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Data are heterogeneous when recorded in different time regimes or taken from multiple sources to some degree. Varying-coefficient models or mixture models are suitable for solving this type of problem. On one hand, existing models are quite complicated and computationally cumbersome especially for large-scale data. On the other hand, common effects among different data sources are unknown. Additionally, some existing models are unable to search the non linear relationship between response and covariates. To address these challenges, we aim at estimating common effects about non parametric regression when data are heterogeneous. Our proposed estimation method is based on basis function expansion. Adaptive basis series and fixed basis series are considered, respectively. We exploit maximin aggregation technique to get a simple non linear model, also the common effects, from all possible grouped data. The mean squared error and asymptotic distribution of the estimator are investigated. Simulation studies and real-data analysis are conducted to verify the efficiency of the estimation procedure. Comparing with ordinary least square estimator and averaging ordinary least square estimator, our proposed estimator can reduce the complexity of data sources and is more robust. [ABSTRACT FROM AUTHOR]

A mediation analysis approach is proposed for multiple exposures, multiple mediators, and a continuous scalar outcome under the linear structural equation modeling framework. It assumes that there exist orthogonal components that demonstrate parallel mediation mechanisms on the outcome, and thus is named principal component mediation analysis (PCMA). Likelihood‐based estimators are introduced for simultaneous estimation of the component projections and effect parameters. The asymptotic distribution of the estimators is derived for low‐dimensional data. A bootstrap procedure is introduced for inference. Simulation studies illustrate the superior performance of the proposed approach. Applied to a proteomics‐imaging dataset from the Alzheimer's disease neuroimaging initiative (ADNI), the proposed framework identifies protein deposition – brain atrophy – memory deficit mechanisms consistent with existing knowledge and suggests potential AD pathology by integrating data collected from different modalities. [ABSTRACT FROM AUTHOR]

In the widely used predictive regression model, any possible serial correlation in innovations leads to estimation bias and statistical inference distortions. Hence, it is important to pretest the existence of such serial correlation. Nevertheless, in the presence of embedded endogeneity, which is a common problem in the predictive regression setting, traditional serial correlation tests such as Box–Pierce (BP) and Ljung–Box (LB) tests are found to perform poorly. Motivated by this, we develop a new portmanteau test in this article as a pretest for serial correlation in predictive regression under possible embedded endogeneity. This test is based on the sample splitting idea and the jackknife empirical likelihood method. The asymptotic distribution of the proposed test has been derived, and the Monte Carlo simulations confirm good finite sample performances. As an illustration, we apply our proposed test in pretesting the serial correlation in predictive regression, where financial variables are used to predict the excess return of S&P 500. [ABSTRACT FROM AUTHOR]

Benford's law is a statement about the frequency that each digit arises as the leading digit of numbers in a dataset. It is satisfied by various common integer sequences, such as the Fibonacci numbers, the factorials, and the powers of most integers. In this paper, we prove that integer sequences resulting from a random integral decomposition process (which we model as discrete "stick breaking") subject to a certain congruence stopping condition approach Benford distribution asymptotically. We also show that our requirement on the number of congruence classes defining the congruence stopping condition is necessary for Benford behavior to occur and is a critical point; deviation from that would result in drastically different behavior. [ABSTRACT FROM AUTHOR]

This study investigates the impacts of economic policy uncertainty (EPU), energy consumption (EC), sustainable technological innovation (STI), and quality of governance on green growth (GG). Besides, it examines the moderating effect of STI and governance quality on the association between EPU and GG. It applies a Pooled Mean Group Autoregressive Distributed Lag estimator for 25 emerging economies for periods 1991–2019. For the robustness test, we utilize the asymptotic distribution of the Cross-section Augmented Distributed Lag to control for cross-sectional dependence concerns. We drive two indicators for GG by applying the principal component approach and directional distance function. The findings imply that STI and quality of governance have significant positive impacts on GG. However, EPU and EC adversely impact GG in emerging economies. Besides, quality of governance and STI positively moderate EPU's influence on GG, implying that countries with better quality of governance and promote STI mitigate the detrimental effects of high EPU on GG. Moreover, we run the causality analysis to investigate the causal relationship between target variables and GG. Policy suggestions are proposed based on the results. [ABSTRACT FROM AUTHOR]

