ‘optimal’ in this sense. The theoretical results are valid under

This paper derives the elliptical matrix variate version of the well known univariate Birnbaum–Saunders distribution of 1969. A generalisation based on a matrix transformation is proposed, instead of the independent element-to-element elliptical extension of the Gaussian univariate case. Some results on Jacobians were needed to derive the new matrix variate distribution. A number of particular distributions

Many estimators for the proportion of true null hypotheses in the literature, which are defined for independent p-values, struggle under dependence. In particular, the variance of the classical Schweder–Spjøtvoll estimator increases with the degree of dependence among the p-values. We propose a technique based on the independent-component bootstrap, which considerably improves this behavior. The idea

We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of poorly identifiable parameters. Moreover, ODEs are generally approximations of the true process and the influence of misspecification on inference is often neglected

In a multiple testing setting, we consider testing n null hypotheses, denoted by H1,…,Hn, with the corresponding p-values Pi for each Hi. We propose a new method which ‘scans’ all intervals in the unit interval [0,1], selects the longest interval with estimated false discovery rate not exceeding the target level, and then rejects a hypothesis if its p-value is contained in this interval. In contrast

The jump behavior of an infinitely active Itô semimartingale can be conveniently characterized by a jump activity index of Blumenthal–Getoor type, typically assumed to be constant in time. We study Markovian semimartingales with a non-constant, state-dependent jump activity index and a non-vanishing continuous diffusion component. A nonparametric estimator for the functional jump activity index is

While multinomial logistic models have been widely applied in practice, the research on design selection has not kept pace. The complication in studying optimal/efficient designs for multinomial logistic models is the complicated structure of information matrices due to the model complexity and existence of many variants. A critical step in deriving optimal/efficient designs is to determine the number

In clinical trials, the response of a given subject often depends on the selected treatment as well as on some covariates. We study optimal approximate designs of experiments in the models with treatment and covariate effects. We allow for the variances of the responses to depend on the chosen treatments, which introduces heteroscedasticity into the models. For estimating systems of treatment contrasts

We study robust designs for generalized linear mixed models (GLMMs) with protections against possible departures from underlying model assumptions. Among various types of model departures, an imprecision in the assumed linear predictor or the link function has a great impact on predicting the conditional mean response function in a GLMM. We develop methods for constructing adaptive sequential designs

Technological advances have enabled an exponential growth in data volumes, and proven statistical methods are no longer applicable for extraordinary large data sets due to computational limitations. Subdata selection is an effective strategy to address this issue. In this study, we investigate existing sampling approaches and propose a novel framework of selecting subsets of data for logistic regression

This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the D-optimality of a rhombic design via the Kiefer–Wolfowitz equivalence theorem. Subsequently, we show that the structure of an optimal rhombic design depends directly

A lack-of-fit test for functional regression models is proposed. The test is based on the fact that checking the no-effect of a functional covariate is equivalent to checking the nullity of the conditional expectation of the error term given a sufficiently rich set of projections of that covariate. The idea then is to search the projection that is, in some sense, the least favorable for the null hypothesis

In biomedical research, increasing attention has been paid to the discovery of regulatory relationships among heterogeneous biological features. We present a new statistical framework to jointly learn multiple heterogeneous exponential Markov Random Fields. We establish an approximate likelihood inference problem regularized by an embedded group lasso penalty, and propose an efficient algorithm in

The area under the receiver operating characteristic curve (AUC) serves as a summary of a binary classifier’s performance. For inference on the AUC, a common modeling assumption is binormality, which restricts the distribution of the score produced by the classifier. However, this assumption introduces an infinite-dimensional nuisance parameter and may be restrictive in certain machine learning settings

In this work, we present the BMM 2D estimator, a robust estimator for the parameters of the bidimensional autoregressive model (AR-2D model). The new estimator is a two-dimensional extension of the BMM estimator for the parameters of the autoregressive models used in time series analysis. We demonstrate that the BMM 2D estimator is consistent and asymptotically normal, which provides a valuable tool

In practice, fractional factorial split-plot (FFSP) designs are widely used when the levels of some factors are very difficult to change or control. The factors of an FFSP design are divided into two groups, the whole plot (WP) and subplot (SP) factors. When the WP factors are more important than SP factors, Wang et al. (2019) gave a new optimal criterion for selecting designs, that is, the minimum

In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we approximate the error covariance matrix with a neighborhood of covariance matrices, in order to define minimax D-optimal designs that are robust against small departures

