Bootstrap Theory Research Articles

Testing in GARCH‐X models: boundary, correlations and bootstrap theory

In this article, we consider the so‐called Fixed Shrinkage (FS) bootstrap for the class of GARCH models with explanatory variables (GARCH‐X). Under the assumption of stationary covariates, the proposed FS bootstrap does not require modeling the covariates, as these are kept fixed in the bootstrap generating process. Our main focus is on testing whether one or more of the covariates can be excluded in the GARCH‐X model. As is well‐known the limiting distribution of the likelihood‐ratio (LR) statistic in this setting is non‐standard and depends in particular on whether nuisance parameters are on the boundary or in the interior of the parameter space. In particular, and as detailed here, the non‐standard limiting distribution depends on correlations, or dependence, between the explanatory variables. The FS bootstrap takes the presence of nuisance parameters into account by implementing shrinking as proposed in Cavaliere et al. (2022) for pure ARCH models. We establish asymptotic validity of the FS bootstrap for GARCH‐X models, and demonstrate by simulations that the bootstrap‐based test performs extremely well even when nuisance parameters lie on the boundary of the parameter space. The empirical illustration amplifies that the presence of nuisance parameters (especially whether or not on the boundary) are vital for interpreting the dynamics of conditional volatility in financial stock market indices.

Does participation in agri-environmental schemes increase eco-efficiency?

The literature on the effectiveness of Agri-Environmental Schemes focuses mainly on the environmental effects; only a few studies have focused on economic aspects. The number of papers that address ecological and economic outcomes simultaneously is even more limited. In this paper, we apply the concept of eco-efficiency to integrate these two factors. The aim of the paper is to analyze the impact of participation in the agri-environmental scheme of Hungarian field crop farmers in terms of eco-efficiency. To make unbiased and consistent comparisons we use advances from aggregation and bootstrap theory in Data Envelopment Analysis (DEA) context. The results indicate that there exists a significant potential for enhancing eco-efficiency in Hungarian crop farms. Furthermore, our results reveal that, in terms of eco-efficiency, perceived as the relationship of farm income to pesticide, fertilizers and energy use, no significant differences exist between participating and non-participating farmers. The results are robust to different methods. Our results pose questions about the efficacy of the Agri-Environmental Scheme.

Clustering with missing data: which equivalent for Rubin’s rules?

Multiple imputation (MI) is a popular method for dealing with missing values. However, the suitable way for applying clustering after MI remains unclear: how to pool partitions? How to assess the clustering instability when data are incomplete? By answering both questions, this paper proposed a complete view of clustering with missing data using MI. The problem of partitions pooling is here addressed using consensus clustering while, based on the bootstrap theory, we explain how to assess the instability related to observed and missing data. The new rules for pooling partitions and instability assessment are theoretically argued and extensively studied by simulation. Partitions pooling improves accuracy, while measuring instability with missing data enlarges the data analysis possibilities: it allows assessment of the dependence of the clustering to the imputation model, as well as a convenient way for choosing the number of clusters when data are incomplete, as illustrated on a real data set.

Bootstrap inference for Hawkes and general point processes

Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihood-based estimators and tests. As an alternative, and to improve finite sample performance, this paper considers bootstrap-based inference for interval estimation and testing. Specifically, for a wide class of point process models we consider a novel bootstrap scheme labeled ‘fixed intensity bootstrap’ (FIB), where the conditional intensity is kept fixed across bootstrap repetitions. The FIB, which is very simple to implement and fast in practice, extends previous ideas from the bootstrap literature on time series in discrete time, where the so-called ‘fixed design’ and ‘fixed volatility’ bootstrap schemes have shown to be particularly useful and effective. We compare the FIB with the classic recursive bootstrap, which is here labeled ‘recursive intensity bootstrap’ (RIB). In RIB algorithms, the intensity is stochastic in the bootstrap world and implementation of the bootstrap is more involved, due to its sequential structure. For both bootstrap schemes, we provide new bootstrap (asymptotic) theory which allows to assess bootstrap validity, and propose a ‘non-parametric’ approach based on resampling time-changed transformations of the original waiting times. We also establish the link between the proposed bootstraps for point process models and the related autoregressive conditional duration (ACD) models. Lastly, we show effectiveness of the different bootstrap schemes in finite samples through a set of detailed Monte Carlo experiments, and provide applications to both financial data and social media data to illustrate the proposed methodology.

