scholarly journals Using a Satisficing Model of Experimenter Decision-Making to Guide Finite-Sample Inference for Compromised Experiments

2021 ◽  
Author(s):  
James J Heckman ◽  
Ganesh Karapakula
Keyword(s):  
Program Effectiveness ◽  
Small Sample ◽  
Economic Approach ◽  
Random Assignment ◽  
Finite Sample ◽  
Worst Case ◽  
Null Distributions ◽  
Covariate Balance ◽  
Social Experiments ◽  
Finite Sample Inference

Abstract This paper presents a simple decision-theoretic economic approach for analyzing social experiments with compromised random assignment protocols that are only partially documented. We model administratively constrained experimenters who satisfice in seeking covariate balance. We develop design-based small-sample hypothesis tests that use worst-case (least favorable) randomization null distributions. Our approach accommodates a variety of compromised experiments, including imperfectly documented re-randomization designs. To make our analysis concrete, we focus much of our discussion on the influential Perry Preschool Project. We reexamine previous estimates of program effectiveness using our methods. The choice of how to model reassignment vitally affects inference.

scholarly journals W.S. Gosset and Some Neglected Concepts in Experimental Statistics: Guinnessometrics II

2011 ◽  
Vol 6 (2) ◽  
pp. 252-277 ◽  
Author(s):  
Stephen T. Ziliak
Keyword(s):  
Experimental Design ◽  
Sample Size ◽  
Large Scale ◽  
Statistical Significance ◽  
Small Sample ◽  
Small Samples ◽  
Significant Advance ◽  
Economic Approach ◽  
Barley Malt ◽  
Level Of Significance

AbstractStudent's exacting theory of errors, both random and real, marked a significant advance over ambiguous reports of plant life and fermentation asserted by chemists from Priestley and Lavoisier down to Pasteur and Johannsen, working at the Carlsberg Laboratory. One reason seems to be that William Sealy Gosset (1876–1937) aka “Student” – he of Student'st-table and test of statistical significance – rejected artificial rules about sample size, experimental design, and the level of significance, and took instead an economic approach to the logic of decisions made under uncertainty. In his job as Apprentice Brewer, Head Experimental Brewer, and finally Head Brewer of Guinness, Student produced small samples of experimental barley, malt, and hops, seeking guidance for industrial quality control and maximum expected profit at the large scale brewery. In the process Student invented or inspired half of modern statistics. This article draws on original archival evidence, shedding light on several core yet neglected aspects of Student's methods, that is, Guinnessometrics, not discussed by Ronald A. Fisher (1890–1962). The focus is on Student's small sample, economic approach to real error minimization, particularly in field and laboratory experiments he conducted on barley and malt, 1904 to 1937. Balanced designs of experiments, he found, are more efficient than random and have higher power to detect large and real treatment differences in a series of repeated and independent experiments. Student's world-class achievement poses a challenge to every science. Should statistical methods – such as the choice of sample size, experimental design, and level of significance – follow the purpose of the experiment, rather than the other way around? (JEL classification codes: C10, C90, C93, L66)

scholarly journals Finite-sample genome-wide regression p-values (GWRPV) with a non-normally distributed phenotype

2017 ◽  
Author(s):  
Gregory Connor ◽  
Michael O’Neill
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Mixture Distribution ◽  
Small Sample ◽  
P Value ◽  
Finite Sample ◽  
P Values ◽  
Genome Wide ◽  
Normally Distributed

AbstractThis paper derives the exact finite-sample p-value for univariate regression of a quantitative phenotype on individual genome markers, relying on a mixture distribution for the dependent variable. The p-value estimator conventionally used in existing genome-wide association study (GWAS) regressions assumes a normally-distributed dependent variable, or relies on a central limit theorem based approximation. The central limit theorem approximation is unreliable for GWAS regression p-values, and measured phenotypes often have markedly non-normal distributions. A normal mixture distribution better fits observed phenotypic variables, and we provide exact small-sample p-values for univariate GWAS regressions under this flexible distributional assumption. We illustrate the adjustment using a years-of-education phenotypic variable.

scholarly journals QTc interval in patients with schizophrenia receiving antipsychotic treatment as monotherapy or polypharmacy

CNS Spectrums ◽  
2017 ◽  
Vol 23 (4) ◽  
pp. 278-283 ◽  
Author(s):  
Anja Elliott ◽  
Thibault Johan Mørk ◽  
Mikkel Højlund ◽  
Thomas Christensen ◽  
Rasmus Jeppesen ◽  
...  
Keyword(s):  
Small Sample Size ◽  
Torsades De Pointes ◽  
Small Sample ◽  
Polymorphic Ventricular Tachycardia ◽  
Antipsychotic Treatment ◽  
Qtc Interval ◽  
Qtc Prolongation ◽  
Worst Case ◽  
Clinical Interviews ◽  
Observational Cohort

ObjectiveAntipsychotics are associated with a polymorphic ventricular tachycardia, torsades de pointes, which, in the worst case, can lead to sudden cardiac death. The QT interval corrected for heart rate (QTc) is used as a clinical proxy for torsades de pointes. The QTc interval can be prolonged by antipsychotic monotherapy, but it is unknown if the QTc interval is prolonged further with antipsychotic polypharmaceutical treatment. Therefore, this study investigated the associations between QTc interval and antipsychotic monotherapy and antipsychotic polypharmaceutical treatment in schizophrenia, and measured the frequency of QTc prolongation among patients.MethodsWe carried out an observational cohort study of unselected patients with schizophrenia visiting outpatient facilities in the region of Central Jutland, Denmark. Patients were enrolled from January of 2013 to June of 2015, with follow-up until June of 2015. Data were collected from clinical interviews and clinical case records.ResultsElectrocardiograms were available for 65 patients, and 6% had QTc prolongation. We observed no difference in average QTc interval for the whole sample of patients receiving no antipsychotics, antipsychotic monotherapy, or antipsychotic polypharmaceutical treatment (p=0.29). However, women presented with a longer QTc interval when receiving polypharmacy than when receiving monotherapy (p=0.01). A limitation of this study was its small sample size.ConclusionsWe recommend an increased focus on monitoring the QTc interval in women with schizophrenia receiving antipsychotics as polypharmacy.

