root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

big line bundles over arithmetic varieties 5 equidistribution theory 26 5 1 a generic equidistribution theorem 27 5 2 equidistribution at infinite places 30 5 3 equidistribution at finite places 32 5 4 equidistribution of small subvarieties 35 5 5 equidistribution over algebraic dynamical systems 37 5 6 equidistribution over multiplicative groups 39 5 7 equidistribution theory 41

nonlinear decision weights in choice under uncertainty in most real world decisions consequences are tied explicitly to the outcome of events previous studies of decision making under uncertainty have indicated that the psychological weight attached to an event called a decision weight usually differs from the probability of that event we investigate two sources of nonlinearity of decision weights subadditivity of probability judgments and the overweighting of small probabilities and underweighting of medium and large probabilities these two sources of nonli nearity are combined into a two stage model of choice under uncertainty in the first stage events are taken into subjective probability judgments and the second stage takes probability judgments into decision weights we then characterize the curvature of the decision weights by extending a condition employed by wu and gonzalez 1996 in the domain of risk to the domain of uncertainty and show that the nonlinearity of decision weights can be decomposed into subadditivity of probability judgments and the curvature of the probability weighting function empirical tests support the proposed two stage model and indicate that decision weights are concave then convex more specifically our results lend support for a new property of subjective probability ju dgments interior additivity subadditive at the boundaries but additive away from the boundaries and show that the probability weighting function is inverse s shaped as in wu and gonzalez 1996

a quantitative measurement of regret theory this paper introduces a method to measure regret theory a popular theory of decision under uncertainty regret theory allows for violations of transitivity and it may seem paradoxical to quantitatively measure an intransitive theory we adopt the trade off method and show that it is robust to violations of transitivity our method makes no assumptions about the shape of the functions reflecting utility and regret it can be performed at the individual level taking account of preference heterogeneity our data support the main assumption of regret theory that people are disproportionately averse to large regrets even when event splitting effects are controlled for the findings are robust similar results were obtained in two measurements using different stimuli the data support the reliability of the trade off method its measurements could be replicated using different stimuli and were not susceptible to strategic responding

matching on the estimated propensity score propensity score matching estimators rosenbaum and rubin 1983 are widely used in evaluation research to estimate average treatment effects in this article we derive the large sample distribution of propensity score matching estimators our derivations take into account that the propensity score is itself estimated in a first step prior to matching we prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect ate and the average treatment effect on the treated atet the adjustment for the ate estimator is negative or zero in some special cases implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples however for the atet estimator the sign of the adjustment term depends on the data generating process and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small

uniformly semiparametric efficient estimation of treatment effects with a continuous treatment this article studies identification estimation and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption we show identification of the parameters of interest the dose response functions under the assumption that selection to treatment is based on observables we propose a semiparametric two step estimator and consider estimation of the dose response functions through moment restriction models with generalized residual functions that are possibly nonsmooth this general formulation includes average and quantile treatment effects as special cases the asymptotic properties of the estimator are derived namely uniform consistency weak convergence and semiparametric efficiency we also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice monte carlo simulations show that the proposed methods have good finite sample properties finally we apply the proposed

robust confidence intervals for average treatment effects under limited overlap limited overlap between the covariate distributions of groups with different treatment assignments does not only make estimates of average treatment effects rather imprecise but can also lead to substantially distorted confidence intervals this paper argues that this is because the coverage error of traditional confidence intervals is driven by the number of observations in the areas of limited overlap some of these local sample sizes can be very small in applications up to the point that distributional approximations derived from classical asymptotic theory become unreliable building on this observation this paper constructs confidence intervals based on classical approaches to small sample inference the approach is easy to implement and has superior theoretical and practical properties relative to standard methods in empirically relevant settings