A multivariate Birnbaum–Saunders distribution is introduced to consider a new nonparametric multivariate density estimation for nonnegative data. By construction, the estimator is the average of varying nonnegative kernel with correlation structure, whose support matches the support of the density to be estimated, unlike the classical Rosenblatt–Parzen kernel density estimator. The proposed kernel

U-statistics enjoy good properties such as asymptotic normality, unbiasedness and minimal variance among unbiased estimators. The estimation of their variance is often of interest, for instance to derive asymptotic tests. It is well-known that an unbiased estimator of the variance of a U-statistic can be formulated explicitly as a U-statistic itself, but specific dependencies on the sample size make

This article considers a Mann–Whitney test of distributional effects in a multivalued treatment. Specifically, we first show that, under the unconfoundedness condition, the counterfactual distributions are weighted averages, with weights satisfying some moment restrictions. We estimate the weights directly from those restrictions by maximizing a globally concave objective function and then construct

In the optimal design literature for paired comparison choice experiments it has been proposed that respondent heterogeneity can be modelled by introducing fixed block effects into the linear predictor of the multinomial logit model and D-optimal utility-neutral designs for the modified version of the model have been derived by orthogonally blocking D-optimal utility-neutral designs for the model without

We consider the estimation of the variance and spatial scale parameters of the covariance function of a one-dimensional Gaussian process with fixed smoothness parameter s. We study the fixed-domain asymptotic properties of composite likelihood estimators. As an improvement of previous references, we allow for any fixed number of neighbor observation points, both on the left and on the right sides,

In this paper, we propose a novel functional coefficient model, useful for direct modeling of nonstationary time series data without needing to detrend the original data. The proposed model could reveal the underlying dynamics and evolutionary nature of the data, and is easy to interpret. Through the local polynomial technique we investigate an estimation procedure for the proposed model and establish

In this paper, we consider the estimation and inference in partially functional linear regression with multiple functional covariates. We estimate the parameters and the slope functions by using functional principal component analysis (FPCA) approach to each functional covariate; establish the asymptotic distribution for the proposed estimators and investigate the semiparametric efficiency. We derive

The problem under study is detecting the presence, and identifying the exact position, of a block Cn of “anomalous” observations in a finite sequence of independent random variables X1,…,Xn. By “anomalous” we mean that the distribution G of the observations in the block Cn is possibly different from the “under control” distribution F of the remaining Xi’s. We first propose a nonparametric approach

In many trials, the duration between patient enrolment and an event occurring is used as the efficacy endpoint. Common endpoints of this type include the time until relapse, progression to the next stage of a disease, or time until remission. The criteria of an event may be defined by multiple components, one or more of which may be a continuous measurement being above or below a threshold. Typical

Paired comparison data is often used to rank or order a set of items. In this paper we study a method for estimating the parameters associated with completely ordered cardinal paired comparison data. The analysis is carried out within the framework of graphical linear models but rather than using the least squares estimator, which may be difficult to analyze, we consider the average of all tree-based

Policy decisions regarding allocation of resources to subgroups in a population, called small areas, are based on reliable predictors of their underlying parameters. However, the information is collected at a different scale than these subgroups. Hence, we need to predict characteristics of the subgroups based on the coarser scale data. In view of this, there is a growing demand for reliable small

We propose kernel-based estimators for both the parametric and nonparametric components of a partially linear additive regression model where a subset of the covariates entering the nonparametric component are generated by the estimation of an auxiliary nonparametric regression. Both estimators are shown to be asymptotically normally distributed. The estimator for the finite dimensional parameter is

Often a problem in linear regression either for correlated data or high-dimensional data is the singularity of the sample covariance matrix. While dealing with an ill-conditioned covariance matrix has been a longstanding challenge in the statistical literature, recent proposals relying on adding noises to the original data have found their successes in obtaining reliable estimates and making predictions

Delattre et al. (2013) considered a system of stochastic differential equations (SDEs) in a random effects setup. Under the independent and identical (iid) situation, and assuming normal distribution of the random effects, they established weak consistency of the maximum likelihood estimators (MLEs) of the population parameters of the random effects. In this article, respecting the increasing importance

We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix An with spectral radius ρ(An)<1 satisfying ρ(An)→1. In that framework, we establish a moderate deviation principle for the empirical covariance only relying on the elements of An through 1−ρ(An) and, as a by-product, we establish

We address a Bayesian regression model with a functional covariate and a scalar response. The model is misspecified in two ways: the posterior distribution is calculated by using normal errors and, mostly, by restraining the functional regression coefficient to a possibly small subset of L2([0,1]). A first general concentration result shows that the posterior distribution concentrates within Kullback–Leibler