For stationary time series with regularly varying marginal distributions, an important problem is to estimate the associated tail index which characterizes the power‐law behavior of the tail distribution. For this, various results have been developed for independent data and certain types of dependent data. In this article, we consider the problem of tail index estimation under a recently proposed notion of serial tail dependence called the tail adversarial stability. Using the technique of adversarial innovation coupling and a martingale approximation scheme, we establish the consistency and central limit theorem of the tail index estimator for a general class of tail dependent time series. Based on the asymptotic normal distribution from the obtained central limit theorem, we further consider an application to cluster a large number of regularly varying time series based on their tail indices by using a robust mixture algorithm. The results are illustrated using numerical examples including Monte Carlo simulations and a real data analysis. [ABSTRACT FROM AUTHOR]

This paper introduces a novel two-sample test for a broad class of orthogonally invariant positive definite symmetric matrix distributions. Our test is the first of its kind, and we derive its asymptotic distribution. To estimate the test power, we use a warp-speed bootstrap method and consider the most common matrix distributions. We provide several real data examples, including the data for main cryptocurrencies and stock data of major US companies. The real data examples demonstrate the applicability of our test in the context closely related to algorithmic trading. The popularity of matrix distributions in many applications and the need for such a test in the literature are reconciled by our findings. [ABSTRACT FROM AUTHOR]

In many studies of human diseases, multiple omics datasets are measured. Typically, these omics datasets are studied one by one with the disease, thus the relationship between omics is overlooked. Modeling the joint part of multiple omics and its association to the outcome disease will provide insights into the complex molecular base of the disease. Several dimension reduction methods which jointly model multiple omics and two-stage approaches that model the omics and outcome in separate steps are available. Holistic one-stage models for both omics and outcome are lacking. In this article, we propose a novel one-stage method that jointly models an outcome variable with omics. We establish the model identifiability and develop EM algorithms to obtain maximum likelihood estimators of the parameters for normally and Bernoulli distributed outcomes. Test statistics are proposed to infer the association between the outcome and omics, and their asymptotic distributions are derived. Extensive simulation studies are conducted to evaluate the proposed model. The method is illustrated by modeling Down syndrome as outcome and methylation and glycomics as omics datasets. Here we show that our model provides more insight by jointly considering methylation and glycomics. [ABSTRACT FROM AUTHOR]

A non parametric estimator of the joint distribution function of a positive bivariate random vector is introduced. The case where one of the two variables is subject to right censoring is considered. To construct the proposed estimator, Poisson distributions are used for smoothing the empirical estimator of Stute (1993). The strong uniform convergence is established. Also, by stating the asymptotic i.i.d. representation, the asymptotic bias, variance, and normality are deduced. The smooth estimator is applied for analyzing survival data from patients with advanced lung cancer. [ABSTRACT FROM AUTHOR]

This article considers the estimation of quantile treatment effects under the assumption of unconfoundedness given quasi-experimental data. We propose a semiparametric single-index method to estimate the propensity score. Our approach overcomes the curse of dimensionality issue of a nonparametric propensity score and can handle a moderately large dimension of covariates. It is more flexible than the parametric propensity score and thereby alleviates the possible model misspecification problem. We derive the asymptotic distribution of the quantile treatment effect estimator that is based on the semiparametric propensity score. We also propose a consistent variance estimator and construct the confidence intervals for the QTE estimator. Monte Carlo simulation results show that the proposed estimator performs well in finite samples and the confidence intervals have adequate coverage rates. We demonstrate the usefulness of our method by applying it to a study of the quantile treatment effects of college education on income. [ABSTRACT FROM AUTHOR]

We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences. (Em+)m=0,∞ (Em-)m=0∞ satisfying a three-term asymptotic formula with the remainder estimate 0(m-1 1n m) when m tends to infinity. Our asymptotic formula can be written so that the third term is given by an explicit oscillatory integral and an explicit remainder estimate. [ABSTRACT FROM AUTHOR]

This paper presents the derivation of an expression for computing the exact distribution of the change-point maximum likelihood estimate (MLE) in the context of a mean shift within a sequence of time-ordered independent multivariate normal random vectors. The study assumes knowledge of nuisance parameters, including the covariance matrix and the magnitude of the mean change. The derived distribution is then utilized as an approximation for the change-point estimate distribution when the magnitude of the mean change is unknown. Its efficiency is evaluated through simulation studies, revealing that the exact distribution outperforms the asymptotic distribution. Notably, even in the absence of a change, the exact distribution maintains its efficiency, a feature not shared by the asymptotic distribution. To demonstrate the practical application of the developed methodology, the monthly averages of water discharges from the Nacetinsky creek in Germany are analyzed, and a comparison with the analysis conducted using the asymptotic distribution is presented. [ABSTRACT FROM AUTHOR]