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

stochastic dominance and cumulative prospect theory we generalize and extend the second order stochastic dominance condition for expected utility to cumulative prospect theory the new definitions include preferences represented by s shaped value functions inverse s shaped probability weighting functions and loss aversion the stochastic dominance conditions supply a framework to test different features of cumulative prospect theory in the experimental part of the paper we offer a test of several joint hypotheses on the value function and the probability weighting function assuming empirically relevant weighting functions we can reject the inverse s shaped value function recently advocated by levy and levy 2002 in favor of the s shaped form in addition we find generally supporting evidence for loss aversion violations of loss aversion can be explained by subjects using the overall probability of winning as a heuristic

simple least squares estimator for treatment effects using propensity score residuals summary propensity score matching is widely used to control covariates when analysing the effects of a nonrandomized binary treatment however it requires several arbitrary decisions such as how many matched subjects to use and how to choose them in this paper a simple least squares estimator is proposed where the treatment and possibly the response variable is replaced by the propensity score residual the proposed estimator controls covariates semiparametrically if the propensity score function is correctly specified furthermore it is numerically stable and relatively easy to use compared with alternatives such as matching regression imputation weighting and doubly robust estimators the proposed estimator also has a simple valid asymptotic variance estimator that works well in small samples the least squares estimator is extended to multiple treatments and noncontinuously distributed responses a simulation study demonstrates that it has lower mean squared error than its competitors

balancing covariates via propensity score weighting abstractcovariate balance is crucial for unconfounded descriptive or causal comparisons however lack of balance is common in observational studies this article considers weighting strategies for balancing covariates we define a general class of weights the balancing weights that balance the weighted distributions of the covariates between treatment groups these weights incorporate the propensity score to weight each group to an analyst selected target population this class unifies existing weighting methods including commonly used weights such as inverse probability weights as special cases general large sample results on nonparametric estimation based on these weights are derived we further propose a new weighting scheme the overlap weights in which each unit s weight is proportional to the probability of that unit being assigned to the opposite group the overlap weights are bounded and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing wei

severi inequality for varieties of maximal albanese dimension in this paper we prove the general severi inequality for varieties of maximal albanese dimension suppose that x is an n dimensional projective normal minimal and mathbb q gorenstein variety of general type in characteristic zero if x is of maximal albanese dimension then k n x ge 2 n chi omega x

model averaging in semiparametric estimation of treatment effects choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects this paper proposes a data driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the att the proposed procedures minimize the estimated mse of the att estimator in a local asymptotic framework we formulate model averaging as a statistical decision problem in a limit experiment and derive an averaging scheme that is bayes optimal with respect to a given prior the averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of bayes asymptotic mse our monte carlo studies illustrate the size of the mse gains we apply the averaging procedure to evaluate the effect of a labor market program

gmm redundancy results for general missing data problems we consider questions of efficiency and redundancy in the gmm estimation problem in which we have two sets of moment conditions where two sets of parameters enter into one set of moment conditions while only one set of parameters enters into the other we then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest and the second set of moment conditions is for the selection process we use these results to explain the counterintuitive result in the literature that under an ignorability assumption that justifies gmm with weighted moment conditions weighting using estimated probabilities of selection is better than weighting using the true probabilities we also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid and we show that when weighting is not needed for consistency it is also not useful for efficiency

fibered algebraic surfaces with low slope the background of this paper is the following conjecture on complex surfaces of general type let s be a smooth projective minimal surface of general type over ti with c 2 throughout the paper

a simple behavioral characterization of subjective expected utility subjective expected utility is the most widely used model to represent preferences under uncertainty when objective probabilities of events may not be known this paper presents a new behavioral characterization preference axiomatization of subjective expected utility the latter is derived from a behavioral assumption of cardinal independence also known as standard sequence invariance this axiom requires that a standard sequence of outcomes equally spaced in terms of utility is independent of the conditional event this axiom is a weaker version of the trade off consistency condition of wakker wakker pp 1984 cardinal coordinate independence for expected utility j math psych 28 110 117 the main representation theorem is derived both in the connected topology approach and the algebraic approach when step continuity is replaced with solvability and archimedean axioms

bayesian estimation of the average treatment effect on the treated using inverse weighting we develop a bayesian approach to estimate the average treatment effect on the treated in the presence of confounding the approach builds on developments proposed by saarela et al in the context of marginal structural models using importance sampling weights to adjust for confounding and estimate a causal effect the bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in bayesian causal estimation relying on a joint likelihood we present results from simulation studies to estimate the average treatment effect on the treated evaluating the impact of sample size and the strength of confounding on estimation we illustrate our approach using the classic right heart catheterization data set and find a negative causal effect of the exposure on 30 day survival in accordance with previous analyses of these data we also apply our approach to the data set of the national center for health statistics birth data and obtain a negative effect of maternal smoking during pregnancy on birth weight

estimation and inference for distribution functions and quantile functions in treatment effect models abstract we propose inverse probability weighted estimators for the distribution functions of the potential outcomes under the unconfoundedness assumption and apply the inverse mapping to obtain the quantile functions we show that these estimators converge weakly to zero mean gaussian processes a simulation method is proposed to approximate these limiting processes based on these results we construct tests for stochastic dominance relations between the potential outcomes monte carlo simulations are conducted to examine the finite sample properties of our tests we apply our test in an empirical example and find that a job training program had a positive effect on incomes

