Integrative interaction analysis using threshold gradient directed regularization

For many complex business and industry problems, high‐dimensional data collection and modeling have been conducted. It has been shown that interactions may have important implications beyond the main effects. The number of unknown parameters in an interaction analysis can be larger or much larger than the sample size. As such, results generated from analyzing a single data set are often unsatisfactory. Integrative analysis, which jointly analyzes the raw data from multiple independent studies, has been conducted in a series of recent studies and shown to outperform single–data set analysis, meta‐analysis, and other multi–data set analyses. In this study, our goal is to conduct integrative analysis in interaction analysis. For regularized estimation and selection of important interactions (and main effects), we apply a threshold gradient directed regularization approach. Advancing from the existing studies, the threshold gradient directed regularization approach is modified to respect the “main effects, interactions” hierarchy. The proposed approach has an intuitive formulation and is computationally simple and broadly applicable. Simulations and the analyses of financial early warning system data and news‐APP (application) recommendation behavior data demonstrate its satisfactory practical performance.     

Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks

Conventional data envelopment analysis (DEA) for measuring the efficiency of a set of decision making units (DMUs) requires the input/output data to be constant. In reality, however, many observations are stochastic in nature; consequently, the resulting efficiencies are stochastic as well. This paper discusses how to obtain the efficiency distribution of each DMU via a simulation technique. The case of Taiwan commercial banks shows that, firstly, the number of replications in simulation analysis has little effect on the estimation of efficiency means, yet 1000 replications are recommended to produce reliable efficiency means and 2000 replications for a good estimation of the efficiency distributions. Secondly, the conventional way of using average data to represent stochastic variables results in efficiency scores which are different from the mean efficiencies of the presumably true efficiency distributions estimated from simulation. Thirdly, the interval-data approach produces true efficiency intervals yet the intervals are too wide to provide valuable information. In conclusion, when multiple observations are available for each DMU, the stochastic-data approach produces more reliable and informative results than the average-data and interval-data approaches do.     

Application of autoregressive modelling for the analysis of clinical and other biological data

This paper deals with the application of autoregressive (AR) modelling for the analysis of biological data including clinical laboratory data. In the first part of the paper, we discuss the necessity of feedback analysis in the field of biochemistry. In order to enable this, relative power contribution analysis was introduced. Next, we utilized the two types of impulse response curves of the open and closed loop systems for elucidating the structure of the metabolic networks under study. Time series data obtained from 31 chronic hemodialysis patients observed for periods of 3 to 7 years were analyzed by these procedures. The results of the analysis were rather uniform among the patients and suggested the consistency of this approach in identifying the dynamical system of individual patients. An example of data set is included in the paper.     

An inverse optimization model for imprecise data envelopment analysis

Inverse data envelopment analysis (InDEA) is a well-known approach for short-term forecasting of a given decision-making unit (DMU). The conventional InDEA models use the production possibility set (PPS) that is composed of an evaluated DMU with current inputs and outputs. In this paper, we replace the fluctuated DMU with a modified DMU involving renewal inputs and outputs in the PPS since the DMU with current data cannot be allowed to establish the new PPS. Besides, the classical DEA models such as InDEA are assumed to consider perfect knowledge of the input and output values but in numerous situations, this assumption may not be realistic. The observed values of the data in these situations can sometimes be defined as interval numbers instead of crisp numbers. Here, we extend the InDEA model to interval data for evaluating the relative efficiency of DMUs. The proposed models determine the lower and upper bounds of the inputs of a given DMU separately when its interval outputs are changed in the performance analysis process. We aim to remain the current interval efficiency of a considered DMU and the interval efficiencies of the remaining DMUs fixed or even improve compared with the current interval efficiencies.     

Variables reduction in data envelopment analysis

In real applications of data envelopment analysis (DEA), there are a number of pitfalls that could have a major influence on the efficiency. Some of these pitfalls are avoidable and the others remain problematic. One of the most important pitfalls that the researchers confront is the closeness of the number of operational units and the number of inputs and outputs. In performance measurement using DEA, the closeness of these two numbers could yield a large number of efficient units. In this article, some inputs or outputs will be aggregated and the number of inputs and outputs are reduced iteratively. Numerical examples show that in comparison to the single DEA method, our approach has the fewest efficient units. This means that our approach has a superior ability to discriminate the performance of the DMUs.     

An analysis of wavelet frame based scattered data reconstruction

In real world applications many signals contain singularities, like edges in images. Recent wavelet frame based approaches were successfully applied to reconstruct scattered data from such functions while preserving these features. In this paper we present a recent approach which determines the approximant from shift invariant subspaces by minimizing an ${?}_1$-regularized least squares problem which makes additional use of the wavelet frame transform in order to preserve sharp edges. We give a detailed analysis of this approach, i.e., how the approximation error behaves dependent on data density and noise level. Moreover, a link to wavelet frame based image restoration models is established and the convergence of these models is analyzed. In the end, we present some numerical examples, for instance how to apply this approach to handle coarse-grained models in molecular dynamics.     

Cutting and scanning methods in set-valued analysis I. An epigraphical and graphical calculus

Cutting analysis of sets (scanning, laser exploration, etc.), when applied to epigraphs of functions and graphs of operators, gives rise to a rich calculus and provides a unifying approach to various operations in optimization and variational analysis.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

Application of multilevel analysis in animal sciences

Multilevel modeling is considerably useful way to analyze hierarchical data sets. The main purpose of this paper is to apply multilevel analysis in animal science and also show that this modeling technique is appropriate to analyze this kind of data. Thus multilevel modeling technique is used to analyze the milk yield data which has hierarchical structures, sires nested within cows. As a result of the analysis done in this paper, it is obvious that multilevel modeling is needed to use for analyzing this data. This illustrates that it is a convenient way to use multilevel analysis for the data which obtained from animals when the data have hierarchies.     

