Motivated by the goal of improving the efficiency of a sequential design with small sample size, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modeling and nonrecursive iteration. Consistency of the Bayes estimator is established. Simulation studies show its superiority in small-sample performance to Robbins–Monro

We consider the well-known white noise test that is available in the literature. Its null distribution is known to be asymptotically normal under different sets of conditions for processes with finite 8th moment. We show that for some specific models, the normality continues to hold under the finiteness of only the 4th moment. This includes various GARCH models, stochastic autoregressive volatility

In recent years, the multi-armed bandit problem regains popularity especially for the case with covariates since it has new applications in customized services such as personalized medicine. To deal with the bandit problem with covariates, a policy called binned subsample mean comparison that decomposes the original problem into some proper classic bandit problems is introduced. The growth rate in

The efficient estimation problem of a semi-parametric periodic integer-valued autoregressive PINARp model of arbitrary order is considered. The unspecified distribution of the innovation process of this model is supposed to satisfy only some mild technical assumptions.We therefore provide efficient estimates for both parameters of the model, namely a periodic autoregressive parameter and a periodic

Methods for validating the assumption of normality of functional data have been only lightly developed to date, with existing methods based primarily on summarizing the data by their projections into random or principal component subspaces, and applying multivariate normality tests to the vectors of scores defining these projections. While this is effective in some cases, we show with both real and

Circular data are data measured in angles or directions, which occur in a wide variety of scientific fields. An often investigated hypothesis is that of circular uniformity, or isotropy. Frequentist methods for assessing the circular uniformity null hypothesis exist, but do not allow the user faced with an insignificant result to distinguish lack of power from support for the null hypothesis. Bayesian

Randomization ensures that observed and unobserved covariates are balanced, on average. However, randomizing units to treatment and control often leads to covariate imbalances in realization, and such imbalances can inflate the variance of estimators of the treatment effect. One solution to this problem is rerandomization – an experimental design strategy that randomizes units until some balance criterion

This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized contrast that is constructed from the Poisson quasi-maximum likelihood of the model. The consistency of the proposed estimator is established. From practical applications

This paper reviews minimax best equivariant estimation in three invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable

In this article, we develop new maximum-type tests to infer the overall significance of coefficients in high-dimensional linear models based on the Wilcoxon scores. The proposed testing procedures are free of error variance estimation and robust to heavy-tailed distributions and outliers, making them widely applicable in practice. We incorporate the dependence structure among predictors in the test

Peaks in the spectral density estimates of seasonally adjusted data are indicative of an inadequate adjustment. Spectral peaks are currently assessed in the X-13ARIMA-SEATS program via the visual significance (VS) approach; this paper provides a rigorous statistical foundation for VS by defining measures of uncertainty for spectral peak measures, allowing for formal hypothesis testing, using the framework

With advancements in medical research, broader range of diseases may be curable, which indicates some patients may not die owing to the disease of interest. The mixture cure model, which can capture patients being cured, has received an increasing attention in practice. However, the existing mixture cure models only focus on major events with potential cures while ignoring the potential risks posed

Quantile functional linear regression was previously studied using functional principal component analysis. Here we consider the alternative penalized estimator based on the reproducing kernel Hilbert spaces (RKHS) setting. The motivation is that, for the functional linear (mean) regression, it has already been shown in Cai and Yuan (2012) that the approach based on RKHS performs better when the coefficient

There is a growing interest in learning how the distribution of a response variable changes with a set of observed 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

In this paper, we review three families of methods in linear sufficient dimension reduction through optimization. Through minimization of general loss functions, we cast classical methods, such as ordinary least squares and sliced inverse regression, and modern methods, such as principal support vector machines and principal quantile regression, under a unified framework. Then we review sufficient

This paper considers screening of adaptive interventions or adaptive treatment strategies embedded in a sequential multiple assignment randomized trial (SMART). As a SMART typically consists of numerous adaptive interventions, inferential procedures based on pairwise comparisons of all interventions may suffer substantial loss in efficiency after accounting for multiplicity. We propose simultaneous

The expectation–maximization (EM) algorithm is a seminal method to calculate the maximum likelihood estimators (MLEs) for incomplete data. However, one drawback of this algorithm is that the asymptotic variance–covariance matrix of the MLE is not automatically produced. Although there are several methods proposed to resolve this drawback, limitations exist for these methods. In this paper, we propose

We explore how violations of the often-overlooked standard assumption that the random effects model matrix in a linear mixed model is fixed (and thus independent of the random effects vector) can lead to bias in estimators of estimable functions of the fixed effects. However, if the random effects of the original mixed model are instead also treated as fixed effects, or if the fixed and random effects

The goal of this paper is to indicate a new method for constructing normal confidence intervals for the mean, when the data is coming from stochastic structures with possibly long memory, especially when the dependence structure is not known or even the existence of the density function. More precisely we introduce a random smoothing suggested by the kernel estimators for the regression function. The

In this paper, we consider the separable covariance model, which plays an important role in wireless communications and spatio-temporal statistics and describes a process where the time correlation does not depend on the spatial location and the spatial correlation does not depend on time. We established a central limit theorem for linear spectral statistics of general separable sample covariance matrices

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

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