Often in multiple testing, the hypotheses appear in non-overlapping blocks with the associated p-values exhibiting dependence within but not between blocks. We consider adapting the Benjamini–Hochberg method for controlling the false discovery rate (FDR) and the Bonferroni method for controlling the familywise error rate (FWER) to such dependence structure without losing their ultimate controls over

Functional principal component analysis for sparse longitudinal data usually proceeds by first smoothing the covariance surface, and then obtaining an eigendecomposition of the associated covariance operator. Here we consider the use of penalized tensor product splines for the initial smoothing step. Drawing on a result regarding finite-rank symmetric integral operators, we derive an explicit spline

The current penalized regression methods for selecting predictor variables and estimating the associated regression coefficients in the sparse Cox model are mainly based on partial likelihood. In this paper, a bias-corrected empirical likelihood method is proposed for the sparse Cox model in conjunction with appropriate penalty functions when the dimensionality of data is high. Theoretical properties

Precision medicine, aka stratified/personalized medicine, is becoming more pronounced in the medical field due to advancement in computational ability to learn about patient genomic backgrounds. A biomaker, i.e. a type of biological process indicator, is often used in precision medicine to classify patient population into several subgroups. The aim of precision medicine is to tailor treatment regimes

Connectivity studies of the brain are usually based on functional Magnetic Resonance Imaging (fMRI) experiments involving many subjects. These studies need to take into account not only the interaction between areas of a single brain but also the differences amongst those subjects. In this paper we develop a methodology called the group-structure (GS) approach that models possible heterogeneity between

As the US health care system undergoes unprecedented changes, the need for adequately powered studies to understand the multiple levels of main and interaction factors that influence patient and other care outcomes in hierarchical settings has taken center stage. We consider two-level models where n lower-level units are nested within each of J higher-level clusters (e.g. patients within practices

In this article we investigate the optimal design problem for some wavelet regression models. Wavelets are very flexible in modeling complex relations, and optimal designs are appealing as a means of increasing the experimental precision. In contrast to the designs for the Haar wavelet regression model (Herzberg and Traves 1994; Oyet and Wiens 2000), the I-optimal designs we construct are different

We introduce a rank-based bent linear regression with an unknown change point. Using a linear reparameterization technique, we propose a rank-based estimate that can make simultaneous inference on all model parameters, including the location of the change point, in a computationally efficient manner. We also develop a score-like test for the existence of a change point, based on a weighted CUSUM process

Modern clinical trials are often complex, with multiple competing objectives and multiple endpoints. Such trials should be both ethical and efficient. In this paper, we overcome the obstacles introduced by the large number of unknown parameters and the possible correlations between the multiple endpoints. We obtain the optimal allocation proportions for the following two optimization problems: (1)

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed

Current status data arise frequently in demography, epidemiology, and econometrics where the exact failure time cannot be determined but is only known to have occurred before or after a known observation time. We propose a quantile regression model to analyze current status data, because it does not require distributional assumptions and the coefficients can be interpreted as direct regression effects

Missing values present challenges in the analysis of data across many areas of research. Handling incomplete data incorrectly can lead to bias, over-confident intervals, and inaccurate inferences. One principled method of handling incomplete data is multiple imputation. This article considers incomplete data in which values are missing for three or more qualitatively different reasons and applies a

This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and

Varying coefficient models are useful for modeling longitudinal data and have been extensively studied in the past decade. Motivated by commonly encountered dichotomous outcomes in medical and health cohort studies, we propose a two-step method to estimate the regression coefficient functions in a logistic varying coefficient model for a longitudinal binary outcome. The model depicts time-varying covariate

In practice, disease outcomes are often measured in a continuous scale, and classification of subjects into meaningful disease categories is of substantive interest. To address this problem, we propose a general analytic framework for determining cut-points of the continuous scale. We develop a unified approach to assessing optimal cut-points based on various criteria, including common agreement and

The Schwarz criterion or Bayes Information Criterion (BIC) is often used to select a model dimension, and some variations of the BIC have been proposed in the context of change-point problems. In this paper, we consider a segmented line regression model with an unknown number of change-points and study asymptotic properties of Schwarz type criteria in selecting the number of change-points. Noticing

We develop a modeling framework for joint factor and cluster analysis of datasets where multiple categorical response items are collected on a heterogeneous population of individuals. We introduce a latent factor multinomial probit model and employ prior constructions that allow inference on the number of factors as well as clustering of the subjects into homogenous groups according to their relevant