In recent years, significant advancements have been made in the field of identifying financial asset price bubbles, particularly through the development of time‐series unit‐root tests featuring fractionally integrated errors and panel unit‐root tests. This study introduces an innovative approach for assessing the sign of the persistence parameter (α) within a panel fractional Ornstein‐Uhlenbeck process, based on the least squares estimator of α. This method incorporates three distinct test statistics based on the Hurst parameter (H), which can take values in the range of (1/2,1), be equal to 1/2, or fall within the interval of (0,1/2). The null hypothesis corresponds to α=0. Based on a panel of continuous records of observations, the null asymptotic distributions are obtained when the time span (T) is fixed and the number of cross sections (N) goes to infinity. The power function of the tests is obtained under the local alternative where α is close to zero in the order of 1/(TN). This alternative covers the departure from the unit root hypothesis from the explosive side, enabling the calculation of lower power in bubble tests. The hypothesis testing problem and the local power function are also considered when a panel of discrete‐sampled observations is available under a sequential limit, that is, the sampling interval shrinks to zero followed by the N goes to infinity. [ABSTRACT FROM AUTHOR]

In this article, the primary aim is to introduce a new flexible family of circular distributions, namely the wrapped Linnik family which possesses the flexibility to model the inflection points and tail behavior often better than the existing popular flexible symmetric unimodal circular models. The second objective of this article is to obtain a simple and efficient estimator of the index parameter α of symmetric Linnik distribution exploiting the fact that it is preserved in the wrapped Linnik family. This is an interesting problem for highly volatile financial data as has been studied by several authors. Our final aim is to analytically derive the asymptotic distribution of our estimator, not available for other estimator. This estimator is shown to outperform the existing estimator over the range of the parameter for all sample sizes. The proposed wrapped Linnik distribution is applied to some real-life data. A measure of goodness of fit proposed in one of the authors' previous works is used for the above family of distributions. The wrapped Linnik family was found to be preferable as it gave better fit to those data sets rather than the popular von-Mises distribution or the wrapped stable family of distributions. [ABSTRACT FROM AUTHOR]

Let { A n } n be a sequence of square matrices such that size (A n) = d n → ∞ as n → ∞. We say that { A n } n has an asymptotic spectral distribution described by a Lebesgue measurable function f : D ⊂ R k → C if, for every continuous function F : C → C with bounded support, lim n → ∞ ⁡ 1 d n ∑ i = 1 d n F (λ i (A n)) = 1 μ k (D) ∫ D F (f (x)) d x , where μ k is the Lebesgue measure in R k and λ 1 (A n) , ... , λ d n (A n) are the eigenvalues of A n. In the last decades, the asymptotic spectral distribution of increasing size matrices has become a subject of investigation by several authors. Special attention has been devoted to matrices A n arising from the discretization of differential equations, whose size d n diverges to ∞ along with the mesh-fineness parameter n. However, despite the popularity that the topic has reached nowadays, the role of the so-called test functions F appearing in the above limit relation has been inexplicably neglected so far. In particular, a natural question such as "Which is the largest set of test functions F for which the above limit relation is satisfied?" is still unanswered. In the present paper, we provide a definitive answer to this question by identifying the largest set of test functions F for which the above limit relation is satisfied. We also present some applications of this result to the analysis of spectral clustering, including new asymptotic estimates on the number of outliers. A special attention is devoted to the so-called "inner outliers" of Hermitian block Toeplitz matrices. We conclude the paper with an interpretation of the main result in the context of the vague convergence of probability measures. [ABSTRACT FROM AUTHOR]

AbstractWe propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

AbstractWe, in this article, focus on functional partially linear quantile regression, where the observations are missing at random, which allows the response or covariates or response and covariates simultaneously missing. Estimation of the unknown function is done based on reproducing kernel method. Under suitable assumptions, we discuss consistency with rates of the estimators, and establish asymptotic normality of the estimator for the parameter. At the same time, we study hypothesis test of the parameter, and prove asymptotic distributions of restricted estimators of the parameter and test statistic under null hypothesis and local alternative hypothesis, respectively. Also, we study variable selection of the linear part of the model. By simulation and real data, finite sample performance of the proposed methods is analyzed. [ABSTRACT FROM AUTHOR]

