arXiv subjects

Aris Spanos

Publications and source records attributed to Aris Spanos.

5 recordsLinked to original sources

arXiv2016

Why the Decision Theoretic Perspective Misrepresents Frequentist Inference: 'Nuts and Bolts' vs. Learning from Data

The primary objective of this paper is to revisit and make a case for the merits of R.A. Fisher's objections to the decision-theoretic framing of frequentist inference. It is argued that this framing is congruent with the Bayesian but incongruent with the frequentist inference. It provides the Bayesian approach with a theory of optimal inference, but it misrepresents the theory of optimal frequentist inference by framing inferences solely in terms of the universal quantifier `for all values of theta in the parameter space'. This framing is at odds with the primary objective of model-based frequentist inference, which is to learn from data about the true value of theta (unknown parameter(s)); the one that gave rise to the particular data. The frequentist approach relies on factual (estimation, prediction), as well as hypothetical (testing) reasoning whose primary aim is to learn from data about the true theta. The paper calls into question the appropriateness of admissibility and reassesses Stein's paradox as it relates to the capacity of frequentist estimators to pinpoint the true theta. The paper also compares and contrasts loss-based errors with traditional frequentist errors, such as coverage, type I and II; the former are attached to θ, but the latter to the inference procedure itself.

stat.ME↗

arXiv2016

Revisiting Simpson's Paradox: a statistical misspecification perspective

The primary objective of this paper is to revisit Simpson's paradox using a statistical misspecification perspective. It is argued that the reversal of statistical associations is sometimes spurious, stemming from invalid probabilistic assumptions imposed on the data. The concept of statistical misspecification is used to formalize the vague term `spurious results' as `statistically untrustworthy' inference results. This perspective sheds new light on the paradox by distingusing between statistically trustworthy vs. untrustworthy association reversals. It turns out that in both cases there is nothing counterintuitive to explain or account for. This perspective is also used to revisit the causal `resolution' of the paradox in an attempt to delineate the modeling and inference issues raised by the statistical misspecification perspective. The main arguments are illustrated using both actual and hypothetical data from the literature, including Yule's "nonsense-correlations" and the Berkeley admissions study.

stat.ME↗

arXiv2013

Revisiting the Neyman-Scott model: an Inconsistent MLE or an Ill-defined Model?

The Neyman and Scott (1948) model is widely used to demonstrate a serious weakness of the Maximum Likelihood (ML) method: it can give rise to inconsistent estimators. The primary objective of this paper is to revisit this example with a view to demonstrate that the culprit for the inconsistent estimation is not the ML method but an ill-defined statistical model. It is also shown that a simple recasting of this model renders it well-defined and the ML method gives rise to consistent and asymptotically efficient estimators.

stat.ME↗

arXiv2013

The Two Envelope Problem: a Paradox or Fallacious Reasoning?

The primary objective of this note is to revisit the two envelope problem and propose a simple resolution. It is argued that the paradox arises from the ambiguity associated with the money content $x of the chosen envelope. When X=x is observed it is not know which one of the two events, X=θ or X=2θ, has occurred. Moreover, the money in the other envelope Y is not independent of X; when one contains θ the other contains 2θ. By taking these important features of the problem into account, the paradox disappears.

stat.ME↗

arXiv2006

Where do statistical models come from? Revisiting the problem of specification

R. A. Fisher founded modern statistical inference in 1922 and identified its fundamental problems to be: specification, estimation and distribution. Since then the problem of statistical model specification has received scant attention in the statistics literature. The paper traces the history of statistical model specification, focusing primarily on pioneers like Fisher, Neyman, and more recently Lehmann and Cox, and attempts a synthesis of their views in the context of the Probabilistic Reduction (PR) approach. As argued by Lehmann [11], a major stumbling block for a general approach to statistical model specification has been the delineation of the appropriate role for substantive subject matter information. The PR approach demarcates the interrelated but complemenatry roles of substantive and statistical information summarized ab initio in the form of a structural and a statistical model, respectively. In an attempt to preserve the integrity of both sources of information, as well as to ensure the reliability of their fusing, a purely probabilistic construal of statistical models is advocated. This probabilistic construal is then used to shed light on a number of issues relating to specification, including the role of preliminary data analysis, structural vs. statistical models, model specification vs. model selection, statistical vs. substantive adequacy and model validation.

math.ST↗