Distributional Theory Research Articles

Transmuted inverse unit Teissier distribution: Properties, estimations and applications to medical and radiation sciences

The efficiency of probability distributions, which are fundamental to statistical analysis in many domains, is directly related to how well they match particular data attributes. Nonetheless, several real-world facts cast doubt on the presumptions of conventional distributions, highlighting the need for continuous improvements in probabilistic modeling. A new, adaptable two-parameter modification of the inverse unit Teissier distribution (IUTD) developed using the transmutation approach is presented in this paper and called the transmuted inverse unit Teissier distribution (TrIUTD). By adding a transmutation parameter, the TrIUTD is better able to represent intricate data patterns that conventional distributions might not be able to fully represent. Because the TrIUTD’s probability density function is right-skewed and unimodal, it can be used in a variety of contexts, including economic modeling, survival analysis, and reliability engineering. A growing failure rate is revealed by its hazard function, which makes it suitable for lifetime data analysis. The TrIUTD’s quantile function, moments, survival function, odds ratio, failure rate average, Mills ratio, and order statistics were among its important attributes that were carefully deduced. Maximum likelihood estimation was shown to be the most reliable method out of fifteen various approaches used to estimate parameters for this model. Applications to three real-world datasets from the medical and radiation sciences proved the model’s performance, and simulation tests verified the estimators’ dependability. According to goodness-of-fit criteria, the TrIUTD showed a better fit than well-known distributions, indicating its potential as a useful supplement to practical statistical modeling and distributional theory.

Legitimating Activism as a meaningful category: Negotiation of the protest lexicon in The Guardian and Times since the 1960s

Research on the relationship between contentious action and news production has often focused on the coverage and framing of specific events, not on the careers of keywords of the protest lexicon itself. However, these keywords play a central role in the negotiation of common understandings of social problems, the legitimation of claims and tactics, and even the shared imaginary of grassroots politics within communities of readers. This article seeks to contribute to this second avenue of media research by studying use of the concept activism and associated subject, activists. I ask how this word, which was a negative term for most of the twentieth century until the introduction and popularization of its modern sense in the 1960s, became a keyword of modern political participation by the public. A conceptual history grounded in insights of distributional semantics and semantic field theory, this article studies patterns of use of ‘activist’ and ‘activism’ in two major British quality newspapers, The Guardian and The Times. This comparative approach aims to identify both historical and media-internal factors that contributed to activism becoming a meaningful category in news reporting. Coverage is compared for three episodes of heightened civic contention: the student protests of 1967–1969; Eastern European human rights activism around the Helsinki Accords, 1975–1977; and the industrial strikes of the 1980s, particularly the period around the miner's strike, 1984–1986.

Robust nonparametric frontier estimation in two steps

We propose a robust methodology for estimating production frontiers with multi-dimensional input via a two-step nonparametric regression, in which we estimate the level and shape of the frontier before shifting it to an appropriate position. Our main contribution is to derive a novel frontier estimation method under a variety of flexible models which is robust to the presence of outliers and possesses some inherent advantages over traditional frontier estimators. Our approach may be viewed as a simplification, yet a generalization, of those proposed by Martins-Filho and coauthors, who estimate frontier surfaces in three steps. In particular, outliers, as well as commonly seen shape constraints of the frontier surfaces, such as concavity and monotonicity, can be straightforwardly handled by our estimation procedure. We show consistency and asymptotic distributional theory of our resulting estimators under standard assumptions in the multi-dimensional input setting. The competitive finite-sample performances of our estimators are highlighted in both simulation studies and empirical data analysis.

Context Synthesis Accelerates Vocabulary Learning Through Reading: The Implication of Distributional Semantic Theory on Second Language Vocabulary Research

Abstract Besides explicit inference of word meanings, associating words with diverse contexts may be a key mechanism underlying vocabulary learning through reading. Drawing from distributional semantic theory, we developed a text modification method called reflash to facilitate both word-context association and explicit inference. Using a set of left and right arrows, learners can jump to a target word’s previous or subsequent occurrences in digital books to synthesize clues across contexts. Participants read stories with target words modified by reflash-only, gloss-only, gloss + reflash, or unmodified. Learning outcomes were measured via Vocabulary Knowledge Scale and a researcher-developed interview to probe word-context association. We modeled the learning trajectories of words across five weeks among three adolescent L2 English learners (113 word-learner pairings) using Bayesian multilevel models. We found that reflash-only words made more gains than words in other conditions on both outcomes, controlling for key covariates such as types of existing knowledge. Our analysis also revealed that context synthesis may be particularly useful for learning specific types of words like homonyms, which has significant pedagogical implications.

