Rerandomization is a strategy for improving balance on observed covariates in randomized controlled trials. It has been both advocated and advised against by renowned scholars of experimental design. However, the relationship and differences between stratification, rerandomization, and the combination of the two have not been previously investigated. In this paper, we show that stratified designs can

The problem of fitting two concentric objects (circles and ellipses) to noisy data plays a vital role in many fields. In this paper, statistical methodologies are deployed by additionally assuming that the angular differences between successively measured data points are known, which is known as Berman’s model. The heteroscedasticity between covariates is also assumed here, and hence, several estimators

In this paper, in view of the Rao’s inequalities on the parameters of an orthogonal array, we define some extended matrices for asymmetric orthogonal arrays of strength t (t≥2). According to these matrices, necessary conditions for the existence of tight asymmetric orthogonal arrays of strengths 2 and 4 described by Mukerjee and Wu (1995) are generalized to the existence of tight asymmetric orthogonal

Plausibility is a formalization of exact tests for parametric models and generalizes procedures such as Fisher’s exact test. The resulting tests are based on cumulative probabilities of the probability density function and evaluate consistency with a parametric family while providing exact control of the α level for finite sample size. Model comparisons are inefficient in this approach. We generalize

In this paper, we consider model averaging for expectile regressions, which are common in many fields. The J-fold cross-validation criterion is developed to determine averaging weights. Under some regularity conditions, we prove that the resulting model averaging estimators are asymptotically optimal in the sense that they produce an expectile loss that is asymptotically equivalent to that of an infeasible

In a finite population sampling survey, auxiliary information is commonly used to improve the Horvitz–Thompson estimators and calibration has been extensively used by national statistical agencies over the last decades for that purpose. This method enables to make estimators consistent with known totals of auxiliary variables and to reduce variance if the calibration variables are explanatory for the

Testing the dependence between the response and the functional predictor in a functional linear model is of fundamental importance. In this paper, based on a U-statistic of order two, we develop a computationally more efficient test for lacking of dependence in functional linear regression model. By the martingale central limit theorem, we prove that the asymptotic normality of the proposed test statistic

We consider parametric tests for multidimensional ergodic diffusions based on high frequency data. We propose two-step testing method for diffusion parameters and drift parameters. To construct test statistics of the tests, we utilize the adaptive estimator and provide three types of test statistics: likelihood ratio type test, Wald type test and Rao’s score type test. It is proved that these test

In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on information matrices (if criteria depend on designs via information matrices) or with respect to the designs themselves (for finite design regions). We apply the obtained optimality conditions to multiple-group random coefficient regression models and illustrate

Empirical distributions in a range of fields are often substantially non-Gaussian but smooth enough to suggest that the underlying population distribution has at least several derivatives. Linear combinations of many random variables often have smooth densities even if the random variables are not independent. The main result here generalizes the elementary result that a convolution of densities has

Sequential (or adaptive) designs are common in acceptance sampling and pharmaceutical trials. This is because they can achieve the same type 1 and type 2 error rate with fewer subjects on average than fixed sample trials. After the trial is completed and the test result decided, we need full inference on the main parameter Δ. In this paper, we are interested in exact one-sided lower and upper limits

Spike-and-slab priors model predictors as arising from a mixture of distributions: those that should (slab) or should not (spike) remain in the model. The spike-and-slab lasso (SSL) is a mixture of double exponentials, extending the single lasso penalty by imposing different penalties on parameters based on their inclusion probabilities. The SSL was extended to Generalized Linear Models (GLM) for application

The cumulative incidence function (CIF) plays an important role in the comparison of competing risks in a competing risks model. Its value at time t is the probability of failure by time t from a particular type of risk in the presence of other risks. In this paper we consider the estimation of two CIFs, F1 and F2, corresponding to two competing risks when the ratio R(t)≡F1(t)∕F2(t) is nondecreasing