A higher-order correct fast moving-average bootstrap for dependent data

We develop the theory of a novel fast bootstrap for dependent data. Our scheme deploys i.i.d. resampling of smoothed moment indicators. We characterize the class of parametric and semiparametric estimation problems for which the method is valid. We show the asymptotic refinements of the new procedure, proving that it is higher-order correct under mild assumptions on the time series, the estimating functions, and the smoothing kernel. We illustrate the applicability and the advantages of our procedure for M-estimation, generalized method of moments, and generalized empirical likelihood estimation. In a Monte Carlo study, we consider an autoregressive conditional duration model and we compare our method with other extant, routinely-applied first- and higher-order correct methods. The results provide numerical evidence that the novel bootstrap yields higher-order accurate confidence intervals, while remaining computationally lighter than its higher-order correct competitors. A real-data example on dynamics of trading volume of US stocks illustrates the empirical relevance of our method.

Reforming thought.

This article discusses a proposal for a reform in thinking, grounded on Heisenberg’s principle of uncertanty, Chew’s bootstrap theory and Bohm’s principle of implicated order. By synthetizing all three grounds together, it is concluded that thought ought to be turned to the uncertainty of phenomena. Behind uncertainty lies an implicated order, which mantains the interactive pattern with onself, the others and the world.

Bootstrap’s Monadology. Symmetry and Mirroring Connections between Chew’s Bootstrap Theory and Leibniz’s Monadology

The scientific paradigm which I rely upon in the framework of this article is quantum mechanics, whose “cognitive revolution” consisted of replacing the classical principle of separability with the principle of nonseparability or global intercorrelation. According to this intercorrelation, highlighted at the subatomic level, the part cannot be separated from the whole, because every part has a global and instantaneous connection with the whole universe. For this reason the foundation of the world cannot be the part (elementary particles), but the whole, which is therefore logically and ontologically prior to the part, i.e., self-consistent. Consequently, the principle of global intercorrelation elucidates and validates some of the oldest philosophical problems and intuitions about the unity or self-consistency of the world. An example in this sense is the bootstrap theory of American physicist Geoffrey Chew, which presents such striking similarities to the metaphysical system of Leibniz's Monadology that the two intertwine and mirror each other, like twin souls, to the extent that it could be stated that if Chew’s bootstrap theory represents the explanatory physical level of Leibniz’s metaphysics, then, analogously, Leibniz’s Monadology represents the explanatory metaphysical level of Chew’s physics.

On What Ground Do Thin Objects Exist? In Search of the Cognitive Foundation of Number Concepts

AbstractLinnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter‐argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations.

Bootstrapping of integer concepts: the stronger deviant-interpretation challenge (and how to solve it)

Beck (Cognition 158:110–121, 2017) presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey (The Origin of Concepts, 2009). According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system (OTS), which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system (ANS). Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge.

Bootstrap inference for Hawkes and general point processes

Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihoodbased estimators and tests, as originally developed in Ogata (1978). As an alternative, and to improve finite sample performance, this paper considers bootstrap-based inference for interval estimation and testing. Specifically, for a wide class of point process models we consider a novel bootstrap scheme labeled 'fixed intensity bootstrap' (FIB), where the conditional intensity is kept fixed across bootstrap repetitions. The FIB, which is very simple to implement and fast in practice, naturally extends previous ideas from the bootstrap literature on time series in discrete time, where the so-called 'fixed design' and 'fixed volatility' bootstrap schemes have shown to be particularly useful and effective. We compare the FIB with the classic recursive bootstrap, which is here labeled 'recursive intensity bootstrap' (RIB). In RIB algorithms, the intensity is stochastic in the bootstrap world and implementation of the bootstrap is more involved, due to its sequential structure. For both bootstrap schemes, no asymptotic theory is available; we therefore provide here a new bootstrap (asymptotic) theory, which allows to assess bootstrap validity. We also introduce novel 'nonparametric' FIB and RIB schemes, which are based on resampling time-changed transformations of the original waiting times. We show effectiveness of the different bootstrap schemes in finite samples through a set of detailed Monte Carlo experiments. As far as we are aware, this is the first detailed Monte Carlo study of bootstrap implementations for Hawkes-type processes. Finally, in order to illustrate, we provide applications of the bootstrap to both financial data and social media data.