scholarly journals Dynamic Regression and Filtered Data Series: A Laplace Approximation to the Effects of Filtering in Small Samples

1996 ◽  
Vol 12 (3) ◽  
pp. 432-457 ◽  
Author(s):  
Eric Ghysels ◽  
Offer Lieberman
Keyword(s):  
Regression Model ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
Small Sample ◽  
Data Series ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Lagged Dependent Variable ◽  
Dynamic Regression Model

It is common for an applied researcher to use filtered data, like seasonally adjusted series, for instance, to estimate the parameters of a dynamic regression model. In this paper, we study the effect of (linear) filters on the distribution of parameters of a dynamic regression model with a lagged dependent variable and a set of exogenous regressors. So far, only asymptotic results are available. Our main interest is to investigate the effect of filtering on the small sample bias and mean squared error. In general, these results entail a numerical integration of derivatives of the joint moment generating function of two quadratic forms in normal variables. The computation of these integrals is quite involved. However, we take advantage of the Laplace approximations to the bias and mean squared error, which substantially reduce the computational burden, as they yield relatively simple analytic expressions. We obtain analytic formulae for approximating the effect of filtering on the finite sample bias and mean squared error. We evaluate the adequacy of the approximations by comparison with Monte Carlo simulations, using the Census X-11 filter as a specific example

Estimation of Dynamic Term Structure Models

2012 ◽  
Vol 02 (02) ◽  
pp. 1250008 ◽  
Author(s):  
Gregory R. Duffee ◽  
Richard H. Stanton
Keyword(s):  
Maximum Likelihood ◽  
Term Structure ◽  
Empirical Work ◽  
Interest Rate Risk ◽  
Small Sample ◽  
Accurate Estimation ◽  
Parameter Estimates ◽  
Finite Sample ◽  
Term Structure Models ◽  
Finite Sample Properties

We study the finite-sample properties of some of the standard techniques used to estimate modern term structure models. For sample sizes and models similar to those used in most empirical work, we reach three surprising conclusions. First, while maximum likelihood works well for simple models, it produces strongly biased parameter estimates when the model includes a flexible specification of the dynamics of interest rate risk. Second, despite having the same asymptotic efficiency as maximum likelihood, the small-sample performance of Efficient Method of Moments (a commonly used method for estimating complicated models) is unacceptable even in the simplest term structure settings. Third, the linearized Kalman filter is a tractable and reasonably accurate estimation technique, which we recommend in settings where maximum likelihood is impractical.

Tail events in the FX markets since 1740

2014 ◽  
Vol 15 (3) ◽  
pp. 294-311 ◽  
Author(s):  
Kim Abildgren
Keyword(s):  
Exchange Rate ◽  
Small Sample ◽  
Nominal Exchange Rate ◽  
Stress Tests ◽  
Worst Case ◽  
Data Set ◽  
Content Type ◽  
Frequency Distributions ◽  
Quarterly Data ◽  
Tail Events

Purpose – The purpose of this paper is to explore the extent of the so-called “small-sample problem” within quantitative exchange-rate risk management. Design/methodology/approach – The authors take a closer look at the frequency distribution of nominal price changes in the European foreign exchange markets. Findings – The analysis clearly illustrates the risk of seriously underestimating the probability and magnitude of tail events when frequency distributions are derived from fairly short data samples. Practical implications – The authors suggest that financial institutions and regulators should have an eye for the long-term historical perspective when designing sensitivity tests or “worst case” scenarios in relation to risk assessments and stress tests. Originality/value – The authors add to the literature by analysing the distribution of nominal exchange-rate fluctuations on the basis of a unique quarterly data set for ten European exchange-rate pairs covering a time span of 273 years constructed by the authors. To the best of the authors' knowledge this is the first study on nominal exchange-rate changes for a large number of exchange-rate pairs based on quarterly data spanning almost three centuries.

scholarly journals Interpretable Predictive Modeling for Climate Variables with Weighted Lasso

2019 ◽  
Vol 33 ◽  
pp. 1385-1392
Author(s):  
Sijie He ◽  
Xinyan Li ◽  
Vidyashankar Sivakumar ◽  
Arindam Banerjee
Keyword(s):  
Estimation Error ◽  
Climate Science ◽  
Small Sample ◽  
Sea Surface ◽  
Spatial Distance ◽  
Climate Variables ◽  
Finite Sample ◽  
Empirical Performance ◽  
Complex Models ◽  
Surface Location

An important family of problems in climate science focus on finding predictive relationships between various climate variables. In this paper, we consider the problem of predicting monthly deseasonalized land temperature at different locations worldwide based on sea surface temperature (SST). Contrary to popular belief on the trade-off between (a) simple interpretable but inaccurate models and (b) complex accurate but uninterpretable models, we introduce a weighted Lasso model for the problem which yields interpretable results while being highly accurate. Covariate weights in the regularization of weighted Lasso are pre-determined, and proportional to the spatial distance of the covariate (sea surface location) from the target (land location). We establish finite sample estimation error bounds for weighted Lasso, and illustrate its superior empirical performance and interpretability over complex models such as deep neural networks (Deep nets) and gradient boosted trees (GBT). We also present a detailed empirical analysis of what went wrong with Deep nets here, which may serve as a helpful guideline for application of Deep nets to small sample scientific problems.

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