Motivated by a certain type of infinite-patch metapopulation model, this current work proposes a new mixed INAR(p) model (SDMINAR(p)) based on binomial thinning and negative binomial thinning operators, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the population at time { t − 1 , t − 2 , ... , t − p } are large. Strict stationarity ergodicity property is proved. Conditional maximum likelihood estimation are adopted to estimate the model parameters. Asymptotic normality property of the estimators are displayed. The performances of the estimators are investigated in simulation, which manifests that the maximum likelihood estimation performs better when sample size increases. Finally, the practical relevance of the model is demonstrated by the COVID-19 data of suspected cases and severe cases imported from outside China with a comparison with relevant models that exist so far in the literature. [ABSTRACT FROM AUTHOR]

The ERW model was introduced twenty years ago to study memory effects in a one-dimensional discrete-time random walk with a complete memory of its past throughout a parameter p between zero and one. Several variations of the ERW model have recently been introduced. In this work, we investigate the asymptotic normality of the ERW model with a random step size and gradually increasing memory and delays. In particular, we extend some recent results in this subject. [ABSTRACT FROM AUTHOR]

Summary: The dynamic ranking, due to its increasing importance in many applications, is becoming crucial, especially with the collection of voluminous time‐dependent data. One such application is sports statistics, where dynamic ranking aids in forecasting the performance of competitive teams, drawing on historical and current data. Despite its usefulness, predicting and inferring rankings pose challenges in environments necessitating time‐dependent modelling. This paper introduces a spectral ranker called Kernel Rank Centrality, designed to rank items based on pairwise comparisons over time. The ranker operates via kernel smoothing in the Bradley–Terry model, utilising a Markov chain model. Unlike the maximum likelihood approach, the spectral ranker is nonparametric, demands fewer model assumptions and computations and allows for real‐time ranking. We establish the asymptotic distribution of the ranker by applying an innovative group inverse technique, resulting in a uniform and precise entrywise expansion. This result allows us to devise a new inferential method for predictive inference, previously unavailable in existing approaches. Our numerical examples showcase the ranker's utility in predictive accuracy and constructing an uncertainty measure for prediction, leveraging data from the National Basketball Association (NBA). The results underscore our method's potential compared with the gold standard in sports, the Arpad Elo rating system. [ABSTRACT FROM AUTHOR]

This article investigates a variable selection method in semi-functional partially linear regression (SFPLR) models for strong α -mixing functional time series data. We construct penalized least squares estimators for unknown parameters and unknown link functions in our models. Under some regularity assumptions, we establish the asymptotic convergence rate and asymptotic distribution for the proposed estimators. Furthermore, we make a comparison of our variable selection method with the oracle method without variable selection in simulation studies and an electricity consumption data analysis. Simulation experiments and real data analysis results indicate that the variable selection method performs well at extracting the primary information and reducing dimensionality. [ABSTRACT FROM AUTHOR]

In capture–recapture experiments, the presence of overdispersion and heterogeneity necessitates the use of the negative binomial regression model for inferring population sizes. However, within this model, existing methods based on likelihood and ratio regression for estimating the dispersion parameter often face boundary and nonidentifiability issues. These problems can result in nonsensically large point estimates and unbounded upper limits of confidence intervals for the population size. We present a penalized empirical likelihood technique for solving these two problems by imposing a half-normal prior on the population size. Based on the proposed approach, a maximum penalized empirical likelihood estimator with asymptotic normality and a penalized empirical likelihood ratio statistic with asymptotic chi-square distribution are derived. To improve numerical performance, we present an effective expectation-maximization (EM) algorithm. In the M-step, optimization for the model parameters could be achieved by fitting a standard negative binomial regression model via the R basic function glm.nb(). This approach ensures the convergence and reliability of the numerical algorithm. Using simulations, we analyze several synthetic datasets to illustrate three advantages of our methods in finite-sample cases: complete mitigation of the boundary problem, more efficient maximum penalized empirical likelihood estimates, and more precise penalized empirical likelihood ratio interval estimates compared to the estimates obtained without penalty. These advantages are further demonstrated in a case study estimating the abundance of black bears (Ursus americanus) at the U.S. Army's Fort Drum Military Installation in northern New York. [ABSTRACT FROM AUTHOR]

Subgraph counts, in particular the number of occurrences of small shapes such as triangles, characterize properties of random networks. As a result, they have seen wide use as network summary statistics. Subgraphs are typically counted globally, making existing approaches unable to describe vertex-specific characteristics. In contrast, rooted subgraphs focus on vertex neighbourhoods, and are fundamental descriptors of local network properties. We derive the asymptotic joint distribution of rooted subgraph counts in inhomogeneous random graphs, a model that generalizes most statistical network models. This result enables a shift in the statistical analysis of graphs, from estimating network summaries to estimating models linking local network structure and vertex-specific covariates. As an example, we consider a school friendship network and show that gender and race are significant predictors of local friendship patterns. [ABSTRACT FROM AUTHOR]

