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In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born-Oppenheimer approximation. In this article, we analyze the tailored coupled-cluster method (TCC), one particular and promising method for treating molecular electronic-structure problems with static correlation. The TCC method combines the single-reference coupled-cluster (CC) approach with an approximate reference calculation in a subspace (complete active space (CAS)) of the considered Hubert space that covers the static correlation. A one-particle spectral gap assumption is introduced, separating the CAS from the remaining Hubert space. This replaces the nonexisting or nearly nonexisting gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital usually encountered in standard single-reference quantum chemistry. The analysis covers, in particular, CC methods tailored by tensor-network states (TNS-TCC methods). The problem is formulated in a nonlinear functional analysis framework, and, under certain conditions such as the aforementioned gap, local uniqueness and existence are proved using Zarantonello's lemma. From the Aubin-Nitscheduality method, a quadratic error bound valid for TNS-TCC methods is derived, e.g., for lineartensor-network TCC schemes using the density matrix renormalization group method.

The mathematical foundation of the so-called extended coupled-cluster method for the solution of the many-fermion Schrödinger equation is here developed. We prove an existence and uniqueness result, both in the full infinite-dimensional amplitude space as well as for discretized versions of it. The extended coupled-cluster method is formulated as a critical point of an energy function using a generalization of the Rayleigh-Ritz principle: the bivariational principle. This gives a quadratic bound for the energy error in the discretized case. The existence and uniqueness results are proved using a type of monotonicity property for the flipped gradient of the energy function. A comparison to the analysis of the standard coupled-cluster method is made, and it is argued that the bivariational principle is a useful tool, both for studying coupled-cluster type methods and for developing new computational schemes in general.

The rapid growth of the Chinese travel market has gained attention in the tourism industry. However, very few studies have been conducted to examine travel constraints that prevent Chinese outbound travelers from going somewhere quite accessible to their major destination from a multidestination perspective. Drawing upon the leisure constraint model (LCM), this study explored Chinese independent tourists' perceived travel constraints in selecting second-tier destinations in their destination choice and analyzed the market segments. A self-administered survey was collected from 393 Chinese travelers who did not visit Gyeonggi Province close to Seoul during their travels in South Korea. Based on the findings, four distinct groups were formed. The findings provide important insights into destinations that desire to attract more Chinese independent travelers.

The cluster robust variance estimator (CRVE) relies on the number of clusters being sufficiently large. Monte Carlo evidence suggests that the ‘rule of 42’ is not true for unbalanced clusters. Rejection frequencies are higher for datasets with 50 clusters proportional to US state populations than with 50 balanced clusters. Using critical values based on the wild cluster bootstrap performs much better. However, this procedure fails when a small number of clusters is treated. We explain why CRVE t statistics and the wild bootstrap fail in this case, study the ‘effective number’ of clusters and simulate placebo laws with dummy variable regressors.

In most classification tasks, there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classifiers assuming the true distribution to be known. We show that the oracle classifiers are obtained from level sets of the functions that define the conditional probability of each class. Then we develop estimators with good asymptotic and finite sample properties. The proposed estimators build on existing single-label classifiers. The optimal classifier can sometimes output the empty set, but we provide two solutions to fix this issue that are suitable for various practical needs. Supplementary materials for this article are available online.

Clusters are geographic concentrations of industries related by knowledge, skills, inputs, demand and/or other linkages. There is an increasing need for cluster-based data to support research, facilitate comparisons of clusters across regions and support policymakers in defining regional strategies. This article develops a novel clustering algorithm that systematically generates and assesses sets of cluster definitions (i.e., groups of closely related industries). We implement the algorithm using 2009 data for U.S. industries (six-digit NAICS), and propose a new set of benchmark cluster definitions that incorporates measures of inter-industry linkages based on co-location patterns, input–output links, and similarities in labor occupations. We also illustrate the algorithm’s ability to compare alternative sets of cluster definitions by evaluating our new set against existing sets in the literature. We find that our proposed set outperforms other methods in capturing a wide range of inter-industry linkages, including the grouping of industries within the same three-digit NAICS.

Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian data analysis, like all data analysis, is an iterative process of model building, inference, model checking and evaluation, and model expansion. Visualization is helpful in each of these stages of the Bayesian workflow and it is indispensable when drawing inferences from the types of modern, high dimensional models that are used by applied researchers.

Various techniques have been employed to assess the stability and adaptability of crops, where mixed models or BLUP-based indexes like WAASB proving particularly more benefit. We introduce rYWAASB, an open-source R package designed to offer a novel index for quantifying both stability and performance of a biological trait. It quantifies the stability and performance of individuals/genotypes e.g. in plant breeding programs. It simultaneously considers the trait of interest, along with the WAASB index in a new perspective. The package then provides bar plots, PCA diagrams, and optimum cluster number estimate and cluster categorization by MCMC algorithms. For executing the package, a field experiment was conducted on chickpea (Cicer arietinum L.) from 2018 to 2020, evaluating the grain yield and days to maturity in rainfed conditions. The genotypes have put in 7 clusters for grain yield while genotypes 18, 69, and 5 were the most stable, exhibiting the highest grain yields, but genotypes 2, 103, 27, and 88 are identified as the earliest ripening varieties, exhibiting a higher degree of stability. The findings highlighted the effectiveness of the novel rYWAASB index in distinguishing observations in the experiment, suggesting its potential application in agronomic and plant breeding stability and adaptability programs.

An ever-increasing share of human interaction, communication, and culture is recorded as digital text. We provide an introduction to the use of text as an input to economic research. We discuss the features that make text different from other forms of data, offer a practical overview of relevant statistical methods, and survey a variety of applications.

Existing approaches for multivariate functional principal component analysis are restricted to data on the same one-dimensional interval. The presented approach focuses on multivariate functional data on different domains that may differ in dimension, such as functions and images. The theoretical basis for multivariate functional principal component analysis is given in terms of a Karhunen-Loève Theorem. For the practically relevant case of a finite Karhunen-Loève representation, a relationship between univariate and multivariate functional principal component analysis is established. This offers an estimation strategy to calculate multivariate functional principal components and scores based on their univariate counterparts. For the resulting estimators, asymptotic results are derived. The approach can be extended to finite univariate expansions in general, not necessarily orthonormal bases. It is also applicable for sparse functional data or data with measurement error. A flexible R implementation is available on CRAN. The new method is shown to be competitive to existing approaches for data observed on a common one-dimensional domain. The motivating application is a neuroimaging study, where the goal is to explore how longitudinal trajectories of a neuropsychological test score covary with FDG-PET brain scans at baseline. Supplementary material, including detailed proofs, additional simulation results, and software is available online.