Function‐on‐function linear regression is an essential tool in characterizing the linear relationship between a functional response and a functional predictor. However, most of the estimation methods for this model are based on the least‐squares procedure, which is sensitive to atypical observations. In this paper, we present a robust method for the function‐on‐function linear model using M‐estimation

Network data are becoming increasingly available, and so there is a need to develop a suitable methodology for statistical analysis. Networks can be represented as graph Laplacian matrices, which are a type of manifold‐valued data. Our main objective is to estimate a regression curve from a sample of graph Laplacian matrices conditional on a set of Euclidean covariates, for example, in dynamic networks

We propose a constrained minimum method for converting a hypothesis test into a model selection criterion that pursues consistency and sparsity of the selected model explicitly. The method achieves consistency by letting the significance level of the test go to zero at a certain speed depending on the sample size. It maximizes the sparsity by choosing the most sparse model among models not rejected

Sliced uniform designs are useful for generating experimental data with batch structures. In this paper, we employ the discrete discrepancy as the measure of uniformity to constructing sliced uniform designs. The construction method is based on an important class of combinatorial configurations, namely resolvable balanced incomplete block designs, hence the construction method does not require any

Quantile regression estimate gives more complete information about the response distribution but is more costly to compute than mean regression. When the dimension is large, a ridge penalty is conventionally used to stabilize the estimate which achieves better bias‐variance trade‐off. We investigate a random projection approach to ease the computational burden and establish its statistical properties

This paper derives a criterion for deciding conditional independence that is consistent with small‐sample corrections of Akaike's Information Criterion, but is easier to apply in such problems as selecting variables in Canonical Correlation Analysis and selecting graphical models. The criterion reduces to mutual information when the assumed distribution equals the true distribution, hence it is called

In binary classification, class imbalance is undesirable in that it may worsen the performance of a classifier. One of the remedies to handle this problem is rebalancing with the optimal rate. Theoretical derivation of the rate is not usually considered and often empirically detected, because it is complex and depends on the classifier. To simplify this, we used a linear discriminant classifier, deriving

Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance function, and maximum likelihood (ML) methods can be used to estimate these parameters from data. ML methods, however, are computationally demanding. For example,

We pursue the problem of modeling and analyzing latent space dynamics in collections of networks. Towards this end, we pose and study latent space generative models for signed networks that are amenable to inference via spectral methods. Permitting signs, rather than restricting to unsigned networks, enables richer latent space structure and permissible dynamic mechanisms that can be provably inferred

Determination of optimal individual treatment rules (ITR) is a rapidly growing area in precision medicine; various parametric and non‐parametric methods have been proposed. Existing methods, however, focus on the mean outcome and thus are sensitive to outliers, skewed and heavy‐tailed outcome distributions. In this paper, we propose an optimal ITR estimation framework using a weighted classifier with

Many applications of regression study the predictors with complex forms such as tensors. Besides low dimensional assumption, the effects of predictors with a tensor structure typically show clustered or smooth phenomena in the sense that adjacent elements have a similar effect on the response. To simultaneously incorporate the low‐rank and smoothness in tensor regression, we generalize the CANDECOMP/PARAFAC

When the null hypothesis constrains parameters to the boundary of the parameter space, the asymptotic null distribution of the composite likelihood ratio statistic is often a mixture of weighted chi‐squared distributions. The mixing weights depend on the true unknown parameter and can be very difficult to calculate, except in a few special cases. We propose a Monte Carlo algorithm to estimate the mixing

Laplace approximations are commonly used to approximate high‐dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we provide a new result on the size of the error in first‐ and higher‐order Laplace approximations, in terms of the rate of growth of information about each of the integrated

Delayed rewards problem in contextual bandits has been of interest in various practical settings. We study randomized allocation strategies and provide an understanding on how the exploration–exploitation trade‐off is affected by delays in observing the rewards. In randomized strategies, the extent of exploration–exploitation is controlled by a user‐determined exploration probability sequence. In the