Matrix-variate logistic regression is useful in facilitating the relationship between the binary response and complex-featured matrix-variates arising commonly from medical imaging research. However, standard inference procedures based on such a model are impaired by the presence of the response misclassification as well as inactive covariates. It is imperative to account for the misclassification

We consider estimating a factor model for high-dimensional time series that contains structural breaks in the factor loading space at unknown time points. We first study the case when there is one change point in factor loadings, and propose a consistent estimator for the structural break location, whose convergence rate is shown to depend on an interplay between the dimension of the observed time

A mean zero spatial process X(t) on the n-dimensional Euclidean space Rn is isotropic if its covariance function (c.f.) is of the form: Rn(τ)=Cov[X(t),X(s)], where τ=|t−s|, t, s ∈Rn, and Rn is an admissible function on R1. An isotropic spatial process X has a bounded range of dependence if sup{τ:Rn(τ)≠0} <∞. Here we consider a class of isotropic c.f.’s Rn(τ), n=1,2,… with bounded ranges of dependence

This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent clusters and the cluster sizes (the number of observations in each cluster) go to infinity. Under very mild conditions, the estimators are shown to be asymptotically normal

In this paper, we consider the problem of estimating the density function of a Chi-squared variable on the basis of observations of another Chi-squared variable and a normal variable under the Kullback–Leibler divergence. We assume that these variables have a common unknown scale parameter and that the mean of the normal variable is also unknown. We compare the risk functions of two Bayesian predictive

We investigate an asymptotic behaviour of probabilities of large deviations for normalized combinatorial sums. We find a zone in which these probabilities are equivalent to the tail of the standard normal law. Our conditions are similar to the classical Bernstein conditions. The range of the zone of the normal convergence can be of a power order.

The problem of constructing the most powerful test for random number generators (RNGs) is considered, where the generators are modelled by stationary ergodic processes. At present, RNGs are widely used in data protection, modelling and simulation systems, computer games, and in many other areas where the generated random numbers should look like binary numbers of a Bernoulli equiprobable sequence.

In nonparametric models, numerous penalization methods using a nonparametric series estimator have been developed for model selection and estimation. However, a penalization has been poorly understood combined with kernel smoothing. This can be attributed to the intrinsic technical and computational difficulties, which leads to different treatments from the developments of the penalized series estimators

We study entropy as a measure of randomness in a sequential clinical trial. For any randomization design, we consider the well-known sequence of conditional treatment assignment probabilities, Pn, which complements the random allocation proportion. We then use Pn to formulate and prove a statement about conditions for the asymptotic mean entropy of a randomization design to achieve its optimum value

Orthogonal array has been used in various fields, as it possesses attractive combinatorial properties. However, for a long time, combinatorially equivalent orthogonal arrays are thought to be indistinguishable, especially when an ANOVA model is established. Later on, some papers pointed out that permuting levels of orthogonal arrays will alter their statistical inference abilities. Criteria have been

In this article, we develop a generalized linear-quadratic model with a change point due to a covariate threshold, with one line segment and another quadratic segment intersecting at a change point. A two-step method is proposed to estimate the regression coefficients and the change point. The asymptotic properties of the proposed estimator are derived by modern empirical processes theory. A sup-likelihood

Denote Sn(p)=kn−1∑i=1knlog(Xn+1−i,n∕Xn−kn,n)p, where p>0, kn≤n is a sequence of integers such that kn→∞ and kn∕n→0, and X1,n≤⋯≤Xn,n are the order statistics of iid random variables X1,…,Xn with regularly varying upper tail of index 1∕γ. The estimator γ̂(n)=(Sn(p)∕Γ(p+1))1∕p is an extension of the Hill estimator. We investigate the asymptotic properties of Sn(p) and γ̂(n) both for fixed p>0 and for

For integers $n>2$ and $k>0$, an $(n\times n)/k$ semi-Latin square is an $n\times n$ 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