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

the rich domain of ambiguity explored ellsberg and others suggested that decision under ambiguity is a rich empirical domain with many phenomena to be investigated beyond the ellsberg urns we provide a systematic empirical investigation of this richness by varying the uncertain events the outcomes and combinations of both although ambiguity aversion is prevailing we also find systematic ambiguity seeking confirming insensitivity we find that ambiguity attitudes depend on the kind of uncertainty the source but not on the kind of outcomes ambiguity attitudes are closer to rationality ambiguity neutrality for natural uncertainties than for artificial ellsberg urn uncertainties this also appears from the reductions of monotonicity violations and of insensitivity ambiguity attitudes have predictive power across different outcomes and sources of uncertainty with individual specific components our rich domain serves well to test families of weighting functions for fitting ambiguity attitudes we find that two parameter families capt

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

testing and characterizing properties of nonadditive measures through violations of the sure thing principle in expected utility theory risk attitudes are modeled entirely in terms of utility in the rank dependent theories a new dimension is added chance attitude modeled in terms of nonadditive measures or nonlinear probability transformations that are independent of utility most empirical studies of chance attitude assume probabilities given and adopt parametric fitting for estimating the probability transformation only a few qualitative conditions have been proposed or tested as yet usually quasi concavity or quasi convexity in the case of given probabilities this paper presents a general method of studying qualitative properties of chance attitude such as optimism pessimism and the inverse s shape pattern both for risk and for uncertainty these qualitative properties can be characterized by permitting appropriate relatively simple violations of the sure thing principle in particular this paper solves a hitherto open problem the preference axiomatization of convex pessimistic or uncertainty averse nonadditive measures under uncertainty the axioms of this paper preserve the central feature of rank dependent theories i e the separation of chance attitude and utility

risk aversion in cumulative prospect theory this paper characterizes the conditions for strong risk aversion and second order stochastic dominance for cumulative prospect theory strong risk aversion implies a convex weighting function for gains and a concave one for losses it does not necessarily imply a concave utility function the latter does follow if the weighting functions are continuous by investigating the exact relationship between loss aversion and strong risk aversion a natural index for the degree of loss aversion is derived

relative noether inequality on fibered surfaces abstract we prove effective upper bounds on the global sections of nef line bundles of small generic degree over a fibered surface over a field of any characteristic it can be viewed as a relative version of the classical noether inequality for surfaces as a consequence we give a new proof of the slope inequality for fibered surface without using any stability method the treatment is essentially different from those of xiao cornalba harris and moriwaki we also study the geography problem of surfaces in positive characteristics and show that the severi inequality is true for surfaces of general type in positive characteristic whose albanese map is generically finite moreover the geography of surfaces with albanese fibrations is studied

irregular identification support conditions and inverse weight estimation in weighted moment condition models we show a subtle link between identification and estimability that limits the practical usefulness of estimators based on these models in particular if it is necessary for point identification that the weights take arbitrarily large values then the parameter of interest though point identified cannot be estimated at the regular parametric rate and is said to be irregularly identified this rate depends on relative tail conditions and can be as slow in some examples as n 1 4 this nonstandard rate of convergence can lead to numerical instability and or large standard errors we examine two weighted model examples i the binary response model under mean restriction introduced by lewbel 1997 and further generalized to cover endogeneity and selection where the estimator in this class of models is weighted by the density of a special regressor and ii the treatment effect model under exogenous selection rosenbaum and rubin 1983 where the resulting estimator of the average treatment effect is one that is weighted by a variant of the propensity score without strong relative support conditions these models similar to well known identified at infinity models lead to estimators that converge at slower than parametric rate since essentially to ensure point identification one requires some variables to take values on sets with arbitrarily small probabilities or thin sets for the two models above we derive some rates of convergence and propose that one conducts inference using rate adaptive procedures that are analogous to andrews and schafgans 1998 for the sample selection model