Inferential theory for generalized dynamic factor models

We provide the asymptotic distributional theory for the so-called General or Generalized Dynamic Factor Model (GDFM), laying the foundations for an inferential approach in the GDFM analysis of high-dimensional time series. By exploiting the duality between common shocks and dynamic loadings, we derive the asymptotic distribution and associated standard errors for a class of estimators for common shocks, dynamic loadings, common components, and impulse response functions. We present an empirical application aimed at constructing a “core” inflation indicator for the U.S. economy, which demonstrates the superiority of the GDFM-based indicator over the most common approaches, particularly the one based on Principal Components.

Uncertainty Quantification for Nonconvex Tensor Completion: Confidence Intervals, Heteroscedasticity and Optimality

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion—the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation algorithm proposed by Cai <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , we characterize the distribution of this nonconvex estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and the unknown tensor factors. The proposed inferential procedure enjoys several important features: (1) it is fully adaptive to noise heteroscedasticity, and (2) it is data-driven and automatically adapts to unknown noise distributions. Furthermore, our findings unveil the statistical optimality of nonconvex tensor completion: it attains un-improvable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> accuracy—including both the rates and the pre-constants—when estimating both the unknown tensor and the underlying tensor factors.

Divergent semantic integration (DSI): Extracting creativity from narratives with distributional semantic modeling

We developed a novel conceptualization of one component of creativity in narratives by integrating creativity theory and distributional semantics theory. We termed the new construct divergent semantic integration (DSI), defined as the extent to which a narrative connects divergent ideas. Across nine studies, 27 different narrative prompts, and over 3500 short narratives, we compared six models of DSI that varied in their computational architecture. The best-performing model employed Bidirectional Encoder Representations from Transformers (BERT), which generates context-dependent numerical representations of words (i.e., embeddings). BERT DSI scores demonstrated impressive predictive power, explaining up to 72% of the variance in human creativity ratings, even approaching human inter-rater reliability for some tasks. BERT DSI scores showed equivalently high predictive power for expert and nonexpert human ratings of creativity in narratives. Critically, DSI scores generalized across ethnicity and English language proficiency, including individuals identifying as Hispanic and L2 English speakers. The integration of creativity and distributional semantics theory has substantial potential to generate novel hypotheses about creativity and novel operationalizations of its underlying processes and components. To facilitate new discoveries across diverse disciplines, we provide a tutorial with code (osf.io/ath2s) on how to compute DSI and a web app ( osf.io/ath2s ) to freely retrieve DSI scores.

The basic distributional theory for the product of zero mean correlated normal random variables

AbstractThe product of two zero mean correlated normal random variables, and more generally the sum of independent copies of such random variables, has received much attention in the statistics literature and appears in many application areas. However, many important distributional properties are yet to be recorded. This review paper fills this gap by providing the basic distributional theory for the sum of independent copies of the product of two zero mean correlated normal random variables. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other random variables, and a list of related distributions. We also review how the product of two zero mean correlated normal random variables arises naturally as a limiting distribution, with an example given for the distributional approximation of double Wiener‐Itô integrals.

GMM with Nearly-Weak Identification

A unified framework for the asymptotic distributional theory of GMM with nearly-weak instruments is provided. It generalizes a previously proposed framework in two main directions: first, by allowing instruments’ weakness to be less severe in the sense that some GMM estimators remain consistent, while featuring low precision; and second, by relaxing the so-called ”separability assumption” and considering generalized versions of local-to-zero asymptotics without partitioning a priori the vector of parameters in two subvectors converging at different rates. It is shown how to define directions in the parameter space whose estimators come with different rates of convergence characterized by the Moore-Penrose inverse of the Jacobian matrix of the moments. Furthermore, regularity conditions are provided to ensure standard asymptotic inference for these estimated directions.