Follow the Money: The Funding Acquisition Process of Nascent Ventures

This paper integrates the largely separate literatures of financial bootstrapping and pecking-order theory (POT) in order to explore how funding acquisition processes evolve at the firm level. Based on novel optimal matching techniques combined with binary logistic regressions, we identify how the most typical funding acquisition processes of nascent ventures evolve in specific circumstances. In accordance with financial bootstrapping theory, the majority of nascent ventures rely on bootstrapped finance. Importantly, we are additionally able to theorize – in line with pecking order theory – under which circumstances the minority of nascent ventures transition from founder and insider equity towards market-based (debt and equity) finance. As a result we offer a novel theoretical approach to understand how funding acquisition processes evolve in nascent venture.

“Old” conformal bootstrap on AdS: O(N) symmetric scalar model

Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger–Keldysh formalism is used in AdS/CFT instead of conventional Feynman–Witten diagrams technique, permits to calculate values of conformal dimensions in the [Formula: see text] symmetric model with conformal or composite Habbard–Stratonovich field.

Melam Group: Bootstrapped Entrepreneurship

This is a story of Melam Group of Companies, a vivid example of Business Bootstrapping theory. A personal interview with the founder, Mr Kurian John Melamparambil (Padma Shri awardee) revealed how the Melam Group started a business with zero or limited resources. This case is to enlighten the young mind that it is not always huge capital/funding/venture capital/angel investing that builds a successful business. It is the determination and passion for the idea than the money that propels a business to success.

Soft bootstrap and effective field theories

The soft bootstrap program aims to construct consistent effective field theories (EFT’s) by recursively imposing the desired soft limit on tree-level scattering amplitudes through on-shell recursion relations. A prime example is the leading two-derivative opera­ tor in the EFT of SU(N) x SU(N)/SU(N) nonlinear sigma model (NLSM), where \U0001d4aa(p2 ) amplitudes with an arbitrary multiplicity of external particles can be soft-bootstrapped. We extend the program to \U0001d4aa(p4) operators and introduce the “soft blocks,” which are the seeds for soft bootstrap. The number of soft blocks coincides with the number of independent operators at a given order in the derivative expansion and the incalculable Wilson coefficient emerges naturally. We also uncover a new soft-constructible EFT involving the “multi-trace” operator at the leading two-derivative order, which is matched to SO(N + 1) /SO(N) NLSM. In addition, we consider Wess-Zumino-Witten (WZW) terms, the existence of which, or the lack thereof, depends on the number of flavors in the EFT, after a novel application of Bose symmetry. Remarkably, we find agreements with group­ theoretic considerations on the existence of WZW terms in SU(N) NLSM for N ≥ 3 and the absence of WZW terms in SO(N) NLSM for N ≠ 5.

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

We develop theory of a novel fast bootstrap for dependent data. Our scheme deploys i.i.d. resampling of smoothed moment indicators. We characterize the class of parametric and semiparametric estimation problems for which the method is valid. We show the asymptotic re refinements of the new procedure, proving that it is higher-order correct under mild assumptions on the time series, the estimating functions, and the smoothing kernel. We illustrate the applicability and the advantages of our procedure for M-estimator, generalized method of moments, and generalized empirical likelihood estimation. In a Monte Carlo study, we consider an autoregressive conditional duration model and we compare our method with other extant, routinely-applied first- and higher-order correct methods. The results provide numerical evidence that the novel bootstrap yields higher-order accurate confidence intervals, while remaining computationally lighter than its higher-order correct competitors. A real-data example on dynamics of trading volume of US stocks illustrates the empirical relevance of our method.

On the use of bootstrap with variational inference: Theory, interpretation, and a two-sample test example

Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and to carry out Bayesian inference, however, quantification of uncertainty with variational inference remains challenging from both theoretical and practical perspectives. This paper is concerned with developing uncertainty measures for variational inference by using bootstrap procedures. We first develop two general bootstrap approaches for assessing the uncertainty of a variational estimate and the study the underlying bootstrap theory in both fixed- and increasing-dimension settings. We then use the bootstrap approach and our theoretical results in the context of mixed membership modeling with multivariate binary data on functional disability from the National Long Term Care Survey. We carry out a two-sample approach to test for changes in the repeated measures of functional disability for the subset of individuals present in 1989 and 1994 waves.

