We develop a new method to estimate the projection direction in the debiased Lasso estimator. The basic idea is to decompose the overall bias into two terms corresponding to strong and weak signals respectively. We propose to estimate the projection direction by balancing the squared biases associated with the strong and weak signals as well as the variance of the projection-based estimator. Standard

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has several optimal properties, a major drawback of Bayesian inference is the lack of robustness against data contamination and model misspecification, which becomes pernicious

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the principal component directions are not consistent, the sample and prediction principal component scores can be useful in revealing the population structure. We further show

Integrating the summary statistics from genome-wide association study (GWAS) and expression quantitative trait loci (eQTL) data provides a powerful way of identifying the genes whose expression levels are causally associated with complex diseases. A parameter that quantifies the genetic sharing (colocalisation) between disease phenotype and gene expression of a given gene based on the summary statistics

Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient models and single index models, becoming the latest state-of-the-art for semiparametric regression. This new class of models offers greater flexibility to characterize

It is important to quantify and predict rare events that have huge societal effects. Existing works on analyzing such events mainly rely on either inflexible parametric models or nonparametric models that are subject to “the curse of dimensionality”. We propose a new semi-parametric approach based on the tail single-index model to better balance between the model flexibility and parsimony. The procedure

We study sparse high-dimensional negative binomial regression problem for count data regression by showing non-asymptotic merits of the Elastic-net regularized estimator. With the KKT conditions, we derive two types of non-asymptotic oracle inequalities for the elastic net estimates of negative binomial regression by utilizing Compatibility factor and Stabil Condition, respectively. Based on oracle

To deal with the region selection problem in functional linear models, a functional information criterion is suggested to identify the null region where the functional predictor has no contribution to the response. It is shown that the null region identified by our proposal is asymptotically consistent under some mild conditions. In addition, we obtain the convergence rate of the length of the null

Conventional likelihood-based information criteria for model selection rely on the distribution assumption of data. However, for complex data that are increasingly available in many scientific fields, the specification of their underlying distribution turns out to be challenging, and the existing criteria may be limited and are not general enough to handle a variety of model selection problems. Here

We investigate two important properties of M-estimator, namely, robustness and tractability, in linear regression setting, when the observations are contaminated by some arbitrary outliers. Specifically, robustness means the statistical property that the estimator should always be close to the underlying true parameters {\em regardless of the distribution of the outliers}, and tractability indicates

Suppose one is interested in estimating causal effects in the presence of potentially unmeasured confounding with the aid of a valid instrumental variable. This paper investigates the problem of making inferences about the average treatment effect when data are fused from two separate sources, one of which contains information on the treatment and the other contains information on the outcome, while

This supplementary material contains technical details and proofs of the major theoretical results presented in the main paper and additional simulation results on point estimation, hypothesis tests and variable selection for linear regression and quantile regression models.

In this paper, we consider Bayesian inference on a class of multivariate median and the multivariate quantile functionals of a joint distribution using a Dirichlet process prior. Since, unlike univariate quantiles, the exact posterior distribution of multivariate median and multivariate quantiles are not obtainable explicitly, we study these distributions asymptotically. We derive a Bernstein-von Mises

We propose a new Conditional BEKK matrix-F (CBF) model for the time-varying realized covariance (RCOV) matrices. This CBF model is capable of capturing heavy-tailed RCOV, which is an important stylized fact but could not be handled adequately by the Wishart-based models. To further mimic the long memory feature of the RCOV, a special CBF model with the conditional heterogeneous autoregressive (HAR)

Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network links. Besides, the observed data often take the form of vectors or matrices, and the problem is formulated as comparing two covariance or precision matrices under

We study the consistency of the estimator in spatial regression with partial differential equation (PDE) regularization. This new smoothing technique allows to accurately estimate spatial fields over complex two-dimensional domains, starting from noisy observations; the regularizing term involves a PDE that formalizes problem specific information about the phenomenon at hand. Differently from classical

During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable missing data problems is quite limited. The main difficulty in solving such problems is that the missing probability and the regression likelihood function are tangled

Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to achieve efficient estimation of population parameters of interest. In this paper, we formulate a regularized regression estimator in the framework of Bayesian inference

Motivated by applications of mixed longitudinal studies, where a group of subjects entering the study at different ages (cross-sectional) are followed for successive years (longitudinal), we consider nonparametric covariance estimation with samples of noisy and partially-observed functional trajectories. To ensure model identifiability and estimation consistency, we introduce and carefully discuss

Since model selection is ubiquitous in data analysis, reproducibility of statistical results demands a serious evaluation of reliability of the employed model selection method, no matter what label it may have in terms of good properties. Instability measures have been proposed for evaluating model selection uncertainty. However, low instability does not necessarily indicate that the selected model

In the regime of two-sample comparison, tests based on a graph constructed on observations by utilizing similarity information among them is gaining attention due to their flexibility and good performances for high-dimensional/non-Euclidean data. However, when there are repeated observations, these graph-based tests could be problematic as they are versatile to the choice of the similarity graph. We

Fractional factorial designs are widely used for designing screening experiments. Nonregular fractional factorial designs can have better properties than regular designs, but their construction is challenging. Current research on the construction of nonregular designs focuses on two-level designs. We provide a novel class of multilevel nonregular designs by permuting levels of regular designs. We develop

Analysis of tail quantiles of the response distribution is sometimes more important than the mean in biomarker studies. Inference in quantile regression is complicated when there exist a large number of candidate markers together with some pre-specified controlled covariates. In this paper, we develop a new and simple testing procedure to detect the effects of biomarkers in high-dimensional quantile

Set classification aims to classify a set of observations as a whole, as opposed to classifying individual observations separately. To formally understand the unfamiliar concept of binary set classification, we first investigate the optimal decision rule under the normal distribution, which utilizes the empirical covariance of the set to be classified. We show that the number of observations in the

Random survival forest and survival trees are popular models in statistics and machine learning. However, there is a lack of general understanding regarding consistency, splitting rules and influence of the censoring mechanism. In this paper, we investigate the statistical properties of existing methods from several interesting perspectives. First, we show that traditional splitting rules with censored

This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different optimal sequential tests can be constructed for different performance measures of detection delay times. We also provide a formula to calculate the value of the generalized

Sufficient dimension reduction often resorts to inverse regression, and most inverse regression methods rely on slicing a quantitative response. The choice of a particular slicing scheme is critical, but there are no current methods in the literature about how to select an optimal slicing scheme. We consider two popular slicing-based methods, namely, the sliced inverse regression and the sliced average

Multiple imputation (MI) inference handles missing data by first properly imputing the missing values $m$ times, and then combining the $m$ analysis results from applying a complete-data procedure to each of the completed datasets. However, the existing method for combining likelihood ratio tests has multiple defects: (i) the combined test statistic can be negative in practice when the reference null

This paper provides robust estimators for the first canonical correlation and directions of random elements on Hilbert separable spaces by using robust association and scale measures combined with basis expansion and/or penalizations as a regularization tool. Under regularity conditions, the resulting estimators are consistent.

A new classification tree algorithm is presented. It has a novel variable selection algorithm that can effectively detect interactions. The algorithm uses a look-ahead approach that considers not only the significance at the current node, but also the significance at child nodes to detect the interaction. It is also different from other classification tree methods in that it finds the splitting point

The computational prediction algorithm of neural network, or deep learning, has drawn much attention recently in statistics as well as in image recognition and natural language processing. Particularly in statistical application for censored survival data, the loss function used for optimization has been mainly based on the partial likelihood from Cox's model and its variations to utilize existing

Doubly-intractable posterior distributions arise in many applications of statistics concerned with discrete and dependent data, including physics, spatial statistics, machine learning, the social sciences, and other fields. A specific example is psychometrics, which has adapted high-dimensional Ising models from machine learning, with a view to studying the interactions among binary item responses