Testing independence between high-dimensional random vectors is fundamentally different from testing independence between univariate random variables. Taking the projection correlation as an example, it suffers from at least three problems. First, it has a high computational complexity of O { n 3 (p + q) } ⁠ , where n , p and q are the sample size and dimensions of the random vectors; this limits its usefulness substantially when n is extremely large. Second, the asymptotic null distribution of the projection correlation test is rarely tractable; therefore, random permutations are often suggested as a means of approximating the asymptotic null distribution, which further increases the complexity of implementing independence tests. Third, the power performance of the projection correlation test deteriorates in high dimensions. To address these issues, the projection correlation is improved by using a modified weight function, which reduces the complexity to O { n 2 (p + q) } ⁠. We estimate the improved projection correlation with U -statistic theory. Importantly, its asymptotic null distribution is standard normal, thanks to the high dimesnionality of the random vectors. This expedites the implementation of independence tests substantially. To enhance the power performance in high dimensions, we propose incorporating a cross-validation procedure with feature screening into the projection correlation test. The implementation efficacy and power enhancement are confirmed through extensive numerical studies. [ABSTRACT FROM AUTHOR]

The equilibrium of two rigidly connected elastic half-planes made of different materials, with a thin rigid inclusion placed on the border of their separation, is considered. One side of the inclusion is connected to one of the half-planes, and the other is exfoliated with the formation of a crack. The frictional contact of the crack faces near its tips is taken into account. Using the Wiener–Hopf method, the solution of the system of integral equations of the problem is obtained in a closed form. The dimensions of the areas of contact of the crack faces, stress distributions in the areas of contact, at the boundary of the separation of the half-planes outside the crack and at the junction of the inclusion with the half-plane, asymptotic distributions of stresses and displacements in the vicinity of the end of the inclusion were found. [ABSTRACT FROM AUTHOR]

In this paper, we establish Abelian and Tauberian results that characterize the quasiasymptotic behavior of Lizorkin distributions via the asymptotic behavior of their shearlet transform. [ABSTRACT FROM AUTHOR]

The primary aim of this paper is to investigate the asymptotic distribution of the zeros of certain classes of hypergeometric $ {}_{q+1}F_{q} $ q + 1 F q polynomials. We employ classical analytical techniques, including Watson's lemma and the method of steepest descent, to understand the asymptotic behavior of these polynomials: $$\begin{align*} & _{q+1}F_{q}\left(-n,kn+\alpha,\ldots, kn+\alpha+\frac{q-1}{q};kn+\beta,\ldots,kn+\beta+\frac{q-1}{q};z\right)\\ &\quad (n\rightarrow \infty), \end{align*} $$ q + 1 F q (− n , kn + α , ... , kn + α + q − 1 q ; kn + β , ... , kn + β + q − 1 q ; z) (n → ∞) , where n is a nonnegative integer, q is a positive integer and the constant parameters α and β are constrained by $ \alpha { α < β. By applying the general results established in this paper, we generate numerical evidence and graphical illustrations using Mathematica to show the clustering of zeros on certain curves. [ABSTRACT FROM AUTHOR]

We propose a new threshold selection method for nonparametric estimation of the extremal index of stochastic processes. The discrepancy method was proposed as a data-driven smoothing tool for estimation of a probability density function. Now it is modified to select a threshold parameter of an extremal index estimator. A modification of the discrepancy statistic based on the Cramér–von Mises–Smirnov statistic $ \omega ^2 $ ω 2 is calculated by k largest order statistics instead of an entire sample. Its asymptotic distribution as $ k\to \infty $ k → ∞ is proved to coincide with the $ \omega ^2 $ ω 2 -distribution. Its quantiles are used as discrepancy values. The convergence rate of an extremal index estimate coupled with the discrepancy method is derived. The discrepancy method is used as an automatic threshold selection for the intervals and K-gaps estimators. It may be applied to other estimators of the extremal index. The performance of our method is evaluated by simulated and real data examples. [ABSTRACT FROM AUTHOR]