Technical efficiency, unions and decentralized labor contracts

This paper explores the link between the presence of unions in the workplace, the adoption of decentralized labor agreements and technical efficiency, using a large sample of Italian manufacturing firms. We apply the Data Envelopment Analysis, and its robust version based on bootstrap theory, to get reliable estimates of technical efficiency at the firm level in a standard first stage. We devote particular attention to the specific technology adopted, by distinguishing 20 different sector frontiers, as well as to the presence of outliers. The obtained efficiency scores are analyzed in a second stage applying a truncated regression model estimated via Maximum Likelihood, following the Simar and Wilson (2007, 2011) methodology. Our results highlight that the presence of workplace unionization decreases the level of technical efficiency, while aspects limiting the unions’ power such as a strong exposure to international markets, high debt levels or the prevalence of flexible assets partially reduce the negative effect. However, when firms adopt decentralized labor contracts agreements, the effect on efficiency is positive and partially compensates the negative unions’ effect.

Technical Efficiency, Unions and Decentralized Labor Contracts

This paper explores the link between the presence of unions in the workplace, the adoption of decentralized labor agreements and technical efficiency, using a large sample of Italian manufacturing firms. We apply the Data Envelopment Analysis, and its robust version based on bootstrap theory, to get reliable estimates of technical efficiency at the firm level in a standard first stage. We devote particular attention to the specific technology adopted, by distinguishing 20 different sector frontiers, as well as to the presence of outliers. The obtained efficiency scores are analyzed in a second stage applying a truncated regression model estimated via Maximum Likelihood, following the Simar and Wilson (2007, 2011) methodology. Our results highlight that the presence of workplace unionization decreases the level of technical efficiency, while aspects limiting the unions' power such as a strong exposure to international markets, high debt levels or the prevalence of flexible assets partially reduce the negative effect. However, when firms adopt decentralized labor contracts agreements, the effect on efficiency is positive and partially compensates the negative unions' effect. The results are robust to the inclusion of many firm characteristics and to different model specifications.

Cognitive aspects of a temporality concept in the comparative analysis of post-nonclassical scientificity and myth

The paper considers ‘time’, a fundamental category of human existence, in the context of cognitive processes research in modern culture. Main methodological approaches to determining temporality in myth have been outlined. The authors validate a thesis that methods of understanding time in science and myth at the current development stage of research of the specified worldview forms as cognitive practices correlate. Main features of a ‘time’ concept and its function in mythological thinking, such as unity, interpenetrability, verticality, have been formulated. Myth creates senses, forms a steady ontological picture of the world, makes a human an active source in “constructing the reality”. In this connection, myth mostly plays the role of one of the algorithms of cognitive activity in the context of modern cognitive science. A “temporality” concept realized in myth forms conditions to use it as one of ontological foundations in the modern research of cognitive processes. Main types of temporality in classical and nonclassical science have been described. The specificity of time concept transformation in non-classical science and actualization of relativity and probability of processes and their complementary nature have been revealed. D.Chou’s bootstrap theory of particles has been studied. There has been shown that temporary processes of the micro-world are discrete, diverse and do not exist within the framework of universal integrity which to a great extent correlates with the modern scientific worldview and principles of cognitive practices.

Dynamic Assessment of Vibration of Tooth Modification Gearbox Using Grey Bootstrap Method

The correlation analysis between gear modification and vibration characteristics of transmission system was difficult to quantify; a novel small sample vibration of gearbox prediction method based on grey system theory and bootstrap theory was presented. The method characterized vibration base feature of tooth modification gearbox by developing dynamic uncertainty, estimated true value, and systematic error measure, and these parameters could indirectly dynamically evaluate the effect of tooth modification. The method can evaluate the vibration signal of gearbox with installation of no tooth modification gear and topological modification gear, respectively, considering that 100% reliability is the constraints condition and minimum average uncertainty is the target value. Computer simulation and experiment results showed that vibration amplitude of gearbox was decreased partly due to topological tooth modification, and each value of average dynamic uncertainty, mean true value, and systematic error measure was smaller than the no tooth modification value. The study provided an important guide for tooth modification, dynamic performance optimization.