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

We deal with the problem of feature selection for high-dimensional additive models in this article. The existing feature selection methods for additive models in the literature mainly concentrate on the penalized likelihood approach. We propose a sequential group selection method for additive models (sgsAM) in this article. The additive functions are estimated by B-spline method and are treated as

We consider the model Y=X+ξ where Y is observable, ξ is a noise random variable with density fξ, X has an unknown mixed density such that P(X=Xc)=1−p, P(X=a)=p with Xc being continuous and p∈(0,1), a∈R. Typically, in the last decade, the model has been widely considered in a number of papers for the case of fully known quantities a,fξ. In this paper, we relax the assumptions and consider the parametric

We consider estimation of the inverse scatter matrix Σ−1 for a scale mixture of Wishart matrices under various Efron-Morris type losses, tr[{Σˆ−1−Σ−1}2Sk] for k=0,1,2..., where S is the sample covariance matrix. We improve on the standard estimators aS+, where S+ denotes the Moore–Penrose inverse of S and a is a positive constant, through an unbiased estimator of the risk difference between the new

The semiparametric estimation of multivariate fractional processes based on the tapered periodogram of the differenced series is considered in this paper. We construct multivariate local Whittle estimators by incorporating the maximal efficient taper developed by Chen (2010). The proposed estimation method allows a wide range of potentially nonstationary long-range dependent series, being invariant

Geometric and hidden projection are two important properties to consider for three-level fractional factorials. The effective development of methods that can address tasks involving both these properties requires a unified design framework that integrates them. We highlight one integrative framework that is based on indicator functions for three-level designs under the linear-quadratic parameterization

In Siotani and Fujikoshi (1984), a precise local limit theorem for the multinomial distribution is derived by inverting the Fourier transform, where the error terms are explicit up to order N−1. In this paper, we give an alternative (conceptually simpler) proof based on Stirling’s formula and a careful handling of Taylor expansions, and we show how the result can be used to approximate multinomial

A generalized spiked Fisher matrix is considered in this paper. We establish a criterion for the description of the support of the limiting spectral distribution of high-dimensional generalized Fisher matrix and study the almost sure limits of the sample spiked eigenvalues where the population covariance matrices are arbitrary which successively removed an unrealistic condition posed in the previous

In this work, optimal design problems for estimation of unknown parameters for a flexible class of non-normal distributions useful for describing various data types are considered. A particular model, designated the simplex dispersion model, can be applied to model proportional (or compositional) outcomes confined within the (0, 1) interval. The main interest here is to determine the optimal experimental

Strong orthogonal arrays enjoy more attractive space-filling properties than ordinary orthogonal arrays for computer experiments. In this paper, we propose two methods for constructing column-orthogonal nearly strong orthogonal arrays. These designs enjoy column orthogonality, inherit the attractive two-dimensional space-filling property of strong orthogonal arrays, and can accommodate twice or more

We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether observed increments have jumps or not at each small-time interval, hence to estimate the unknown parameters separately. However, a data-adapted and quantitative choice

We introduce new shape-constrained classes of distribution functions on R, the bi-s∗-concave classes. In parallel to results of Dümbgen et al. (2017) for what they called the class of bi-log-concave distribution functions, we show that every s-concave density f has a bi-s∗-concave distribution function F for s∗≤s∕(s+1). Confidence bands building on existing nonparametric confidence bands, but accounting

This paper is concerned with testing the second-order stationarity of a time series. By using a blockwise scheme, the test is transformed to compare local spectra of different segments of the blocked time series. Based on periodogram-ratios of each pair of segments at the same frequency points, an Anderson–Darling-like statistic is constructed to compare their spectra. By maximizing several Anderson–Darling-like

We investigate adaptive density estimation in the additive model Z=X+Y, where X and Y are independent d-dimensional random vectors with non-negative coordinates. Our goal is to recover the density of X from independent observations of Z, assuming the density of Y is known. In the d=1 case, an estimation procedure using projection on the Laguerre basis has already been studied. We generalize this procedure