Modern data are often collected in a matrix form. In this paper, we consider modelling the varying coefficient regression with matrix valued covariate X and scalar index variable U. The proposed model simultaneously makes principal component analysis for both the row and column dimensions of the matrix objects, maintaining the matrix structure while achieving substantial dimension reduction. We develop an iterative estimation method for the involved principal parameters and nonparametric functions. Under regularity conditions, the asymptotic distributions of the estimators are derived. In addition, by incorporating the estimation with the adaptive group Lasso and the group SCAD penalties, variables of X in entire rows or columns are selected. The proximal gradient algorithm is further utilised to solve the regularised optimisation problems. The asymptotic properties of the penalised estimators are also studied. Our model and estimation methods are demonstrated by simulated experiments. Real applications to the primary biliary cirrhosis (PBC) data reveal that the effects of the blood measurements to the survival time vary with levels of age. [ABSTRACT FROM AUTHOR]

Single-index model is one of the most popular semiparametric models in applied econometrics. Estimation of the derivative function is often of crucial importance, as studying "marginal effects" serves as a cornerstone of microeconomics. A prerequisite for the successful application of nonparametric/semiparametric kernel estimation methods is to select smoothing parameters properly to balance the estimation squared bias and variance. Henderson et al. (2015) propose a novel method for selecting the smoothing parameters optimally for derivative function estimation. However, their method suffers from the "curse of diemnsionality" problem in a multivariate nonparametric regression model. In this article, we extend the work of Henderson et al. (2015) to estimation of the derivative function of a single-index model. Specifically, we propose a data-driven method to select smoothing parameters optimally for single-index model derivative function estimation. We also derive the asymptotic distribution of the resulting local linear estimator of the derivative function. Both simulations and empirical applications show that the proposed method works well in practice. [ABSTRACT FROM AUTHOR]

We propose a new functional additive hazards model to investigate the potential effects of functional and scalar predictors on mortality risks, and develop a penalized least squares estimation method for model parameters based on a pseudoscore estimating equation. A reproducing kernel Hilbert space approach is used to establish the consistency, convergence rate, and joint asymptotic distribution of the resulting estimators for finite‐dimensional and infinite‐dimensional parameters. Our simulation studies demonstrate that the proposed estimation procedure performs well. For illustration, we apply the proposed method to the Medical Information Mart for Intensive Care III dataset. [ABSTRACT FROM AUTHOR]

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators. [ABSTRACT FROM AUTHOR]

In this article, we show a limit result for the reliability function of a system—that is, the probability that the whole system is still operational after a certain given time—when the number of components of the system grows to infinity. More specifically, we consider a sequence of mixed coherent systems whose components are homogeneous and non‐repairable, with failure‐times governed by a Lévy‐Frailty Marshall–Olkin (LFMO) distribution—a distribution that allows simultaneous component failures. We show that under integrability conditions the reliability function converges to the probability of a first‐passage time of a Lévy subordinator process. To the best of our knowledge, this is the first result to tackle the asymptotic behavior of the reliability function as the number of components of the system grows. To illustrate our approach, we give an example of a parametric family of reliability functions where the system failure time converges in distribution to an exponential random variable, and give computational experiments testing convergence. [ABSTRACT FROM AUTHOR]

We offer an alternative proof, using the Stein-Chen method, of Bollobás' theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices. [ABSTRACT FROM AUTHOR]

In this paper we study the drift parameter estimation for reflected stochastic linear differential equations of a large signal. We discuss the consistency and asymptotic distributions of trajectory fitting estimator (TFE). [ABSTRACT FROM AUTHOR]

The network autoregressive model is a super high-dimensional time series model that can fully explain social relationships. This model can fully reflect the complex relationships in reality. Therefore, it plays a vital role in detecting the inflection point problem of this network autoregressive model for economics and finance. In this paper, we proposed the change-point problem of detecting network autoregressive models using empirical likelihood statistics based on the expected error term of the switching rule being 0, using the empirical likelihood method. Moreover, the asymptotic null distribution of the proposed empirical likelihood statistic was investigated. Simulation studies based on different settings were considered, and the results showed that the power of test statistics is significant. In the end, the Chinese stock market was investigated to demonstrate the significance of the proposed method. [ABSTRACT FROM AUTHOR]