Abstract This paper rigorously studies large sample properties of a surrogate L 0 penalization method via iteratively performing reweighted L 2 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

Abstract 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

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

Abstract 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

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 for functional data. We extract the features of a sequence of functional data by the discrete wavelet transform (DWT), and treat each sequence of feature independently. We believe there is potentially a change in each feature at possibly different time points. The functional data evolves through such changes throughout the sequences of observations

Abstract 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

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

Abstract 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

Abstract 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

Abstract 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

Abstract 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 ( mod 4 ) 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)

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

Abstract 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

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

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

Abstract 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

In this paper, we consider admixture models which are two-component mixture distributions having one known component. This is the case when a gold standard reference component is well known, and when a population contains such a component plus another one with different features. When two populations are drawn from such models, we propose a penalized χ2-type testing procedure allowing a pairwise comparison

A new family of matrix variate distributions indexed by elliptical models is proposed in this work. The termed multimatricvariate distributions emerge as a generalisation of the bimatrix variate distributions based on matrix variate Gamma distributions and independence. Some properties and special cases of the multimatricvariate distributions are also derived. Two new interesting Jacobians in the area

We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric priors are constructed using this basis and a simulation study shows that the use of the resulting Bayes estimator may provide gains over comparable circular density

A Bayesian treatment of the proportional hazard (PH) model is revisited using Dirichlet process and gamma process priors for the baseline survival and cumulative hazard functions respectively. Such priors, due to their discrete support, conflict with the absolutely continuous nature of survival responses expressed through the hazard function structure that defines the PH model. We resolve this conflict

We propose a construction of simultaneous confidence bands (SCBs) for functional parameters over arbitrary dimensional compact domains using the Gaussian Kinematic formula of t-processes (tGKF). Although the tGKF relies on Gaussianity, we show that a central limit theorem (CLT) for the parameter of interest is enough to obtain asymptotically precise covering even if the observations are non-Gaussian

A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly weighted kernel estimator with a fully data-driven bandwidth selection method, in the spirit of the Goldenshluger and Lepski method. An oracle-type inequality for

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power δ, which quantifies the degree of discounting of the historical information in making inference with the current data. When δ is not pre-specified and is treated as random, it can be estimated from the data using Bayesian updating

High dimensional data are frequently collected across research fields such as genomics, health sciences, economics, and social sciences. Recently, variable selection in the high dimensional setting has drawn great attention, with many effective methods developed to reduce the dimensionality of the data. However, most of these methods apply only to normally or near normally distributed outcomes in a

We consider general semiparametric inference when data are merged from multiple overlapping sources. Merged data exhibit several characteristics including heterogeneity across multiple data sources, potential unidentified duplicated records, and dependence due to sampling without replacement within each data source. In this paper, we establish a large sample theory for the weighted semiparametric M-estimation

We consider nonparametric estimation of a distribution function when data are collected from two-phase stratified sampling without replacement. We study the inverse probability weighted empirical distribution function and propose a novel computational procedure to construct a confidence band. Two-phase sampling design induces heterogeneity across strata and dependence due to sampling without replacement

Variability assessment of qualitative data has an important role in diverse areas such as sociology, quality engineering, healthcare, decision making, genetics, metrology in chemistry and many others. To test the homogeneity hypothesis, we use two main categorical factors. Using a cross-balanced design, we provide a decomposition theorem of the sample total-variation into ‘intra’ (within) component

The K-sign depth (K-depth) of a model parameter θ in a data set is the relative number of K-tuples among its residual vector that have alternating signs. The K-depth test based on K-depth, recently proposed by Leckey et al. (2020), is equivalent to the classical residual-based sign test for K=2, but is much more powerful for K≥3. This test has two major drawbacks. First, the computation of the K-depth

Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the inhomogeneous random graph model with missing observations. Using the Stochastic Block Model as a parametric proxy, we bound the risk of the maximum likelihood estimator of network connections probabilities

Abstract 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

Abstract 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

Abstract 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

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