identification and efficient estimation of the natural direct effect among the untreated the natural direct effect nde or the effect of an exposure on an outcome if an intermediate variable was set to the level it would have been in the absence of the exposure is often of interest to investigators in general the statistical parameter associated with the nde is difficult to estimate in the non parametric model particularly when the intermediate variable is continuous or high dimensional in this paper we introduce a new causal parameter called the natural direct effect among the untreated discus identifiability assumptions propose a sensitivity analysis for some of the assumptions and show that this new parameter is equivalent to the nde in a randomized controlled trial we also present a targeted minimum loss estimator tmle a locally efficient double robust substitution estimator for the statistical parameter associated with this causal parameter the tmle can be applied to problems with continuous and high dimensional intermediate variables and can be used to estimate the nde in a randomized controlled trial with such data additionally we define and discuss the estimation of three related causal parameters the natural direct effect among the treated the indirect effect among the untreated and the indirect effect among the treated

nonparametric iv estimation of local average treatment effects with covariates in this paper nonparametric instrumental variable estimation of local average treatment effects late is extended to incorporate covariates estimation of late is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models including covariates in the estimation of late is necessary when the instrumental variable itself is confounded such that the iv assumptions are valid only conditional on covariates previous approaches to handle covariates in the estimation of late relied on parametric or semiparametric methods in this paper a nonparametric estimator for the estimation of late with covariates is suggested that is root n asymptotically normal and efficient

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

the midweight method to measure attitudes toward risk and ambiguity this paper introduces a parameter free method for measuring the weighting functions of prospect theory and rank dependent utility these weighting functions capture risk attitudes subjective beliefs and ambiguity attitudes our method called the midweight method is based on a convenient way to obtain midpoints in the weighting function scale it can be used both for risk known probabilities and for uncertainty unknown probabilities the resulting integrated treatment of risk and uncertainty is particularly useful for measuring ambiguity i e the difference between uncertainty and risk compared to existing methods to measure weighting functions and attitudes toward uncertainty and ambiguity our method is more efficient and can accommodate violations of expected utility under risk an experiment demonstrates the tractability of our method yielding plausible results such as ambiguity aversion for moderate and high likelihoods but ambiguity seeking for low likelihoods as predicted by ellsberg this paper was accepted by george wu decision analysis

a specification test for the propensity score using its distribution conditional on participation propensity score matching has become a popular method for the estimation of average treatment effects in empirical applications researchers almost always impose a parametric model for the propensity score this practice raises the possibility that the model for the propensity score is misspecified and therefore the propensity score matching estimator of the average treatment effect may be inconsistent we show that the common practice of calculating estimates of the densities of the propensity score conditional on the participation decision provides a means for examining whether the propensity score is misspecified in particular we derive a restriction between the density of the propensity score among participants and the density among nonparticipants we show that this restriction between the two conditional densities is equivalent to a particular orthogonality restriction and derive a formal test based upon it the resulting test is shown via a simulation study to have dramatically greater power than competing tests for many alternatives the principal disadvantage of this approach is loss of power against some alternatives

large sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

back to the st petersburg paradox the conventional parameterizations of cumulative prospect theory do not explain the st petersburg paradox to do so the power coefficient of an individual s utility function must be lower than the power coefficient of an individual s probability weighting function

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

investigating generalisations of expected utility theory using experimental data a number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the akaike information criterion is used to distinguish between them the economic superiority of the various generalizations is also explored and the paper concludes that for many subjects the superiority of several of the generalizations is not established copyright 1994 by the econometric society

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

inverse probability weighted estimation for general missing data problems abstract i study inverse probability weighted m estimation under a general missing data scheme examples include m estimation with missing data due to a censored survival time propensity score estimation of the average treatment effect in the linear exponential family and variable probability sampling with observed retention frequencies i extend an important result known to hold in special cases estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation for the treatment effect case the setup allows a general characterization of a double robustness result due to scharfstein et al 1999 rejoinder journal of the american statistical association 94 1135 1146

testing for separability in structural equations abstract separability is an important feature of structural equations as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation this paper provides a nonparametric test for separability in structural equations the test is based on a conditional independence test recently developed by huang et al 2013 building on consistent procedures of bierens 1982 1990 and stinchcombe and white 1998 the test is easy to implement and achieves n local power we apply our test to study interest rate elasticities of loan demand in microfinance and the impact of education on wages