Local polynomial fitting exhibits numerous compelling statistical properties, particularly within the intricate realm of multivariate analysis. However, as functional data analysis gains prominence as a dynamic and pertinent field in data science, the exigency arises for the formulation of a specialized theory tailored to local polynomial fitting. We explored the intricate task of estimating the regression function operator and its partial derivatives for stationary mixing random processes, denoted as (Yi, Xi), using local higher-order polynomial fitting. Our key contributions include establishing the joint asymptotic normality of the estimates for both the regression function and its partial derivatives, specifically in the context of strongly mixing processes. Additionally, we provide explicit expressions for the bias and the variance-covariance matrix of the asymptotic distribution. Demonstrating uniform strong consistency over compact subsets, along with delineating the rates of convergence, we substantiated these results for both the regression function and its partial derivatives. Importantly, these findings rooted in reasonably broad conditions that underpinned the underlying models. To demonstrate practical applicability, we leveraged our results to compute pointwise confidence regions. Finally, we extended our ideas to the nonparametric conditional distribution, and obtained its limiting distribution. [ABSTRACT FROM AUTHOR]

In this paper, we propose a correlation‐based test for the evaluation of two competing forecasts. Under the null hypothesis of equal correlations with the target variable, we derive the asymptotic distribution of our test using the Delta method. This null hypothesis is not necessarily equivalent to the null of equal Mean Squared Prediction Errors (MSPE). Specifically, it might be the case that the forecast displaying the lowest MSPE also exhibits the lowest correlation with the target variable: this is known as "The MSPE paradox." In this sense, our approach should be seen as complementary to traditional tests of equality in MSPE. Monte Carlo simulations indicate that our test has good size and power. Finally, we illustrate the use of our test in an empirical exercise in which we compare two different inflation forecasts for a sample of OECD economies. We find more rejections of the null of equal correlations than rejections of the null of equality in MSPE. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a change-point test for functional time series that uses the full functional information and is less sensitive to outliers compared to the classical CUSUM test. For this aim, the Wilcoxon two-sample test is generalized to functional data. To obtain the asymptotic distribution of the test statistic, we prove a limit theorem for a process of U-statistics with values in a Hilbert space under weak dependence. Critical values can be obtained by a newly developed version of the dependent wild bootstrap for non-degenerate 2-sample U-statistics. [ABSTRACT FROM AUTHOR]

We derive an equation system for finding Maximum Likelihood Estimators (MLEs) for the parameters of a p-dimensional t-distribution with ν degrees of freedom, t p , ν , and use the MLEs for testing covariance structures for the t p , ν -distributed population. The likelihood ratio test (LRT), Rao score test (RST) and Wald test (WT) statistics are derived under the general null-hypothesis H 0 : Σ = Σ 0 , using a matrix derivative technique. Here the p × p -matrix Σ is a dispersion/scale parameter. Convergence to the asymptotic chi-square distribution under the null hypothesis is examined in extensive simulation experiments. Also the convergence to the chi-square distribution is studied empirically in the situation when the MLEs of a t p , ν -distribution are changed to the corresponding estimators for a normal population. Type I errors and the power of the tests are also examined by simulation. In the simulation study the RST behaved more adequately than all remaining statistics in the situation when the dimensionality p was growing. [ABSTRACT FROM AUTHOR]

Various goodness-of-fit tests are designed based on the so-called information matrix equivalence: if the assumed model is correctly specified, two information matrices that are derived from the likelihood function are equivalent. In the literature, this principle has been established for the likelihood function with fully observed data, but it has not been verified under the likelihood for censored data. In this manuscript, we prove the information matrix equivalence in the framework of semiparametric copula models for multivariate censored survival data. Based on this equivalence, we propose an information ratio (IR) test for the specification of the copula function. The IR statistic is constructed via comparing consistent estimates of the two information matrices. We derive the asymptotic distribution of the IR statistic and propose a parametric bootstrap procedure for the finite-sample P-value calculation. The performance of the IR test is investigated via a simulation study and a real data example. [ABSTRACT FROM AUTHOR]

We characterize absolutely continuous symmetric copulas with square integrable densities in this paper. This characterization is used to create new copula families, that are perturbations of the independence copula. The full study of mixing properties of Markov chains generated by these copula families is conducted. An extension that includes the Farlie–Gumbel–Morgenstern family of copulas is proposed. We propose some examples of copulas that generate non-mixing Markov chains, but whose convex combinations generate ψ -mixing Markov chains. Some general results on ψ -mixing are given. The Spearman's correlation ρ S and Kendall's τ are provided for the created copula families. Some general remarks are provided for ρ S and τ . A central limit theorem is provided for parameter estimators in one example. A simulation study is conducted to support derived asymptotic distributions for some examples. [ABSTRACT FROM AUTHOR]

