For integers n>2 and k>0, an (n×n)∕k semi-Latin square is an n×n array of k-subsets (called blocks) of an nk-set (of treatments), such that each treatment occurs once in each row and once in each column of the array. A semi-Latin square is uniform if every pair of blocks, not in the same row or column, intersect in the same positive number of treatments. It is known that a uniform (n×n)∕k semi-Latin

This paper rigorously studies large sample properties of a surrogate L0 penalization method via iteratively performing reweighted L2 penalized regressions for generalized linear models and develop a scalable implementation of the method for sparse high dimensional massive sample size (sHDMSS) data. We show that for generalized linear models, the limit of the algorithm, referred to as the broken adaptive

Crossover designs involve two types of treatment effects, a direct effect and a carryover effect, and several optimality results are available for inferring on these two effects separately. However, an aim of a designed experiment is to recommend a single treatment which will be used over longer time periods. When this treatment is used over many periods, the effect on the subject at any time period

For existing Bayesian cross-validated measure of influence of each observation on the posterior distribution, this paper considers a generalization using the Bregman Divergence (BD). We investigate various practically useful and desirable properties of these BD based measures to demonstrate the superiority of these measures compared to existing Bayesian measures of influence and Bayesian residual based

A design point is inessential when it does not contribute to an optimal design, and can therefore be safely discarded from the design space. We derive three inequalities for the detection of such inessential points in c-optimal design: the first two are direct consequences of the equivalence theorem for c-optimality; the third one is derived from a second-order cone programming formulation of c-optimal

Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence intervals based on higher-order approximate quantiles of the score function. The coverage approximation error is O(n−3∕2) while the approximation error of confidence

We propose a Bayesian method to detect change points in a sequence of functional observations that are signal functions observed with noises. Since functions have unlimited features, it is natural to think that the sequence of signal functions driving the underlying functional observations change through an evolution process, that is, different features change over time but possibly at different times

A life distribution function F is said to have an increasing failure rate average if H(x)∕x is nondecreasing where H(x) is the corresponding cumulative hazard function. In this paper we provide a uniformly strongly consistent estimator of F and derive the convergence in distribution of the estimator at a point where H(x)∕x is increasing using the arg max theorem. We also show using simulations that

This paper presents reference priors for non-regular model whose support depends on an unknown parameter. A multi-parameter family which includes both regular and non-regular structures is considered. The resulting priors are obtained by asymptotically maximizing the expected α-divergence between the prior and the corresponding posterior distribution. Some examples of reference priors for typical multi-parameter

We consider the solution X=(Xt)t≥0 of a multivariate stochastic differential equation with Levy-type jumps and with unique invariant probability measure with density μ. We assume that a continuous record of observations XT=(Xt)0≤t≤T is available. In the case without jumps, Dalalyan and Reiss (2007) and Strauch (2018) have found convergence rates of invariant density estimators, under respectively isotropic

High-dimensional data are frequently encountered with the development of modern data collection techniques. Testing the equality of the mean vectors of two high-dimensional samples with possibly different covariance matrices is usually referred to as a high-dimensional two-sample Behrens–Fisher (BF) problem. In the high-dimensional setting, the classical BF solutions are expected to perform poorly

For designs of computer experiments, column-orthogonality and space-filling property are two desirable properties. In this paper, we develop methods for constructing a new class of designs that include orthogonal Latin hypercube designs as special cases. These designs are not only column-orthogonal but also have good space-filling properties in low dimensions. All these appealing properties make them

In this paper, we conduct simultaneous inference of the non-parametric part of a partially linear model when the non-parametric component is a multivariate unknown function. Based on semi-parametric estimates of the model, we construct a simultaneous confidence region of the multivariate function for simultaneous inference. The developed methodology is applied to perform simultaneous inference for

Component orthogonal arrays, as fractional designs of all possible permutations on experimental factors, are suitable for order-of-addition experiments due to their pairwise balance in any two positions of the orders. The existing component orthogonal arrays are mainly restricted to the case where the number of components is prime power. In this paper, we construct component orthogonal arrays with

Moment-based sufficient dimension reduction methods such as sliced inverse regression may not work well in the presence of heteroscedasticity. We propose to first estimate the expectiles through kernel expectile regression, and then carry out dimension reduction based on random projections of the regression expectiles. Several popular inverse regression methods in the literature are extended under

We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, p, is larger than the sample size n. Specifically, we propose an orthogonally equivariant estimator. The eigenvectors of such estimator are the same as those of the sample covariance matrix. The eigenvalue estimates are obtained from an adjusted profile likelihood function

In this paper, we investigate a class of optimal circulant {0,1}-arrays other than the previously known class of optimal designs for fMRI experiments with a single type of stimulus. We suppose throughout the paper that n≡2(mod4) and discuss the asymptotic optimality and the D-efficiency of k×n circulant almost orthogonal arrays (CAOAs) with 2 levels (presence/absence of the stimulus), strength 2 and

Quantum state tomography, which aims to estimate quantum states that are described by density matrices, plays an important role in quantum science and quantum technology. This paper examines the eigenspace estimation and the reconstruction of large low-rank density matrix based on Pauli measurements. Both ordinary principal component analysis (PCA) and iterative thresholding sparse PCA (ITSPCA) estimators