We propose a generalized non‐linear state‐space model for count‐valued time series of COVID‐19 fatalities. To capture the dynamic changes in daily COVID‐19 death counts, we specify a latent state process that involves second‐order differencing and an AR(1)‐ARCH(1) model. These modelling choices are motivated by the application and validated by model assessment. We consider and fit a progression of

Clustering with Bregman divergence has been used in literature to unify centroid‐based parametric clustering approaches and to allow the detection of nonspherical clusters within the data. Although empirically useful, the large sample theoretical aspects of Bregman clustering techniques remain largely unexplored. In this paper, we attempt to bridge the gap between the theory and practice of centroid‐based

Multi‐layer networks are often used to represent multiple types of relationships between nodes in network studies. In this paper, we investigate the community detection problem in multi‐layer networks. Specifically, we consider the multi‐layer stochastic block model (MLSBM), which assumes that the community memberships are shared across all network layers, while other model parameters can be different

We propose Dirichlet process mixture (DPM) models for prediction and cluster‐wise variable selection, based on two choices of shrinkage baseline prior distributions for the linear regression coefficients, namely, the Horseshoe prior and the Normal‐Gamma prior. We show in a simulation study that each of the two proposed DPM models tends to outperform the standard DPM model based on the non‐shrinkage

We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject‐specific covariates available as predictors. The outcomes are not well‐characterized by simple parametric models, so we use a

We study a variant of user‐item recommendation where each item has a set of attributes, such as tags on an image, user reactions to a post or foods in a meal. We focus on the latter example, with the goal of building a meal recommender for a diet tracking app. Meal recommendation is challenging: (i) each item (meal) is rarely logged by more than a handful of users, (ii) the database of attributes (foods)

In this article, we revisit the problem of how to construct better nonparametric confidence intervals for the conditional quantile function from an optimization perspective. We apply the fully data‐driven bias correction procedure based on local polynomial smoothing to estimate the conditional quantile. To account for the effect of the estimated bias, we apply an asymptotic framework that the ratio

Quantile regression has emerged as an important analytical alternative to the classical mean regression model. However, the analysis could be complicated by the presence of censored measurements due to a detection limit of equipment in combination with unavoidable missing values arising when, for instance, a researcher is simply unable to collect an observation. Another complication arises when measures

More than 720,000 patients with end‐stage renal disease in the United States require life‐sustaining dialysis treatment. In this population of typically older patients with a high morbidity burden, hospitalization is frequent at a rate of about twice per patient‐year. Aside from frequent hospitalizations, which is a major source of death risk, overall mortality in dialysis patients is higher than other

A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the Lp‐norm of the difference between an empirical distribution function and its least concave majorant. It is shown here that the uniform distribution is least favorable for such a test, in the sense that the limiting distribution of the statistic obtained under

In this study, we propose a design for a control chart for the normal distribution using a modified double sampling scheme. The probability of in control, out of control, the average run length (ARL), and the standard deviation of run length (SDRL) of the proposed control chart is derived. The proposed control chart using the modified double sampling scheme is found to be more efficient in detecting

Finite mixture models can be interpreted as a model representing heterogeneous subpopulations within the whole population. However, more care is needed when associating a mixture component with a cluster, because a mixture model may fit more components than the number of clusters. Modal merging via the mean shift algorithm can help identify such multicomponent clusters. So far, most of the related

In this paper, we propose to use sufficient dimension reduction (SDR) in conjunction with nonparametric techniques to estimate the average treatment effect on the treated (ATT), a parameter of common interest in causal inference. The proposed method is applicable under a general low‐dimensional structure in the data, and avoids both the risk of model misspecification and the “curse of dimensionality

We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable data set. The classifier is described by a non‐linear ReLU model and the objective function adopts the exponential loss function. We first characterize the landscape of the loss function and show that there can exist spurious asymptotic local minima besides asymptotic global minima

The Hilbert–Schmidt independence criterion (HSIC) and its d‐variable extension dHSIC are measures of (joint) dependence between random variables. While combining these statistics with a permutation test has become a popular method of testing the null hypothesis of (joint) independence, it had thus far not been proved that this results in a consistent test. In this work, we provide a simple proof that

We propose a multistep screening procedure (MuSP) for the recovery of sparse linear models in high‐dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations. Specifically, in each iteration, an adaptive lasso regression with a small penalty is fit within the reduced feature space obtained from the previous step, rendering

No abstract is available for this article.