Recent developments in the spectral theory of Bayesian Networks has led to a need for a developed theory of estimation and inference on the eigenvalues of the normalized precision matrix, Ω. In this paper, working under conditions where n → ∞ and p remains fixed, we provide multivariate normal asymptotic distributions of the sample eigenvalues of Ω under general conditions and under normal populations, a formula for second-order bias correction of these sample eigenvalues, and a Stein-type shrinkage estimator of the eigenvalues. Numerical simulations are performed which demonstrate under what generative conditions each estimation technique is most effective. When the largest eigenvalue of Ω is small the simulations show that the second order bias-corrected eigenvalue was considerably less biased than the sample eigenvalue, whereas the smallest eigenvalue was estimated with less bias using either the sample eigenvalue or the proposed shrinkage method. [ABSTRACT FROM AUTHOR]

Inference after model selection is a very important problem. This article derives the asymptotic distribution of some model selection estimators for autoregressive moving average time series models. Under strong regularity conditions, the model selection estimators are asymptotically normal, but generally the asymptotic distribution is a non normal mixture distribution. Hence bootstrap confidence regions that can handle this complicated distribution were used for hypothesis testing. A bootstrap technique to eliminate selection bias is to fit the model selection estimator β ̂ M S ∗ to a bootstrap sample to find a submodel, then draw another bootstrap sample, and fit the same submodel to get the bootstrap estimator β ̂ M I X ∗ . [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic distribution of coefficients of general L -functions over arithmetic progressions without the Ramanujan conjecture. As an application, we consider the high mean of Fourier coefficients of holomorphic forms or Maass forms for Γ = SL (2 , Z) over arithmetic progressions, and improve the results of Jiang and Lü [10]. Our new results remove the restriction to prime module and improve the interval length of module q. [ABSTRACT FROM AUTHOR]

Differential privacy is a foundational concept for safeguarding sensitive individual information when releasing data or statistical analysis results. In this study, we concentrate on the protection of privacy in the context of goodness‐of‐fit (GOF) and independence tests, utilizing perturbed contingency tables that adhere to Gaussian differential privacy within the high‐privacy regime, where the degrees of privacy protection increase as the sample size increases. We introduce private test procedures for GOF, independence of two variables and the equality of proportions in paired samples, similar to McNemar's test. For each of these hypothesis testing situations, we propose private test statistics based on the χ2$$ {\chi}^2 $$ statistics and establish their asymptotic null distributions. We numerically confirm that Type I error rates of the proposed private test procedures are well controlled and have adequate power for larger sample sizes and effect sizes. The proposal is demonstrated in private inferences based on the American Time Use Survey data. [ABSTRACT FROM AUTHOR]

Abstract For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators.

Using ‘working’ assumptions on conditional third and fourth moments of errors, we propose a method of moments estimator that can have improved efficiency over the popular Gaussian quasi‐maximum likelihood estimator (GQMLE). Higher‐order moment assumptions are not needed for consistency – we only require the first two conditional moments to be correctly specified – but the optimal instruments are derived under these assumptions. The working assumptions allow both asymmetry in the distribution of the standardized errors as well as fourth moments that can be smaller or larger than that of the Gaussian distribution. The approach is related to the generalized estimation equations (GEE) approach – which seeks the improvement of estimators of the conditional mean parameters by making working assumptions on the conditional second moments. We derive the asymptotic distribution of the new estimator and show that it does not depend on the estimators of the third and fourth moments. A simulation study shows that the efficiency gains over the GQMLE can be non‐trivial. [ABSTRACT FROM AUTHOR]

We examine two binary operations on the set of algebraic polynomials, known as multiplicative and additive finite free convolutions, specifically in the context of hypergeometric polynomials. We show that the representation of a hypergeometric polynomial as a finite free convolution of more elementary blocks, combined with the preservation of the real zeros and interlacing by the free convolutions, is an effective tool that allows us to analyze when all roots of a specific hypergeometric polynomial are real. Moreover, the known limit behavior of finite free convolutions allows us to write the asymptotic zero distribution of some hypergeometric polynomials as free convolutions of Marchenko–Pastur, reciprocal Marchenko–Pastur, and free beta laws, which has an independent interest within free probability. [ABSTRACT FROM AUTHOR]

We obtain new results about the high-energy distribution of resonances for the one-dimensional Schrödinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular support of the potential. We also prove results about the distribution of resonances in sectors away from the real axis, and construct a class of potentials producing multiple sequences of resonances along distinct logarithmic curves, explicitly calculating the asymptotic location of these resonances. The results are unified by the use of an integral representation of the reflection coefficients, refining methods used in (J. Differential Equations 137(2) (1997) 251–272) and (J. Funct. Anal. 178(2) (2000) 396–420). [ABSTRACT FROM AUTHOR]