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

arithmetic height functions over finitely generated fields in this paper we propose a new height function for a variety defined over a finitely generated field over for this height function we prove northcott s theorem and bogomolov s conjecture so that we can recover the original raynaud s theorem manin mumford s conjecture

doubly robust inference for targeted minimum loss based estimation in randomized trials with missing outcome data missing outcome data is a crucial threat to the validity of treatment effect estimates from randomized trials the outcome distributions of participants with missing and observed data are often different which increases bias causal inference methods may aid in reducing the bias and improving efficiency by incorporating baseline variables into the analysis in particular doubly robust estimators incorporate 2 nuisance parameters the outcome regression and the missingness mechanism ie the probability of missingness conditional on treatment assignment and baseline variables to adjust for differences in the observed and unobserved groups that can be explained by observed covariates to consistently estimate the treatment effect one of these nuisance parameters must be consistently estimated traditionally nuisance parameters are estimated using parametric models which often precludes consistency particularly in moderate to high dimensions recent research on missing data has focused on data adaptive estimation to help achieve consistency but the large sample properties of such methods are poorly understood in this article we discuss a doubly robust estimator that is consistent and asymptotically normal under data adaptive estimation of the nuisance parameters we provide a formula for an asymptotically exact confidence interval under minimal assumptions we show that our proposed estimator has smaller finite sample bias compared to standard doubly robust estimators we present a simulation study demonstrating the enhanced performance of our estimators in terms of bias efficiency and coverage of the confidence intervals we present the results of an illustrative example a randomized double blind phase 2 3 trial of antiretroviral therapy in hiv infected persons

asymptotic variance of semiparametric estimators with generated regressors we study the asymptotic distribution of three step estimators of a finite dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step the first step estimator is either parametric or nonparametric using newey s 1994 path derivative method we derive the contribution of the first step estimator to the influence function in this derivation it is important to account for the dual role that the first step estimator plays in the second step nonparametric regression that is that of conditioning variable and that of argument

efficiency bounds for missing data models with semiparametric restrictions this paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random mar coincides with that of a particular augmented moment condition problem the augmented system consists of the inverse probability weighted ipw original moment restriction and an additional conditional moment restriction which exhausts all other implications of the mar assumption the paper also investigates the value of additional semiparametric restrictions on the conditional expectation function cef of the original moment function given always observed covariates in the program evaluation context for example such restrictions are implied by semiparametric models for the potential outcome cefs given baseline covariates the efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem some implications of these results for estimation are briefly discussed

testing conditional independence via rosenblatt transforms this paper proposes new tests of conditional independence of two random variables given a single index involving an unknown finite dimensional parameter the tests employ rosenblatt transforms and are shown to be distribution free while retaining computational convenience some results from monte carlo simulations are presented and discussed

dummy endogenous variables in weakly separable models in this paper we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term the model is not required to be strictly increasing in the error term and the class of models considered includes limited dependent variable models such as discrete choice models conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions

volumes of arithmetic okounkov bodies this paper is an improvement and simpli cation of yuan yu in particular by a simpler method it proves the identity in yu theorem a withouttaking the limit p the method also simpli es the proofs of moriwaki mo where more general arithmetic linear series were treated recall that yu explored a way to construct arithmetic okounkov bodiesfrom an arithmetic line bundle inspired by the idea of okounkov ok1 ok2 and lazarsfeld musta ta lm in the geometric case theorem a of yu asserts that the volumes of the okounkov bodies approximate the volume ofthe arithmetic line bundle the main result of this paper asserts an exactidentity before taking the limit on the other hand boucksom chen bc initiated a di erent way toconstruct okounkov bodies in the arithmetic setting from the proof ofthe main result in this paper it is easy to recognize the similarity of theconstructions in bc and in yu we will make a comparison at the end ofthis paper in the following we recall the construction of yu and state our mainresult we use exactly the same notations as in yu throughout this paper 1