This paper considers the problem of detecting the common gradual changepoint in panel data. Given the situation that each panel/series has the common gradual variance changepoint along with a smoothly functional mean, our focus is on improving the changepoint location estimation accuracy assuming a prior that a single change has occurred. We developed an iterative algorithm motivated by the idea of

Quantile regression with a total variation penalty was previously proposed due to its computational expediency as well as its local adaptiveness. However, the convergence rate of the method in this setting has been not rigorously established. In this short communication, we establish the convergence rate of Op(n−1/3) for the penalized estimator which is the same as in penalized least squares regression

In this paper, we approximate the link and variance functions of the natural exponential family generated by the distribution of the class of time‐changed Lévy processes by the first‐exit time of the inverse Gaussian subordinator. These results leads us to get an approximation for the quasi‐deviance function.

In this article, we explore a nonparametric approach to proportional odds regression with ordinal responses. The setting fits in the general framework of penalized likelihood non‐Gaussian regression as developed earlier in the smoothing spline ANOVA literature. Existing results in the general setting are readily applied or adapted, covering asymptotic convergence, computation, smoothing parameter selection

Case‐crossover design is a popular construction for analyzing the impact of a transient effect, such as ambient pollution levels, on an acute outcome, such as an asthma exacerbation. Case‐crossover design avoids the need to model individual, time‐varying risk factors for cases by using cases as their own ‘controls’, chosen to be time periods for which individual risk factors can be assumed constant

Polycrystalline materials, such as metals, are composed of heterogeneously oriented crystals. Observed crystal orientations are modelled as a sample from an orientation distribution function (ODF), which determines a variety of material properties and is therefore of great interest to practitioners. Observations consist of quaternions, four‐dimensional unit vectors reflecting both orientation and rotation

The generalization error is the difference between the expected risk and the empirical risk of a learning algorithm. This generalization error can be upper bounded by the Rademacher complexity of the underlying hypothesis class with high probability. This paper studies the function class of Lp, q weight normalized deep neural networks. We present a general framework for norm‐based capacity control

High‐dimensional classification have had challenges mainly due to the singularity issue of the sample covariance matrix. In this work, we propose a different approach to get a more reliable sample covariance matrix by adjusting the estimated eigenvalues. This procedure also brings us a non‐singular matrix as a by‐product. We improve the optimization procedure to obtain a linear classifier by incorporating

Standard supervised learning procedures are validated against a test set that is assumed to have come from the same distribution as the training data. However, in many problems, the test data may have come from a different distribution. We consider the case of having many labeled observations from one distribution, P1, and wanting to make predictions at unlabeled points that come from P2. We combine

In this article, a weighted empirical likelihood technique for constructing the empirical likelihood confidence regions is applied to study the heteroscedastic varying coefficient partially nonlinear models with missing response data. We first give the estimator of the error variance based on the Nadaraya‐Watson kernel estimation method. Then a weighted empirical log‐likelihood ratio of the unknown

We develop a new semiparametric Bayes instrumental variables estimation method. We employ the form of the regression function of the first‐stage equation, and the disturbances are modeled nonparametrically to achieve better predictive power of the endogenous variables, whereas we use parametric formulation in the second‐stage equation, which is of interest in inference. Our simulation studies show

There has been much attention in recent years to the problem of detecting mean changes in a piecewise constant time series. Often, methods assume that the noise can be taken to be independent, identically distributed (IID), which in practice may not be a reasonable assumption. There is comparatively little work studying the problem of mean changepoint detection in time series with nontrivial autocovariance

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low‐rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown

The stochastic block model (SBM) is widely employed as a canonical model for network community detection. Recovering community labels under SBM is not a trivial task, since its theoretical optimization problem is NP‐hard. To solve this problem, numerous statistical methods have been developed in the literature, most of which are, however, not applicable to large‐scale networks. To overcome this limitation