The energy test of multivariate normality is an affine invariant test based on a characterization of equal distributions by energy distance. The test statistic is a degenerate kernel V-statistic, which asymptotically has a sampling distribution that is a Gaussian quadratic form under the null hypothesis of normality. The parameters of the limit distribution are the eigenvalues of the integral operator

We consider a design problem where experimental conditions (design points Xi) are presented in the form of a sequence of i.i.d. random variables, generated with an unknown probability measure μ, and only a given proportion α∈(0,1) can be selected. The objective is to select good candidates Xi on the fly and maximize a concave function Φ of the corresponding information matrix. The optimal solution

The matching problem is known since the beginning of the eighteenth century and Bayesian solutions have been proposed. In this paper, we present a Bayesian analysis of an experiment that also leads to the matching problem. Since in this paper we consider the order in which assignments are made and not only the number of matches, our approach is different from the literature on this problem. Our approach

This paper extends the principal component analysis (PCA) to moderately non-stationary vector time series. We propose a method that searches for a linear transformation of the original series such that the transformed series is segmented into uncorrelated subseries with lower dimensions. A columns’ rearrangement method is proposed to regroup transformed series based on their relationships. We discuss

In this paper, we first establish the generalization bounds of Lagrangian Support Vector Machines (LSVM) based on uniformly ergodic Markov chain (u.e.M.c.) samples. As an application, we also obtain the generalization bounds of LSVM based on strongly mixing sequence, independent and identically distributed (i.i.d.) samples, respectively. The fast learning rates of LSVM for u.e.M.c., strongly mixing

When estimating the average causal effect in observational studies, researchers have to tackle both self-selection of treatment and outcome modeling. This is difficult because the parametric form of the outcome model is often unknown and there exists a large number of covariates. In this work, we present a semiparametric strategy for estimating the average causal effect by regressing on the propensity

In this work we study stationary linear time-series models, and construct and analyse “score-matching” estimators based on the Hyvärinen scoring rule. We consider two scenarios: a single series of increasing length, and an increasing number of independent series of fixed length. In the latter case there are two variants, one based on the full data, and another based on a sufficient statistic. We study

In this paper, the problem of simultaneously testing mean vector and covariance matrix of one-sample population is investigated in high-dimensional settings. We propose a new test statistic and obtain its asymptotic distributions under null and local alternative hypotheses, respectively. Our asymptotic result for proposed test does not need some conditions such as linearity between the sample size

For one-parameter exponential families, we provide a unified minimax result for estimating the mean under weighted squared error losses in the presence of a lower-bound restriction. The finding recovers cases for which the result is known, as well as others which are new such as for a negative binomial model. We also study a related self-minimaxity property, obtaining several non-minimax results. Finally

This paper proposes a three-step method for detecting multiple structural breaks for piecewise stationary vector autoregressive processes. The number of structural breaks can be large and unknown with the locations of the breaks being different among different components. The proposed method is established via a link between a structural break problem and a high-dimensional regression problem. By means

A two-sample nonparametric test based on two independent samples is proposed for comparing mean time to failure (MTTF) functions of two life distributions. The proposed test has the flexibility of handling unequal sample sizes and crossings of mean time to failure functions. The test is shown to be consistent and a bound on asymptotic size has been derived. A computational technique is devised for

We introduce a nonparametric measure to quantify the degree of heteroskedasticity at a fixed quantile of the conditional distribution of a random variable. Our measure of heteroskedasticity is based on nonparametric quantile regressions and is expressed in terms of unrestricted and restricted expectations of quantile loss functions. It can be consistently estimated by replacing the unknown expectations

In this paper, a new hidden logistic regression model, i.e., the variant of the parallel regression model, is developed to study the relationship between a sensitive binary response variable and a set of non-sensitive covariates, where the information about the sensitive attribute of interest is collected via the variant of the parallel model originally proposed by Liu and Tian (2013b). The EM–NR algorithm

Functional magnetic resonance imaging (fMRI) techniques involve studying the brain activity of an experimental subject in response to a mental stimulus, such as a picture or a video shown to the subject. The design problem in fMRI studies is to come up with the best sequence of stimuli to be shown to subjects which enables the precise estimation of the brain activity. In previous analytical studies

Penalized spline regression is a popular and flexible method of obtaining estimates in nonparametric models but the classical least-squares criterion is highly susceptible to model deviations and atypical observations. Penalized spline estimation with a resistant loss function is a natural remedy, yet to this day the asymptotic properties of M-type penalized spline estimators have not been studied

The main goal of this paper is to study a new dispersive order in an arbitrary metric space. More precisely, given two random variables on a metric space, the order decides which one has a more concentrated distribution. It is motivated by the wish to be able to make new comparisons that the currently defined orderings cannot make. Related to this problem, several statistical parameters of a random

In this paper, we propose a robust method for the estimation of regression function. By symmetric addition, we change platykurtic errors into leptokurtic errors; and then estimate the nonparametric function by the local polynomial least absolute deviation regression. Different from the local polynomial least squares estimator, the new estimator is robust for outliers and heavy-tailed errors even if

In constructing a confidence interval for the mean difference of two independent populations, we may encounter the problem of having a low coverage probability when there are many zeros in the data, and the non-zero values are highly positively skewed. The violation of the normality assumption makes parametric methods inefficient in such cases. In this paper, jackknife empirical likelihood (JEL) and

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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