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

on the role of the propensity score in efficient semiparametric estimation of average treatment effects in this paper the role of the propensity score in the efficient estimation of average treatment effects is examined under the assumption that the treatment is ignorable given some observed characteristics it is shown that the propensity score is ancillary for estimation of the average treatment effects the propensity score is not ancillary for estimation of average treatment effects on the treated it is suggested that the marginal value of the propensity score lies entirely in the dimension reduction efficient semiparametric estimators of average treatment effects and average treatment effects on the treated are shown to take the form of relevant sample averages of the data completed by the nonparametric imputation method it is shown that the projection on the propensity score is not necessary for efficient semiparametric estimation of average treatment effects on the treated even if the propensity score is known an application to the experimental data reveals that conditioning on the propensity score may even result in a loss of efficiency

nonparametric regression with nonparametrically generated covariates we analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable but have be estimated from data in a preliminary step these so called generated covariates appear in numerous applications including two stage nonparametric regression estimation of simultaneous equation models or censored regression models yet so far there seems to be no general theory for their impact on the final estimator s statistical properties our paper provides such results we derive a stochastic expansion that characterizes the influence of the generation step on the final estimator and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates

a belief based account of decision under uncertainty we develop a belief based account of decision under uncertainty this model predicts decisions under uncertainty from i judgments of probability which are assumed to satisfy support theory and ii decisions under risk which are assumed to satisfy prospect theory in two experiments subjects evaluated uncertain prospects and assessed the probability of the respective events study 1 involved the 1995 professional basketball playoffs study 2 involved the movement of economic indicators in a simulated economy the results of both studies are consistent with the belief based account but violate the partition inequality implied by the classical theory of decision under uncertainty

covariate selection for the nonparametric estimation of an average treatment effect observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology such studies often rel

what determines the shape of the probability weighting function under uncertainty decision weights are an important component in recent theories of decision making under uncertainty to better explain these decision weights a two stage approach has been proposed first the probability of an event is judged and then this probability is transformed by the probability weighting function known from decision making under risk we extend the two stage approach by allowing the probability weighting function to depend on the type of uncertainty using this more general approach properties of decision weights can be attributed to properties of probability judgments and or to properties of probability weighting we present an empirical study that shows that it is indeed necessary to allow the probability weighting function to be source dependent the analysis includes an examination of properties of the probability weighting function under uncertainty that have not been considered yet

effective bounds of linear series on algebraic varieties and arithmetic varieties in this paper we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the volumes they are effective versions of the hilbert samuel formula and the arithmetic hilbert samuel formula the treatments are high dimensional generalizations of duke math j 162 2013 1723 1770 and relative noether inequality on fibered surfaces preprint 2013 similar results are obtained independently by huayi chen majorations explicites de fonctions de hilbert samuel geometrique et arithmetique preprint 2014 with less explicit error terms

curvature of the probability weighting function when individuals choose among risky alternatives the psychological weight attached to an outcome may not correspond to the probability of that outcome in rank dependent utility theories including prospect theory the probability weighting function permits probabilities to be weighted nonlinearly previous empirical studies of the weighting function have suggested an inverse s shaped function first concave and then convex however these studies suffer from a methodological shortcoming estimation procedures have required assumptions about the functional form of the value and or weighting functions we propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function empirical tests of these conditions are independent of the form of the value function we test these conditions using preference ladders a series of questions that differ only by a common consequence the concavity convexity ladders validate previous findings of an s shaped weighting function concave up to p 0 40 and convex beyond that probability the tests also show significant nonlinearity away from the boundaries 0 and 1 finally we fit the ladder data with weighting functions proposed by tversky and kahneman tversky amos daniel kahneman 1992 advances in prospect theory cumulative representation of uncertainty j risk and uncertainty5 297 323 and prelec prelec dra en 1995 the probability weighting function unpublished paper