A New Approach to Automatic Detection and Correction of Derivational Errors in L2 Russian

Learner corpora serve as one of the most valuable sources of statistical data on learners' errors. For instance, data from foreign-language learners’ corpora can be used for the Second Language Acquisition research. However, corpora representativity strongly depends on the quality of its error markup, which is most frequently carried out manually and thus presents a time-consuming and painstaking routine for the annotators. To make annotation process easier, additional tools, such as spellcheckers, are usually used. This paper focuses on developing a program for automatic correction of derivational errors made by learners of Russian as a foreign language. Derivational errors, which are not common for adult Russian native speakers (L1), but occur quite often in written texts or speech of Russian as foreign language learners (L2) [Chernigovskaya, Gor, 2000], were chosen as scope of our research because correction of such mistakes presents a formidable challenge for existing spellcheckers. Using the data from the Russian Learner Corpus (http://www.web-corpora.net/RLC/), we tested two already existing approaches to solve such kind of problems. The first one is based on a finite state automaton principle developed by Dickinson and Herring 2008, and it was test-ed as algorithm for derivational errors detection. The second one which relies on the Noisy Channel model by Brill and Moore, 2000, was used for studying errors correction. After we analyzed effectiveness of these tests, we developed our own system for autocorrection of derivational errors. In our program the algorithm of Dickinson and Herring was used as word-formation error detection module. The Noisy Channel model has been rejected, and we decided to use instead the Continuous Bag of Words FastText model, based on Harris distributional semantics theory [1954]. In addition, filtering rules have been developed for correcting frequent errors that the model is unable to handle. To restore automatically the correct grammatical word form, dictionary of word paradigms is used. Model results were validated on the data of Russian Learner Corpus.

Exact and asymptotic identification-robust inference for dynamic structural equations with an application to New Keynesian Phillips Curves

Many models in econometrics involve endogeneity and lagged dependent variables. We start by observing that usual identification-robust (IR) tests are unreliable when model variables are nonstationary or nearly nonstationary. We propose IR methods which are also robust to nonstationarity: one Anderson-Rubin type procedure and two split-sample procedures. Our procedures are also robust to missing instruments. For distributional theory, three different sets of assumptions are considered. First, on assuming Gaussian structural errors, we show that two of the proposed statistics follow the standard F distribution. Second, for more general cases, we assume that the distribution of errors is completely specified up to an unknown scale factor, allowing the Monte Carlo test method to be applied. This assumption enables one to deal with non-Gaussian error distributions. For example, even when errors follow heavy-tailed distribution, such as the Cauchy distribution or more generally the family of stable distributions—which may not have moments and thus make inference difficult—our procedures provide simple and exact solutions. Third, we establish the asymptotic validity of our procedures under quite general distributional assumptions. We present simulation results showing that our procedures control their level correctly and have good power properties. The methods are applied to an empirical example, the New Keynesian Phillips curve, in which both weak identification and nonstationarity present challenges. The results of this empirical study suggest forward-looking behavior of U.S. inflation.

Investigating heterogeneity in meta-analysis of studies with rare events

In many meta-analyses, the variable of interest is frequently a count outcome reported in an intervention and a control group. Single- or double-zero studies are often observed in this type of data. Given this setting, the well-known Cochran’s Q statistic for testing homogeneity becomes undefined. In this paper, we propose two statistics for testing homogeneity of the risk ratio, particularly for application in the case of rare events in meta-analysis. The first one is a chi-square type statistic. It is constructed based on information of the conditional probability of the number of events in the treatment group given the total number of events. The second one is a likelihood ratio statistic, derived from the logistic regression models allowing fixed and random effects for the risk ratio. Both proposed statistics are well defined even in the situation of single-zero studies. In a simulation study, the proposed tests show a performance better than the traditional test in terms of type I error and power of the test under common and rare event situations. However, as the performance of the two newly proposed tests is still unsatisfactory in the very rare events setting, we suggest a bootstrap approach that does not rely on asymptotic distributional theory and it is shown that the bootstrap approach performs well in terms of type I error. Furthermore, a number of empirical meta-analyses are used to illustrate the methods.

A distributional and dynamic theory of pricing and preference.

Theories that describe how people assign prices and make choices are typically based on the idea that both of these responses are derived from a common static, deterministic function used to assign utilities to options. However, preference reversals-where prices assigned to gambles conflict with preference orders elicited through binary choices-indicate that the response processes underlying these different methods of evaluation are more intricate. We address this issue by formulating a new computational model that assumes an initial bias or anchor that depends on type of price task (buying, selling, or certainty equivalents) and a stochastic evaluation accumulation process that depends on gamble attributes. To test this new model, we investigated choices and prices for a wide range of gambles and price tasks, including pricing under time pressure. In line with model predictions, we found that price distributions possessed stark skew that depended on the type of price and the attributes of gambles being considered. Prices were also sensitive to time pressure, indicating a dynamic evaluation process underlying price generation. The model out-performed prospect theory in predicting prices and additionally predicted the response times associated with these prices, which no prior model has accomplished. Finally, we show that the model successfully predicts out-of-sample choices and that its parameters allow us to fit choice response times as well. This price accumulation model therefore provides a superior account of the distributional and dynamic properties of price, leveraging process-level mechanisms to provide a more complete account of the valuation processes common across multiple methods of eliciting preference. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

One Hundred Years of Migration Discourse in The Times: A Discourse-Historical Word Vector Space Approach to the Construction of Meaning.

This study proposes an experimental method to trace the historical evolution of media discourse as a means to investigate the construction of collective meaning. Based on distributional semantics theory (Harris, 1954; Firth, 1957) and critical discourse theory (Wodak and Fairclough, 1997), it explores the value of merging two techniques widely employed to investigate language and meaning in two separate fields: neural word embeddings (computational linguistics) and the discourse-historical approach (DHA; Reisigl and Wodak, 2001) (applied linguistics). As a use case, we investigate the historical changes in the semantic space of public discourse of migration in the United Kingdom, and we use the Times Digital Archive (TDA) from 1900 to 2000 as dataset. For the computational part, we use the publicly available TDA word2vec models1 (Kenter et al., 2015; Martinez-Ortiz et al., 2016); these models have been trained according to sliding time windows with the specific intention to map conceptual change. We then use DHA to triangulate the results generated by the word vector models with social and historical data to identify plausible explanations for the changes in the public debate. By bringing the focus of the analysis to the level of discourse, with this method, we aim to go beyond mapping different senses expressed by single words and to add the currently missing sociohistorical and sociolinguistic depth to the computational results. The study rests on the foundation that social changes will be reflected in changes in public discourse (Couldry, 2008). Although correlation does not prove direct causation, we argue that historical events, language, and meaning should be considered as a mutually reinforcing cycle in which the language used to describe events shapes explicit meanings, which in turn trigger other events, which again will be reflected in the public discourse.

Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory

We study the distribution of Durbin–Wu–Hausman (DWH) and Revankar–Hartley (RH) tests for exogeneity from a finite-sample viewpoint, under the null and alternative hypotheses. We consider linear structural models with possibly non-Gaussian errors, where structural parameters may not be identified and where reduced forms can be incompletely specified (or nonparametric). On level control, we characterize the null distributions of all the test statistics. Through conditioning and invariance arguments, we show that these distributions do not involve nuisance parameters. In particular, this applies to several test statistics for which no finite-sample distributional theory is yet available, such as the standard statistic proposed by Hausman (1978). The distributions of the test statistics may be non-standard – so corrections to usual asymptotic critical values are needed – but the characterizations are sufficiently explicit to yield finite-sample (Monte-Carlo) tests of the exogeneity hypothesis. The procedures so obtained are robust to weak identification, missing instruments or misspecified reduced forms, and can easily be adapted to allow for parametric non-Gaussian error distributions. We give a general invariance result (block triangular invariance) for exogeneity test statistics. This property yields a convenient exogeneity canonical form and a parsimonious reduction of the parameters on which power depends. In the extreme case where no structural parameter is identified, the distributions under the alternative hypothesis and the null hypothesis are identical, so the power function is flat, for all the exogeneity statistics. However, as soon as identification does not fail completely, this phenomenon typically disappears. We present simulation experiments which confirm the finite-sample theory. The theoretical results are illustrated with an empirical example : the relation between trade and economic growth.

A UNIFIED STUDY OF NONPARAMETRIC INFERENCE FOR MONOTONE FUNCTIONS.

The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the greatest convex minorant or least concave majorant of an estimator of a primitive function. In this paper, we provide general conditions for consistency and pointwise convergence in distribution of a class of generalized Grenander-type estimators of a monotone function. This broad class allows the minorization or majoratization operation to be performed on a data-dependent transformation of the domain, possibly yielding benefits in practice. Additionally, we provide simpler conditions and more concrete distributional theory in the important case that the primitive estimator and data-dependent transformation function are asymptotically linear. We use our general results in the context of various well-studied problems, and show that we readily recover classical results established separately in each case. More importantly, we show that our results allow us to tackle more challenging problems involving parameters for which the use of flexible learning strategies appears necessary. In particular, we study inference on monotone density and hazard functions using informatively right-censored data, extending the classical work on independent censoring, and on a covariate-marginalized conditional mean function, extending the classical work on monotone regression functions.

On Multi-Dimensional Time-Varying Price Staleness

The price staleness is referred to as the extent of the presence of the zero returns in the price dynamics. The proportion of the zero returns could be high in the high-frequency data sets, as pointed by Bandi et al. (2020a). Considering the price staleness as a dynamic system too, in this paper, we extend the framework of Bandi et al. (2020b) and study the statistical inference of the idiosyncratic price staleness and systematic price staleness between assets, where the systematic price staleness characterizes the probability of the presence of com- mon zero returns. We propose consistent estimators for both the idiosyncratic and systematic price stalenesses under the new framework, and their distributional theory are established. Moreover, we develop a feasible nonparametric test for the constancy of the systematic price staleness. All of the methodologies are based on the high-frequency observations, namely, we require the observing intervals shrink to zero. Finally, we conduct simulation studies under various scenarios to assess the finite sample performance of the proposed approaches, and provide an empirical illustration for the proposed theory.

Supplemental Material for A Distributional and Dynamic Theory of Pricing and Preference

Supplemental Material for A Distributional and Dynamic Theory of Pricing and Preference

Understanding the Role of Power in Changes to Pastoral Institutions in Kyrgyzstan

Our article reflects on the Kyrgyz experience of a transformation in pasture use and management, seeking to contribute to the literature on institutional change in post-socialist contexts. We employ the distributional theory of institutional change in order to understand gradual, informal de facto institutional change which emerged because of changes in formal institutions (laws) that changed the bargaining positions of actors involved. The study findings demonstrate the dynamics of change of interrelated formal institutions, power resources, informal institutions, and their distributional consequences. We observe that the enforcement of new pasture legislation introduced in 2009 gradually reducing bargaining asymmetry among actors, in the long run potentially favouring less powerful pasture users, who are herders providing herding services to their community. Evaluating the potential implications of formal institutional change for day-to-day pasture management and informal institutions, we expect changes to contribute to maintenance of pasture health in the medium to long term. However, traditionally powerful actors (individual herders) typically try to resist these changes and the shift to new informal institutions is therefore still highly contested.

Using Word Embeddings to Analyze how Universities Conceptualize “Diversity” in their Online Institutional Presence

The term diversity can be operationalized demographically (in terms of physical or external characteristics such as race, gender, ethnicity and nationality) or intellectually (in terms of mental phenomena such as viewpoints, beliefs, ideas and political opinion). This work examines the context in which the concept of diversity is used by 50 US elite universities in their online institutional presence. Distributional semantics theory is leveraged to quantify semantic similarity between linguistic items based on their distributional properties in a large sample of language data taken from universities online profiles. The language modelling is carried out using Word2vec, a state-of-the-art machine learning model widely used by the natural language processing community to create vector representations of words (i.e. word embeddings). The model uses a neural network trained to reconstruct the linguistic context of words in the training corpus. As a by-product of the training objective, word2vec embeds words into a learned vector space where words that share common contexts and thus semantic meaning according to the distributional hypotheses, are located in close proximity to one another. A quantitative analysis of cosine similarities between word vectors derived from the corpus of text retrieved from universities online institutional profiles shows that the diversity concept is much closer to demographic operationalisations of diversity such as race, gender, ethnicity or nationality than to intellectual ones such as viewpoints, values, beliefs or political orientation. That is, the universities studied tend to use the word diversity predominantly in its demographic denotation to refer to variety of external appearance instead of to variety of mental phenomena. This is significant in light of the severe lack of ideological diversity in universities across the US, with the vast majority of faculty leaning left of center. Universities emphasis on the usage of the term diversity to denote demographic subtypes of diversity could be indicative of a majority power structure in the Academy which tries to hinder the fostering of viewpoint diversity by steering diversity efforts towards demographic interpretations of the word. At the very least, the results of this work suggest that universities, as judged from the way they use language in their own online institutional profiles, prioritize demographic types of diversity around variety of external appearance cues over intellectual heterogeneity.