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This paper introduces a novel measure of inequality of opportunity (IOp) in India, by comparing both ex-ante and ex-post results, which aligns with Roemer’s (1998) equality of opportunity, theory. The study utilizes data-driven machine learning algorithms, namely conditional inference tree and conditional inference forest, to measure ex-ante IOp, and a transformation tree to estimate ex-post IOp. The findings indicate that, according to the ex-ante approach, approximately 58–61 percent of the overall income inequality can be attributed to variations in circumstances, while around 46 percent of the overall income inequality is explained by differences in the degree of efforts. The results from the tree-based analysis reveal that parents’ occupation, sector (rural–urban areas), and geographical regions are the primary circumstances contributing to IOp, which is further confirmed by the Shapley decomposition exercise. Specifically, individuals residing in rural areas in the eastern and central parts of the country, whose parents are employed in low-skilled and unskilled occupations, and have below secondary and no formal education, and who belong to marginalized social groups, exhibit significantly lower average income. Consequently, it is crucial to implement regional-level development policies that specifically target marginalized groups in order to foster a more equitable society and mitigate overall income inequality.

Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently on large and useful classes of problems by harnessing general theory of hypothesis testing in exponential families, but these methods have their limitations. Perhaps most immediate is the gap between theory and practice: implementing the exact theoretical prescription in realistic situations—for example, when new data arrives and inference needs to be adjusted accordingly—may be a prohibitive task. In this paper, we propose a Bayesian framework for carrying out inference after variable selection. Our framework is very flexible in the sense that it naturally accommodates different models for the data instead of requiring a case-by-case treatment. This flexibility is achieved by considering the full selective likelihood function where, crucially, we propose a novel and nontrivial approximation to the exact but intractable expression. The advantages of our methods in practical data analysis are demonstrated in an application to HIV drug-resistance data.

Adaptive experiments have design features that adapt to the accumulating data and are therefore informative about the parameter of interest. As a consequence, the overall information in an adaptive experiment is a combination of information from two sources, the realized design and the observed outcomes. This paper presents a general framework for the analysis of adaptive experiments, based on the decomposition of overall information into design information and outcome information. Likelihood inference is discussed, beginning with assumptions that guarantee insensitivity of the likelihood to the adaptive design. We then focus on the relative merits of unconditional and conditional inference. Although conditional inference is inefficient due to the nonancillary design, unconditional inference may be biased conditional on the realized design. Identifying such conditional bias in a given experiment is a motivation of the proposed framework. We show that conditional bias stems from correlation between the total information and the design information, and that this bias is most pronounced in samples where the design information is inconsistent with the outcome information. Thus, by viewing the unconditional likelihood as the aggregation of information from a design likelihood and a conditional likelihood, we can use meta-analysis principles to assess heterogeneity between the two information sources. When such heterogeneity is detected, conditional inference may be more appropriate. Interpretation from a Bayesian perspective is also discussed.

This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a sufficient statistic for this nuisance parameter in a Gaussian problem and propose conditional tests. These conditional tests have uniformly correct asymptotic size for a large class of models and test statistics. We apply our approach to construct tests based on quasilikelihood ratio statistics, which we show are efficient in strongly identified models and perform well relative to existing alternatives in two examples.

In comparing two treatments via a randomized clinical trial, the analysis of covariance (ANCOVA) technique is often utilized to estimate an overall treatment effect. The ANCOVA is generally perceived as a more efficient procedure than its simple two sample estimation counterpart. Unfortunately, when the ANCOVA model is nonlinear, the resulting estimator is generally not consistent. Recently, various nonparametric alternatives to the ANCOVA, such as the augmentation methods, have been proposed to estimate the treatment effect by adjusting the covariates. However, the properties of these alternatives have not been studied in the presence of treatment allocation imbalance. In this article, we take a different approach to explore how to improve the precision of the naive two-sample estimate even when the observed distributions of baseline covariates between two groups are dissimilar. Specifically, we derive a bias-adjusted estimation procedure constructed from a conditional inference principle via relevant ancillary statistics from the observed covariates. This estimator is shown to be asymptotically equivalent to an augmentation estimator under the unconditional setting. We utilize the data from a clinical trial for evaluating a combination treatment of cardiovascular diseases to illustrate our findings.

Background The random forest (RF) method is a commonly used tool for classification with high dimensional data as well as for ranking candidate predictors based on the so-called random forest variable importance measures (VIMs). However the classification performance of RF is known to be suboptimal in case of strongly unbalanced data, i.e. data where response class sizes differ considerably. Suggestions were made to obtain better classification performance based either on sampling procedures or on cost sensitivity analyses. However to our knowledge the performance of the VIMs has not yet been examined in the case of unbalanced response classes. In this paper we explore the performance of the permutation VIM for unbalanced data settings and introduce an alternative permutation VIM based on the area under the curve (AUC) that is expected to be more robust towards class imbalance. Results We investigated the performance of the standard permutation VIM and of our novel AUC-based permutation VIM for different class imbalance levels using simulated data and real data. The results suggest that the new AUC-based permutation VIM outperforms the standard permutation VIM for unbalanced data settings while both permutation VIMs have equal performance for balanced data settings. Conclusions The standard permutation VIM loses its ability to discriminate between associated predictors and predictors not associated with the response for increasing class imbalance. It is outperformed by our new AUC-based permutation VIM for unbalanced data settings, while the performance of both VIMs is very similar in the case of balanced classes. The new AUC-based VIM is implemented in the R package party for the unbiased RF variant based on conditional inference trees. The codes implementing our study are available from the companion website: http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/070_drittmittel/janitza/index.html

Variational Autoencoders (VAEs) are a popular generative model, but one in which conditional inference can be challenging. If the decomposition into query and evidence variables is fixed, conditionally trained VAEs provide an attractive solution. However, to efficiently support arbitrary queries over pre-trained VAEs when the query and evidence are not known in advance, one is generally reduced to MCMC sampling methods that can suffer from long mixing times. In this paper, we propose an idea of efficiently training small conditional prior networks to approximate the latent distribution of the VAE after conditioning on an evidence assignment; this permits generating query samples without retraining the full VAE. We experimentally evaluate three variations of conditional prior networks showing that (i) they can be quickly optimized for different decompositions of evidence and query and (ii) they quantitatively and qualitatively outperform existing state-of-the-art methods for conditional inference in pre-trained VAEs.

Generalized pivotal quantities (GPQs) and generalized confidence intervals (GCIs) have proven to be useful tools for making inferences in many practical problems. Although GCIs are not guaranteed to have exact frequentist coverage, a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so as to be useful in practice. In this article we single out a subclass of generalized pivotal quantities, which we call fiducial generalized pivotal quantities (FGPQs), and show that under some mild conditions, GCIs constructed using FGPQs have correct frequentist coverage, at least asymptotically. We describe three general approaches for constructing FGPQs-a recipe based on invertible pivotal relationships, and two extensions of it-and demonstrate their usefulness by deriving some previously unknown GPQs and GCIs. It is fair to say that nearly every published GCI can be obtained using one of these recipes. As an interesting byproduct of our investigations, we note that the subfamily of fiducial generalized pivots has a close connection with fiducial inference proposed by R. A. Fisher. This is why we refer to the proposed generalized pivots as fiducial generalized pivotal quantities. We demonstrate these concepts using several examples.

Today, permutation tests represent a powerful and increasingly widespread tool of statistical inference for hypothesis-testing problems. To the best of our knowledge, a review of the application of permutation tests for complex data in practical data analysis for hypothesis testing is missing. In particular, it is essential to review the application of permutation tests in two-sample or multi-sample problems and in regression analysis. The aim of this paper is to consider the main scientific contributions on the subject of permutation methods for hypothesis testing in the mentioned fields. Notes on their use to address the problem of missing data and, in particular, right-censored data, will also be included. This review also tries to highlight the limits and advantages of the works cited with a critical eye and also to provide practical indications to researchers and practitioners who need to identify flexible and distribution-free solutions for the most disparate hypothesis-testing problems.

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including (time-varying) rare-disaster risk models and long-run risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro-finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross-equation restrictions. We apply the proposed conditional specification test to the evaluation of a time-varying rare-disaster risk model and the construction of robust model uncertainty sets.