In partnership with community leaders of Durham, North Carolina, the Duke World Food Policy Center is creating a Durham Food Justice Plan (DFJP) for envisioning an equitable food system. The Food Justice plan serves to incorporate Durham's local food history in terms of combating historical and present injustices in the food system. We propose creating an integrative, interactive visual for DFJP to

A model to classify the lifespan of Drosophila, the fruit fly, into short‐ and long‐lived categories based on a sleep characteristic, extracted from activity data, is developed using a two‐stage process. Stage 1 models the per‐minute activity counts of each fly using a zero‐inflated autoregressive conditional Poisson model. These probabilities are allowed to vary hourly, reflecting the circadian and

We propose the notion of sub‐Weibull distributions, which are characterized by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalizes the sub‐Gaussian and sub‐Exponential families to potentially heavier tailed distributions. Sub‐Weibull distributions are parameterized by a positive tail index θ and reduce to sub‐Gaussian distributions for θ =

An individualized treatment rule is often employed to maximize a certain patient‐specific clinical outcome based on his/her clinical or genomic characteristics as well as heterogeneous response to treatments. Although developing such a rule is conceptually important to personalized medicine, existing methods such as the partial least squares suffers from the difficulty of indirect maximization of a

In this paper, we study the bias of the least squares (LS) estimation for the stationary first‐order bifurcating autoregressive (BAR(1)) model, which is commonly used to model binary tree‐structured data that appear in many applications, most famously cell lineage applications. We first show that the LS estimator can have large bias for both small‐ and moderate‐sized samples and that this bias is dependent

JMP is commercial software designed for interactive data analysis and exploration. JMP's high‐level, visual interface makes it an outstanding tool for teaching best practices, methods and model building techniques. JMP is also designed for extensibility, with features that allow the embedding of and deployment to open‐source packages and environments. In this paper, we will explore use cases that illustrate

We propose a new L2‐type goodness‐of‐fit test for the family of beta distributions based on a conditional moment characterization. The asymptotic null distribution is identified, and since it depends on the underlying parameters, a parametric bootstrap procedure is proposed. Consistency against all alternatives that satisfy a convergence criterion is shown, and a Monte Carlo simulation study indicates

The advancement of scientific knowledge increasingly depends on ensuring that data‐driven research is reproducible: that two people with the same data obtain the same results. However, while the necessity of reproducibility is clear, there are significant behavioral and technical challenges that impede its widespread implementation and no clear consensus on standards of what constitutes reproducibility

Microsimulation and synthetic data are often high dimensional, requiring extensive validation and exploration to compare results against certain benchmarks. In both cases, validation is necessary to ensure that the many univariate distributions and multivariate relationships in the new data are similar to the many univariate distributions and multivariate relationships in the underlying data. This

In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA

The R package glmm enables likelihood‐based inference for generalized linear mixed models with a canonical link. No other publicly available software accurately conducts likelihood‐based inference for generalized linear mixed models with crossed random effects. glmm is able to do so by approximating the likelihood function and two derivatives using importance sampling. The importance sampling distribution

Statistical inference provides the protocols for conducting rigorous science, but data plots provide the opportunity to discover the unexpected. These disparate endeavours are bridged by visual inference, where a lineup protocol can be employed for statistical testing. Human observers are needed to assess the lineups, typically using a crowd‐sourcing service. This paper describes a new approach for

k‐nearest neighbors} (k‐NN) method is one of the oldest statistical/machine learning techniques. It is included in virtually every major package, such as caret, parsnp, mlr3 and scikit‐learn. Yet those packages do not go beyond the basics. With today's high‐speed computation capability, k‐NN can be made much more powerful. Here we present directions in which that can be done:

Nonparametric regression is of primary importance in many statistical applications. For the data with censored outcomes, how to construct a confidence band for a regression function is a basic issue but has limited research. We propose a procedure to construct the pointwise and simultaneous confidence bands for a regression function based on a debiased estimator, which is proposed by correcting the

In this paper, we will detail our experiences developing and organizing an annual machine learning competition at Saint Mary's College. We will detail our process of collecting data for the competition as well as the logistical challenges faced when hosting such an event at a small liberal arts college. We believe that this report will be of interest to colleagues teaching data science at institutions