matching and semi parametric iv estimation a distance based measure of migration and the wages of young men abstract our paper estimates the effect of us internal migration on wage growth for young men between their first and second job our analysis of migration extends previous research by i exploiting the distance based measures of migration in the national longitudinal surveys of youth 1979 nlsy79 ii allowing the effect of migration to differ by schooling level and iii using propensity score matching to estimate the average treatment effect on the treated atet for movers and iv using local average treatment effect late estimators with covariates to estimate the average treatment effect ate and atet for compliers we believe the conditional independence assumption cia is reasonable for our matching estimators since the nlsy79 provides a relatively rich array of variables on which to match our matching methods are based on local linear local cubic and local linear ridge regressions local linear and local ridge regression matching produce relatively similar point estimates and standard errors while local cubic regression matching badly over fits the data and provides very noisy estimates we use the bootstrap to calculate standard errors since the validity of the bootstrap has not been investigated for the matching estimators we use and has been shown to be invalid for nearest neighbor matching estimators we conduct a monte carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching the data generating processes in our monte carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values the estimated standard errors from the bootstrap are very close to those from the monte carlo experiments which lends support to our using the bootstrap to calculate standard errors in our setting from the matching estimators we find a significant positive effect of migration on the wage growth of college graduates and a marginally significant negative effect for high school dropouts we do not find any significant effects for other educational groups or for the overall sample our results are generally robust to changes in the model specification and changes in our distance based measure of migration we find that better data matters if we use a measure of migration based on moving across county lines we overstate the number of moves while if we use a measure based on moving across state lines we understate the number of moves further using either the county or state measures leads to much less precise estimates we also consider semi parametric late estimators with covariates frolich 2007 using two sets of instrumental variables we precisely estimate the proportion of compliers in our data but because we have a small number of compliers we cannot obtain precise late estimates

choice based elicitation and decomposition of decision weights for gains and losses under uncertainty this paper reports the results of an experimental parameter free elicitation and decomposition of decision weights under uncertainty assuming cumulative prospect theory utility functions were elicited for gains and losses at an individual level using the tradeoff method subsequently decision weights were elicited through certainty equivalents of uncertain two outcome prospects furthermore decision weights were decomposed using observable choice instead of invoking other empirical primitives as in previous experimental studies the choice based elicitation of decision weights allows for a quantitative study of their characteristics and also allows among other things for the examination of the sign dependence hypothesis for observed choice under uncertainty our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice based subjective probabilities we also find evidence for sign dependence of decision weights

risk attitudes and decision weights to accommodate the observed pattern of risk aversion and risk seeking as well as common violations of expected utility e g the certainty effect we introduce and characterize a weighting function according to which an event has greater impact when it turns impossibility into possibility or possibility into certainty than when it merely makes a possibility more or less likely we show how to compare such weighting functions of different individuals with respect to the degree of departure from expected utility and we present a method for comparing an individual s weighting functions for risk and for uncertainty

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

empirical likelihood based inference in missing response problems and its application in observational studies summary the problem of missing response data is ubiquitous in medical and social science studies in the case of responses that are missing at random depending on some covariate information analyses focused only on the complete data may lead to biased results various debias methods have been extensively studied in the literature particularly the weighting method that was motivated by horvitz and thompson s estimators to improve efficiency robins rotnitzky and zhao proposed augmented estimating equations based on corrected complete case analyses a nice feature of the augmented method is its double robustness i e the estimator that is derived from the augmented method is asymptotically unbiased if either the underlying missing data mechanism or the underlying regression function is correctly specified furthermore the augmented estimator can achieve full efficiency if both the missing data mechanism and the regression function are correctly specified in general however it is very difficult to specify the regression function correctly especially when the dimension of covariates is high this is the so called curse of dimensionality problem the augmented estimator has much lower efficiency if the working regression model is not close to the true regression model in this paper the empirical likelihood method is employed to seek a constrained empirical likelihood estimation of mean response with the assumption that responses are missing at random the empirical likelihood based estimators enjoy the double robustness property moreover it is possible that the empirical likelihood based inference can produce asymptotically unbiased and efficient estimators even if the true regression function is not completely known simulation results indicate that the empirical likelihood based estimators are very robust to a misspecification of the propensity score and dominate other competitors in the sense of having smaller mean square errors methods that are developed in this paper have a nice application in observational causal inferences the propensity score is used to adjust for differences in pretreatment variables in the estimation of average treatment effects

mann whitney test with adjustments to pretreatment variables for missing values and observational study the conventional wilcoxon mann whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies this is because the missingness of the outcomes or the participation in the treatments may depend on certain pre treatment variables we propose an approach to adjust the mann whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre treatment variables we also propose semiparametric extensions of the adjusted mann whitney test which leads to dimension reduction for high dimensional covariate a novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach