Conventional Statistical Inference Research Articles

Robust Semi-Parametric Inference for Two-Stage Production Models: A Beta Regression Approach

The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of interest affect the performance of productive units. However, some of these procedures, particularly those based on conventional statistical inference, generate inconsistent estimates when dealing with incoherent data-generating processes. This inconsistency arises due to the efficiency scores being limited to the unit interval, and the estimated scores often exhibit serial correlation and have limited observations. To address such inconsistency, several strategies have been suggested, with the most well-known being an algorithm based on a parametric bootstrap procedure using the truncated normal distribution and its regression model. In this work, we present a modification of this algorithm that utilizes the beta distribution and its regression structure. The beta model allows for better accommodation of asymmetry in the data distribution. Our proposed algorithm introduces inferential characteristics that are superior to the original algorithm, resulting in a more statistically coherent data-generating process and improving the consistency property. We have conducted computational experiments that demonstrate the improved results achieved by our proposal.

Inference on the best policies with many covariates

Understanding the impact of the most effective policies or treatments on a response variable of interest is desirable in many empirical works in economics, statistics and other disciplines. Due to the widespread winner’s curse phenomenon, conventional statistical inference assuming that the top policies are chosen independent of the random sample may lead to overly optimistic evaluations of the best policies. In recent years, given the increased availability of large datasets, such an issue can be further complicated when researchers include many covariates to estimate the policy or treatment effects in an attempt to control for potential confounders. In this manuscript, to simultaneously address the above-mentioned issues, we propose a resampling-based procedure that not only lifts the winner’s curse in evaluating the best policies observed in a random sample, but also is robust to the presence of many covariates. The proposed inference procedure yields accurate point estimates and valid frequentist confidence intervals that achieve the exact nominal level as the sample size goes to infinity for multiple best policy effect sizes. We illustrate the finite-sample performance of our approach through Monte Carlo experiments and two empirical studies, evaluating the most effective policies in charitable giving and the most beneficial group of workers in the National Supported Work program.

Exact results on high-dimensional linear regression via statistical physics.

It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation techniques that call for rigorous results against which they can be tested. In this context, the simplest case of high-dimensional linear regression has acquired significant new relevance and attention. In this paper we use the statistical physics perspective on inference to derive several exact results for linear regression in the high-dimensional regime.

Cavalier Use of Inferential Statistics Is a Major Source of False and Irreproducible Scientific Findings

I uncover previously underappreciated systematic sources of false and irreproducible results in natural, biomedical and social sciences that are rooted in statistical methodology. They include the inevitably occurring deviations from basic assumptions behind statistical analyses and the use of various approximations. I show through a number of examples that (a) arbitrarily small deviations from distributional homogeneity can lead to arbitrarily large deviations in the outcomes of statistical analyses; (b) samples of random size may violate the Law of Large Numbers and thus are generally unsuitable for conventional statistical inference; (c) the same is true, in particular, when random sample size and observations are stochastically dependent; and (d) the use of the Gaussian approximation based on the Central Limit Theorem has dramatic implications for p-values and statistical significance essentially making pursuit of small significance levels and p-values for a fixed sample size meaningless. The latter is proven rigorously in the case of one-sided Z test. This article could serve as a cautionary guidance to scientists and practitioners employing statistical methods in their work.

Extraction of Protein Conformational Modes from Distance Distributions Using Structurally Imputed Bayesian Data Augmentation.

Protein conformational changes are known to play important roles in assorted biochemical and biological processes. Driven by thermal motions of surrounding solvent molecules, such a structural remodeling often occurs stochastically. Yet, regardless of how random the conformational reconfiguration may appear, it could in principle be described by a linear combination of a set of orthogonal modes which, in turn, are contained in the intramolecular distance distributions. The central challenge is how to obtain the distribution. This contribution proposes a Bayesian data-augmentation scheme to extract the predominant modes from only few distance distributions, be they from computational sampling or directly from experiments such as single-molecule Förster-type resonance energy transfer (smFRET). The inference of the complete protein structure from insufficient data was recognized as isomorphic to the missing-data problem in Bayesian statistical learning. Using smFRET data as an example, the missing coordinates were deduced, given protein structural constraints and multiple but limited number of smFRET distances; the Boltzmann weighing of each inferred protein structure was then evaluated using computational modeling to numerically construct the posterior density for the global protein conformation. The conformational modes were then determined from the iteratively converged overall conformational distribution using principal component analysis. Two examples were presented to illustrate these basic ideas as well as their practical implementation. The scheme described herein was based on the theory behind the powerful Tanner-Wang algorithm that guarantees convergence to the true posterior density. However, instead of assuming a mathematical model to calculate the likelihood as in conventional statistical inference, here the protein structure was treated as a statistical parameter and was imputed from the numerical likelihood function based on structural information, a probability model-free method. The framework put forth here is anticipated to be generally applicable, offering a new way to articulate protein conformational changes in a quantifiable manner.