A mesh simplification strategy for a spatial regression analysis over the cortical surface of the brain

We present a new mesh simplification technique developed for a statistical analysis of a large data set distributed on a generic complex surface, topologically equivalent to a sphere. In particular, we focus on an application to cortical surface thickness data. The aim of this approach is to produce a simplified mesh which does not distort the original data distribution so that the statistical estimates computed over the new mesh exhibit good inferential properties. To do this, we propose an iterative technique that, for each iteration, contracts the edge of the mesh with the lowest value of a cost function. This cost function takes into account both the geometry of the surface and the distribution of the data on it. After the data are associated with the simplified mesh, they are analyzed via a spatial regression model for non-planar domains. In particular, we resort to a penalized regression method that first conformally maps the simplified cortical surface mesh into a planar region. Then, existing planar spatial smoothing techniques are extended to non-planar domains by suitably including the flattening phase. The effectiveness of the entire process is numerically demonstrated via a simulation study and an application to cortical surface thickness data.     

Additive super-efficiency in integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) methods assume that input and output variables are continuous. However, in many real managerial cases, some inputs and/or outputs can only take integer values. Simply rounding the performance targets to the nearest integers can lead to misleading solutions and efficiency evaluation. Addressing this kind of integer-valued data, the current paper proposes models that deal directly with slacks to calculate efficiency and super-efficiency scores when integer values are present. Compared with standard radial models, additive (super-efficiency) models demonstrate higher discrimination power among decision making units, especially for integer-valued data. We use an empirical application in early-stage ventures to illustrate our approach.     

Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.     

Reformulation of the support set selection problem in the logical analysis of data

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed.     

A Data-Adaptive Principal Component Analysis: Use of Composite Asymmetric Huber Function

This article considers a new type of principal component analysis (PCA) that adaptively reflects the information of data. The ordinary PCA is useful for dimension reduction and identifying important features of multivariate data. However, it uses the second moment of data only, and consequently, it is not efficient for analyzing real observations in the case that these are skewed or asymmetric data. To extend the scope of PCA to non-Gaussian distributed data that cannot be well represented by the second moment, a new approach for PCA is proposed. The core of the methodology is to use a composite asymmetric Huber function defined as a weighted linear combination of modified Huber loss functions, which replaces the conventional square loss function. A practical algorithm to implement the data-adaptive PCA is discussed. Results from numerical studies including simulation study and real data analysis demonstrate the promising empirical properties of the proposed approach. Supplementary materials for this article are available online.     

Efficiency measurement using independent component analysis and data envelopment analysis

Efficiency measurement is an important issue for any firm or organization. Efficiency measurement allows organizations to compare their performance with their competitors’ and then develop corresponding plans to improve performance. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, problems of discrimination between efficient and inefficient decision-making units also exist in the DEA context (Adler and Yazhemsky, 2010). In this paper, a two-stage approach of integrating independent component analysis (ICA) and data envelopment analysis (DEA) is proposed to overcome this issue. We suggest using ICA first to extract the input variables for generating independent components, then selecting the ICs representing the independent sources of input variables, and finally, inputting the selected ICs as new variables in the DEA model. A simulated dataset and a hospital dataset provided by the Office of Statistics in Taiwan’s Department of Health are used to demonstrate the validity of the proposed two-stage approach. The results show that the proposed method can not only separate performance differences between the DMUs but also improve the discriminatory capability of the DEA’s efficiency measurement.     

Subgroup analysis of zero-inflated Poisson regression model with applications to insurance data

Customized personal rate offering is of growing importance in the insurance industry. To achieve this, an important step is to identify subgroups of insureds from the corresponding heterogeneous claim frequency data. In this paper, a penalized Poisson regression approach for subgroup analysis in claim frequency data is proposed. Subjects are assumed to follow a zero-inflated Poisson regression model with group-specific intercepts, which capture group characteristics of claim frequency. A penalized likelihood function is derived and optimized to identify the group-specific intercepts and effects of individual covariates. To handle the challenges arising from the optimization of the penalized likelihood function, an alternating direction method of multipliers algorithm is developed and its convergence is established. Simulation studies and real applications are provided for illustrations.     

Recent models in data envelopment analysis: Theory and applications

A critical review of the recent models of data envelopment analysis (DEA) is attempted here. Three new lines of approach involving dynamic changes in parameters, the error correction models and a stochastic sensitivity analysis are discussed in some detail. On the applications side, two new formulations are presented and discussed, e.g. a model of technical change and a cost frontier for testing economies of scale and adjustment due to risk factors. Thus the critical review of recent DEA models of productivity measurement provides new insight into the frontier of research in this field.     

On regularity concepts in variational analysis

The paper offers a new approach that allows unifying various regularity concepts used in variational analysis: the most fundamental local regularity triad (openness at a linear rate – metric regularity – Aubin property), the calmness–subregularity pair, directional regularity, upper Lipschitz continuity etc. The main new element of the approach is the appearance of a new parameter which is a set to which regularity is related (whence the term “relative regularity” used in the paper to name the general property). The main emphasis is put on characterizations of relative regularity and its stability with respect to additive perturbations of the (generally set-valued) mapping. A discussion of a relative extension of strong regularity properties concludes the paper.