This article discusses diagnostic checking for vector autoregressive models with uncorrelated but not independent innovations. In this situation, the multivariate portmanteau tests are severely over-sized due to the misspecification of critical values obtained from the χ2 distribution. To address this issue, a random weighting bootstrap procedure is proposed to approximate the null distribution when

Many biological high-throughput datasets, such as targeted amplicon-based and metagenomic sequencing data, are compositional. A common exploratory data analysis task is to infer robust statistical associations between high-dimensional microbial compositions and habitat- or host-related covariates. To address this, a general robust statistical regression framework RobRegCC (Robust Regression with Compositional

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

Roger was born on 18 December 1928 to French and English parents and passed away peacefully on 30 April 2021. He was raised mainly in London, educated initially at Battersea Grammar School and progressing to Imperial College London where he gained a First in Mathematics. Having completed his National Service in the RAF, he joined Reckitt and Colman in Hull in 1956 and worked in the Statistics Department

Benford’s law became a prevalent concept for fraud and anomaly detection. It examines the frequencies of the leading digits of numbers in a collection of data and states that the leading digit is most often 1, with diminishing frequencies up to 9. In this paper we propose a multivariate approach to test whether the observed frequencies follow the theoretical Benford distribution. Our approach is based

Proportional reversed hazard rate distribution family plays an important role in the reliability and lifetime data modelling. In this manuscript this family of distributions is generalized in order to enhance its modelling capability. Considering a special case, we introduce the extended generalized exponential distribution. Its mathematical properties are also studied. New model is applied in fitting

A general method is proposed to build exact artificial boundary conditions for the one-dimensional nonlocal Schrödinger equation. To this end, we first consider the spatial semi-discretization of the nonlocal equation, and then develop an accurate numerical method for computing the Green's function of the semi-discrete nonlocal Schrödinger equation. These Green's functions are next used to build the

Accurate numerical simulation of moving contact lines on complex boundaries with surface wettability effect remains a challenging problem. In this paper, we introduce a robust and accurate method to perform 3D contact line simulations on unstructured meshes with an imposed contact angle. The contact angle is imposed through a sub-grid scale curvature term and the contact line motion is enabled thanks

This article presents a new method to sample on manifolds, based on the Dirichlet distribution. The proposed strategy allows to completely respect the underlying manifold around which data are observed, and to do massive sampling with low computational effort. This can be very helpful, for instance, in neural networks training process, as well as in uncertainty analysis and stochastic optimization

Classified mixed model prediction (CMMP) is a new method that has embedded the traditional mixed model prediction (MMP) with a modern flavour. The basic idea is to first identify a class among the training data that matches the potential class corresponding to the new observations, whose associated mixed effect is of interest for prediction. Once such a matching is established, the MMP method can be

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an inferential perspective, most notably the absence of explicit conditioning formula. This paper extends earlier work on linear PDEs to a general class of initial value

Rao–Blackwellisation is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao–Blackwell theorem as established by C.R. Rao in 1945 and D. Blackwell in 1947, including a reduction of the variance of the resulting Monte Carlo approximations. This survey reviews some of the meanings of the term.

In this article, the authors provide a glimpse into the legendary career of centenarian Professor C. Radhakrishna Rao, a career that is inextricably linked to the history of modern statistics from Pearson and Fisher to the age of big data and Artificial Intelligence. A scientist of extraordinary vision, his ground-breaking contributions have influenced not only the field of statistics, but the mathematical

Statistical inference is constructed upon a statistical model consisting of a parameterised family of probability distributions, which forms a manifold. It is important to study the geometry of the manifold. It was Professor C. R. Rao who initiated information geometry in his monumental paper published in 1945. It not only included fundamentals of statistical inference such as the Cramér–Rao theorem

Two recently introduced model-based bias-corrected estimators for proportion of true null hypotheses ( π0) under multiple hypotheses testing scenario have been restructured for random observations under a suitable failure model, available for each of the common hypotheses. Based on stochastic ordering, a new motivation behind formulation of some related estimators for π0 is given. The reduction of