Experimental technique for the performance evaluation and optimization of 1/f noise spectrum investigation in electron devices

Abstract In this paper, a fast and systematic experimental technique is proposed, which is devoted to the performance evaluation of power spectral density non-parametric estimators, in the framework of 1/f-noise bias-varying investigation at the ports of semiconductor electron devices. The methodology, which allows to overcome the need both for cumbersome analytical computation of a-priori moments, and non-reliable and time-consuming conventional statistical inference, provides the performance of the estimator and related parameters under investigation from a single realization, by exploiting the frequency stationarity of non-parametric algorithms in the relative and asymptotical sense. The technique has been applied to the case-study of a power MOSFET, by considering Bartlett, Welch and circular Welch estimators and different time windows and data record segmentation strategies, in order to verify its capabilities and, in particular, to identify the optimal non-parametric estimation of 1/f noise spectrum. In addition, results obtained by means of conventional statistical inference are compared to the estimates provided by the technique proposed, to the aim of further experimental assessment.

Statistical Challenges in the Design of Late-Stage Cancer Immunotherapy Studies.

The past several years have witnessed a revival of interest in cancer immunology and immunotherapy owing to striking immunologic and clinical responses to immune-directed anticancer therapies and leading to the selection of "Cancer Immunotherapy" as the 2013 Breakthrough of the Year by Science. But statistical challenges exist at all phases of clinical development. In phase III trials of immunotherapies, survival curves have been shown to demonstrate delayed clinical effects, as well as long-term survival. These unique survival kinetics could lead to loss of statistical power and prolongation of study duration. Statistical assumptions that form the foundations for conventional statistical inference in the design and analysis of phase III trials, such as exponential survival and proportional hazards, require careful considerations. In this article, we describe how the unique characteristics of patient response to cancer immunotherapies will impact our strategies on statistical design and analysis in late-stage drug development.

Clinical and practical importance vs statistical significance: Limitations of conventional statistical inference

Background: Decisions about support for therapies are often made using statistical inference in light of data. The dominant approach is null hypothesis significance testing (NHST). Applied correctly, NHST provides a procedure for making dichotomous decisions about zero-effect null hypotheses with known and controlled error rates. Type I and Type II error rates must be specified in advance, and the latter controlled by a priori sample size calculation. However, NHST does not provide the probability of hypotheses or the strength of support for hypotheses in light of data. The outcomes allow conclusions about the existence of non-zero effects, but provide no information about the likely size of true effects or their practical or clinical value. Content: Magnitude-based inference allows researchers to estimate the ‘true’ or large sample magnitude of effects with a specified likelihood, and how likely they are to exceed an effect magnitude of practical or clinical importance. This approach integrates the elements of subjective judgement that are central to clinical practice into a formal analysis of data, which facilitates more considered and enlightened interpretations of data, and avoids rejection of possibly highly beneficial therapies that are not statistically significant. Conclusions: Magnitude-based inference is gaining acceptance, but progress will be hastened if the shortcomings of NHST are understood.

Statistical Inference After Model Selection

Conventional statistical inference requires that a model of how the data were generated be known before the data are analyzed. Yet in criminology, and in the social sciences more broadly, a variety of model selection procedures are routinely undertaken followed by statistical tests and confidence intervals computed for a “final” model. In this paper, we examine such practices and show how they are typically misguided. The parameters being estimated are no longer well defined, and post-model-selection sampling distributions are mixtures with properties that are very different from what is conventionally assumed. Confidence intervals and statistical tests do not perform as they should. We examine in some detail the specific mechanisms responsible. We also offer some suggestions for better practice and show though a criminal justice example using real data how proper statistical inference in principle may be obtained.

LIMIT THEORY FOR EXPLOSIVELY COINTEGRATED SYSTEMS

A limit theory is developed for multivariate regression in an explosive cointegrated system. The asymptotic behavior of the least squares estimator of the cointegrating coefficients is found to depend upon the precise relationship between the explosive regressors. When the eigenvalues of the autoregressive matrix Θ are distinct, the centered least squares estimator has an exponential Θn rate of convergence and a mixed normal limit distribution. No central limit theory is applicable here, and Gaussian innovations are assumed. On the other hand, when some regressors exhibit common explosive behavior, a different mixed normal limiting distribution is derived with rate of convergence reduced to $\sqrt{n}$ . In the latter case, mixed normality applies without any distributional assumptions on the innovation errors by virtue of a Lindeberg type central limit theorem. Conventional statistical inference procedures are valid in this case, the stationary convergence rate dominating the behavior of the least squares estimator.