In survey domain estimation, a priori information can often be imposed in the form of linear inequality constraints on the domain estimators. Wu et al. (2016) formulated the isotonic domain mean estimator, for the simple order restriction, and methods for more general constraints were proposed in Oliva-Avilés et al. (2020). When the assumptions are valid, imposing restrictions on the estimators will

We propose a method for testing hypothesis on parametric family of transition probabilities of a Markov sequence, when the asymptotic distribution of the empirical processes involved is, largely, independent from the specific form of the parametric family. We first consider function-parametric empirical process for the Markov sequence and describe its weak limit as a certain projection. Then we establish

Phase II clinical trials in oncology are used to initially evaluate the therapeutic efficacy of a new treatment. In the past, the total response was a frequently used endpoint to access the effectiveness of the treatment. When the total response is modest, clinicians may also be interested in disease control (defined as the total response or stable disease) since it may better predict clinical outcomes

There is ample research on false discovery rate (FDR) control for testing hypotheses classified according to one criterion. However, scenarios of hypotheses partitioned via two different criteria are often encountered in practice. Such two-way classification encodes more structural information in the associated multiple testing of the hypotheses than its one-way or un-classified counterparts. Unfortunately

The research in this paper gives a systematic investigation of the asymptotic behaviors of four inverse probability weighting (IPW)-based estimators for conditional average treatment effects, with nonparametrically, semiparametrically, parametrically estimated, and true propensity score, respectively. To this end, we first pay particular attention to semiparametric dimension reduction structure such

We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) t-statistic is considered, and we determine its rejection region using a common rejection limit. When there are unknown correlations among test statistics, the multiplicity adjusted p-values are dependent on the unknown correlations

This work studies the properties of the maximum likelihood estimator (MLE) of a multidimensional parameter in a nonlinear model with additive Gaussian errors. The observations are collected in a two-stage experimental design and are dependent because the second stage design is determined by the observations at the first stage. The MLE maximizes the total likelihood. Unlike most theory in the literature

A zero-inflated Bernoulli (ZIBer) regression model is an alternative model in order to improve fitting the binary outcome data that have many more zeros than expected under a regular logistic regression model. Because some covariates often have missing values, we propose the validation likelihood (VL) method to estimate the parameters of the ZIBer regression model with covariates missing at random

We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data, with distributions belonging to the exponential family, and which may also vary in terms of other component series. Within a quasi-likelihood approach, we construct

Functional regression allows for a scalar response to be dependent on a functional predictor, however, not much work has been done when scalar predictors that interacts with the functional predictor are introduced. In this paper, we introduce a new functional single-index varying coefficient model with the functional predictor being single-index part. By means of functional principal components analysis

A new class of designs is introduced for both estimating the variance components of nested factors and testing hypotheses about those variance components. These designs are flexible, and can be chosen so that the degrees of freedom are more evenly spread among the factors than they are in balanced nested designs. The variances of the estimators are smaller than those in stair nested designs of comparable

In medical researches such as case-control studies with contaminated controls, frequently encountered is a particular two-sample testing problem in which one sample has a mixture structure. It is a very common case that the exposure in a case-control study may have a positive (or negative) effect on the response variable if the effect exists. This is often ignored by existing tests, which would lead

Multiple hypotheses testing problems are highly relevant whenever data is evaluated statistically. In business research, for example, the topic gains more importance due to the increase in data driven approaches for efficient decision making. By now, the decision on a suitable multiple hypotheses method presupposes a two-step selection. First, the user has to decide on the multiple type I error definition

In this paper, we develop a method for handling nonignorable missing data in fitting time series models for longitudinal surveys. We assume that the response probability not only depends on auxiliary variables but also the current and past outcomes which are subject to missingness. Under a nonignorable missing mechanism, an observed likelihood estimation approach is proposed based on the distribution

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