We extend to the multidimensional case a Wong–Zakai-type theorem proved by Hu and Øksendal (1996) for scalar quasi-linear Itô stochastic differential equations (SDEs). More precisely, with the aim of approximating the solution of a quasilinear system of Itô’s SDEs, we consider for any finite partition of the time interval [0,T] a system of differential equations, where the multidimensional Brownian

Frequency estimation of multiple complex and real sinusoids in noise has attracted wide attention in many fields. In this paper, two frequency domain parametric methods are proposed to estimate the frequencies of multiple complex and real sinusoids accurately. The first method for complex sinusoids adopts Discrete Fourier Transform (DFT) and interpolation algorithm to obtain the coarsely estimated

Molecular Communications (MC) is a bio-inspired communication technique that uses molecules to transfer information among bio-nano devices. In this paper, we focus on the detection problem for biological MC receivers employing ligand receptors to infer the transmitted messages encoded into the concentration of molecules, i.e., ligands. In practice, receptors are not ideally selective against target

In this paper, an efficient and practical solution to cope with random linear network coding (RLNC) drawbacks and maximize the system throughput is proposed. No header overheads and no retransmissions are required as a result of the introduction of a unique codebook at the nodes in charge of RLNC coding and decoding. The codebook contains the seeds that allow for the pseudo-random generation of full-rank

Abstract In this article, we propose an estimator for a bivariate residual entropy function based on smoothed kernel procedure. Asymptotic properties of the proposed estimator are established under some regularity conditions. Simulation studies demonstrate that the estimator performs well even for increased sample sizes and different combinations of lifetimes. The performances of the proposed estimator

The emerging orthogonal time frequency space (OTFS) modulation is demonstrated to offer reliable communication performance advantages over orthogonal frequency division multiplexing (OFDM) in doubly-dispersive fading channel. However, the existing embedded pilot-aided method to estimate channel impulse response (CIR) requires enormous spectral overhead to avoid the contamination of pilot symbols. In

There are sometimes cost, scientific, or logistical reasons to allocate individuals unequally in an individually randomized trial. In cluster randomized trials we can allocate clusters unequally and/or allow different cluster size between trial arms. We consider parallel group designs with a continuous outcome, and optimal designs that require the smallest number of individuals to be measured given

Abstract The article is devoted to the approximate solutions of the Fredholm integral equations of the second kind with the weak singular kernel that can have additional singularity in the numerator. We describe two problems that lead to such equations. They are the problem of minimization of small deviations and the entropy minimization problem. Both of them appear when considering a dynamical system

Let S⊂L2⊂S∗ be the Gel'fand triple over the Bernoulli space, where elements of S∗ are called Bernoulli generalized functionals. In this paper, we define integrals of Bernoulli generalized functionals with respect to a spectral measure (projection operator-valued measure) in the framework of S⊂L2⊂S∗, and examine their fundamental properties. New notions are introduced, several results are obtained and

In this paper, we consider two-stage least squares (2SLS) and simple instrumental variable (IV) type estimation of dynamic panel data models with both individual-specific effects and heterogeneous time trend when both N and T tend to infinity. We consider the forward orthogonal deviations (FOD) proposed by (Hayakawa, et al. Econometric Reviews, 2019. Vol. 38, pp. 1055–1088) and the double first difference

Suppose that risk reserves of an insurance company are governed by a Markov-modulated classical risk model with parameters modulated by a finite-state irreducible Markov chain. The main purpose of this paper is to calculate ultimate ruin probability that ruin time, the first time when risk reserve is negative, is finite. We apply Banach contraction principle, q-scale functions and Markov property to

This paper contributes to the current discussion on longevity by investigating the long-term dynamics of life expectancy, and lifespan variation. The analysis provides the expectiles of the life expectancy distribution, relating them to the values of lifespan variation measured by Keyfitz’s index. This allows us to study both the location and the spread of the life expectancy over time in light of

ABSTRACT Three level control charts are used to monitor processes, where the quality of products is characterized by classifying the product characteristic into three discrete levels. Recent studies have approved the advantages of using adaptive schemes rather than static one in monitoring such processes. In this paper, we develop adaptive control charts for monitoring three level products from an