Measuring Firm Performance By Using Linear and Non-Parametric Quantile Regressions

Summary Quantile regression models are examined from the standpoint of their suitability to analyse company profitability. Some linear and non-linear (B-spline) structures are proposed. Linear conditional quantile models provide an intuitive framework which permits conventional statistical inference tools to be applied. Non-parametric spline-based quantile regression is a flexible approach, allowing a different grade of curvature for each conditional quantile, thus providing the possibility of capturing certain non-linear effects that are predicted by economic theory. The behaviour of these variants of the quantile framework is tested on a representative database, which was obtained from the Spanish book publishing industry. Our results confirm the usefulness of the quantile regression approach. Linear models seem to provide suitable descriptions for the behaviour of average performing firms, whereas non-parametric estimates provide the best fit for the extreme conditional quantiles (i.e. companies which exhibit the highest and the lowest performance in terms of profitability).

A fractal approach for detecting spatial hierarchy and structure on mussel beds

Within beds of blue mussel (Mytilus edulis L.), individuals are aggregated into small patches, which in turn are incorporated into bigger patches, revealing a complex hierarchy of spatial structure. The present study was done to find the different scales of variation in the distribution of mussel biomass, and to describe the spatial heterogeneity on these scales. The three approaches compared for this purpose were fractal analysis, spatial autocorrelation and hierarchical (or nested) analysis of variances (ANOVA). The complexity (i.e. patchiness) of mussel aggregations was described with fractal dimension, calculated with the semivariogram method. Three intertidal mussel beds were studied on the west coast of Sweden. The distribution of wet biomass was studied along transects up to 128 m. The average biomasses of blue mussels on the three mussel beds were 1825±210, 179±21 and 576±66 g per0.1 m2, respectively, and the fractal dimensions of the mussel distribution were 1.726±0.010, 1.842±0.014 and 1.939±0.029 on transects 1–3, respectively. Distributions of mussels revealed multiscaling behaviour. The fractal dimension significantly changed twice on different scales on the first bed (thus showing three scaling regions), the second and third beds revealed two and three scaling regions, respectively. High fractal dimension was followed by significant spatial autocorrelation on smaller scales. The fractal analysis detects the multiple scaling regions of spatial variance even when the spatial structure may not be distinguished significantly by conventional statistical inference. The study shows that the fractal analysis, the spatial autocorrelation analysis and the hierarchical ANOVA give complementary information about the spatial variability in mussel populations.

Statistical significance and fragility criteria for assessing a difference of two proportions

This paper compares the traditional methods of statistical inference on the data from biomedical studies with a proposed index of fragility in the results. In general, for any given study there are 8 possible combinations of conclusions regarding statistical significance, quantitative significance and fragility. The 8 possibilities are considered in turn with respect to how studies in each group might be interpreted. Numerical examples show that not all 8 possibilities need be attainable with a given study design, and that the relative likelihood of them occurring can vary widely. It is concluded that the fragility index may be a useful adjunct to conventional statistical inference, with certain intuitive appeal, but that more empirical experience is needed with the fragility method.

Joint Confidence Intervals for Income Shares and Lorenz Curves

In a recent paper, Beach and Davidson [1983] extended the principles of statistical inference to Lorenz curves and income shares by establishing the (asymptotic) distribution and covariance structure of a vector of Lorenz curve ordinates corresponding to a set of quantile abscissae. One can thus use the Lorenz curve and income shares, no longer just as descriptive devices for summarizing distribution information, but now also as analytical tools for comparing alternative distributions and carrying out conventional statistical inference on them. It would clearly be desirable, however, to extend and complement this work by providing a method for computing a set of joint confidence intervals about these income shares and for illustrating graphically a joint confidence band about a set of estimated Lorenz curve ordinates. The present paper provides a new and simple technique for doing this. When analyzing differences between sets of income shares or Lorenz curves, one typically wants to elicit more detailed information than is provided by a standard joint chi-square test on the overall set of shares. That is, when the hypothesis of two sets of shares being the same is rejected, we generally want to know further which particular differences in shares are different from zero, and of these nonzero differences which are positive and which negative (Savin [1980]). A natural way of providing such information is through multiple comparison procedures developed in this paper. In a recent work, Richmond [1982] has developed a general method of finding multiple comparison intervals that is particularly suited to the present problem and in this situation appears to dominate other conventional alternatives. In contrast, for example, to Scheff&'s S-projection method, Richmond's approach focuses on a set of primary points of interest (income shares) among a more general set of points (including the Lorenz curve ordinates) and optimizes the joint confidence interval lengths on this primary set of points. Since estimated Lorenz curve ordinates are built up from underlying income shares, these shares (perhaps further supplemented) are natural choices for the primary set. The method, however, also provides a joint confidence band that geometrically bounds the set of Lorenz curve ordinates (and interpolated segments between them). The present