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Logistic Regression in Rare Events Data
, 1999
"... We study rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, such as wars, vetoes, cases of political activism, or epidemiological infections) than zeros (“nonevents”). In many literatures, these variables have proven difficult to explain and predict, a ..."
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Cited by 56 (4 self)
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We study rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, such as wars, vetoes, cases of political activism, or epidemiological infections) than zeros (“nonevents”). In many literatures, these variables have proven difficult to explain and predict, a problem that seems to have at least two sources. First, popular statistical procedures, such as logistic regression, can sharply underestimate the probability of rare events. We recommend corrections that outperform existing methods and change the estimates of absolute and relative risks by as much as some estimated effects reported in the literature. Second, commonly used data collection strategies are grossly inefficient for rare events data. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables, such as in international conflict data with more than a quartermillion dyads, only a few of which are at war. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all available events (e.g., wars) and a tiny fraction of nonevents (peace). This enables scholars to save as much as 99 % of their (nonfixed) data collection costs or to collect much more meaningful explanatory
Reference analysis
 In Handbook of Statistics 25
, 2005
"... This chapter describes reference analysis, a method to produce Bayesian inferential statements which only depend on the assumed model and the available data. Statistical information theory is used to define the reference prior function as a mathematical description of that situation where data would ..."
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Cited by 13 (2 self)
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This chapter describes reference analysis, a method to produce Bayesian inferential statements which only depend on the assumed model and the available data. Statistical information theory is used to define the reference prior function as a mathematical description of that situation where data would best dominate prior knowledge about the quantity of interest. Reference priors are not descriptions of personal beliefs; they are proposed as formal consensus prior functions to be used as standards for scientific communication. Reference posteriors are obtained by formal use of Bayes theorem with a reference prior. Reference prediction is achieved by integration with a reference posterior. Reference decisions are derived by minimizing a reference posterior expected loss. An information theory based loss function, the intrinsic discrepancy, may be used to derive reference procedures for conventional inference problems in scientific investigation, such as point estimation, region estimation and hypothesis testing.
Financial options and statistical prediction intervals
 ANN. STATIST
, 2003
"... The paper shows how to convert statistical prediction sets into worst case hedging strategies for derivative securities. The prediction sets can, in particular, be ones for volatilities and correlations of the underlying securities, and for interest rates. This permits a transfer of statistical conc ..."
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Cited by 10 (5 self)
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The paper shows how to convert statistical prediction sets into worst case hedging strategies for derivative securities. The prediction sets can, in particular, be ones for volatilities and correlations of the underlying securities, and for interest rates. This permits a transfer of statistical conclusions into prices for options and similar financial instruments. A prime feature of our results is that one can construct the trading strategy as if the prediction set had a 100 % probability. If, in fact, the set has probability 1−α, the hedging strategy will work with at least the same probability. Different types of prediction regions are considered. The starting value A0 for the trading strategy corresponding to the 1 − α prediction region is a form of long term value at risk. At the same time, A0 is coherent.
Bayesian analysis of extreme values by mixture modeling
 Extremes
, 2003
"... Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific l ..."
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Cited by 8 (1 self)
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Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a wellknown insurance company over a 15year period.
Measuring Risk With Extreme Value Theory
 Extremes and Integrated Risk Management
, 2000
"... this paper, but taking account of the variation in t estimated for the GARCH process. In another recent paper, Tsay (1999) has used methods similar to those of the present paper, but allowing the extreme value parameters to depend on daily interest rates. ..."
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Cited by 7 (0 self)
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this paper, but taking account of the variation in t estimated for the GARCH process. In another recent paper, Tsay (1999) has used methods similar to those of the present paper, but allowing the extreme value parameters to depend on daily interest rates.
Explaining Rare Events in International Relations
, 2000
"... Some of the most important phenomena in international conflict are coded as "rare events data," binary dependent variables with dozens to thousands of times fewer events, such as wars, coups, etc., than "nonevents". Unfortunately, rare events data are difficult to explain and predict, a problem that ..."
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Cited by 5 (2 self)
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Some of the most important phenomena in international conflict are coded as "rare events data," binary dependent variables with dozens to thousands of times fewer events, such as wars, coups, etc., than "nonevents". Unfortunately, rare events data are difficult to explain and predict, a problem that seems to have at least two sources. First, and most importantly, the data collection strategies used in international conflict are grossly inefficient. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all available events (e.g., wars) and a tiny fraction of nonevents (peace). This enables scholars to save as much as 99% of their (nonfixed) data collection costs, or to collect much more meaningful explanatory variables. Second, logistic regression, and other commonly ...
Inferring Welfare Maximizing Treatment Assignment under Budget Constraints. NBER Working Paper No
, 2008
"... This paper concerns the problem of allocating a binary treatment among a target population based on discrete and continuous observed covariates. The goal is to maximize the mean social utlity of an eventual outcome when a budget constraint limits what fraction of the population can be treated. We pr ..."
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Cited by 2 (0 self)
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This paper concerns the problem of allocating a binary treatment among a target population based on discrete and continuous observed covariates. The goal is to maximize the mean social utlity of an eventual outcome when a budget constraint limits what fraction of the population can be treated. We propose a treatment allocation procedure based on sample data from randomized treatment assignment. We examine this procedure in the light of statistical decision theory and derive asymptotic frequentist properties of the allocation rule and the welfare generated from it. The resulting distribution theory is used to conduct inference on the welfare loss resulting from restricted covariate choice and on the dual value, i.e. the minimum resources needed to attain aspecific average welfare via efficient treatment assignment. The methodology is applied to the optimal provision of antimalaria bed net subsidies, using data from a randomized experiment conducted in western Kenya. We find that a government which can afford to distribute bed net subsidies to only 50 % of its target population can, with an efficient allocation rule based on multiple covariates, increase bednet use by 8 percentage points (25 percent) relative to random allocation and by 4 percentage points (11 percent) relative to one based on wealth only. Our methods do not rely on functional form assumptions and can be extended to situations encompassing conditional cash transfers, imperfect treatment takeup and spillover effects on noneligibles. 1
$EVWUDFW Operational Risk Capital Allocation and Integration of Risks
"... framework which is based upon the assumption that for D ZHOO PDQDJHG bank market and credit risk management yield sufficient capital provision against these risks and give a threshold for the identification of the extreme losses being characterized as operational from the regulators ’ viewpoint. Our ..."
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Cited by 1 (0 self)
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framework which is based upon the assumption that for D ZHOO PDQDJHG bank market and credit risk management yield sufficient capital provision against these risks and give a threshold for the identification of the extreme losses being characterized as operational from the regulators ’ viewpoint. Our capital allocation rule links operational with market and credit risks and provides a risk measure for the tails of loss distributions at both the firmwide and business unit levels. 1