on extremal pure nash equilibria for mixed extensions of normal form games abstract in this paper we derive conditions under which mixed extensions of normal form games have least and greatest nash equilibria in pure strategies and either of them gives best utilities among all mixed nash equilibria when strategy spaces are complete separable metric spaces equipped with closed partial orderings and the values of utility functions are in separable ordered banach spaces the obtained results are applied to supermodular normal form games whose strategy spaces are multidimensional

the hybrid wild bootstrap for time series we introduce a new and simple bootstrap procedure for general linear processes called the hybrid wild bootstrap the hybrid wild bootstrap generates frequency domain replicates of the periodogram that imitate asymptotically correct the first and second order properties of the ordinary periodogram including its weak dependence structure at different frequencies as a consequence the hybrid wild bootstrapped periodogram succeeds in approximating consistently the distribution of statistics that can be expressed as functionals of the periodogram including the important class of spectral means for which all so far existing frequency domain bootstrap methods generally fail moreover by inverting the hybrid wild bootstrapped discrete fourier transform pseudo observations in the time domain are obtained the generated time domain pseudo observations can be used to approximate correctly the random behavior of statistics the distribution of which depends on the first second and to some extent on the fo

caratheodory helly and radon numbers for sublattice and related convexities the caratheodory helly and radon numbers are three main invariants in convexity theory these invariants have been determined exactly or approximately for a number of different convexity structures we consider convexity structures defined by the sublattices and by the convex sublattices of finite dimensional euclidian integer and boolean spaces such sublattices arise in submodular optimization lattice programming and in monotone comparative statics of optimization and fixed point problems we also consider integral l natural convexities induced by dual network flow constraint systems we determine the exact caratheodory helly and radon numbers of most of these convexities and very close upper and lower bounds for the other caratheodory numbers our results imply for example that if a set can be obtained with unions and intersections from a given family of subsets of a finite set then it can be obtained with unions and intersections from a small subfamily we also show that finding the cara

double exponential utility functions ordinal additivity between two attributes x and y is a property that permits the utility function ux y to be represented as vx wy for some functions v and w where may be thought of as a single attribute utility function over v w in applications is usually taken to be either linear the additive decomposition or exponential the multiplicative decomposition the utility function can be shown to be exactly one of these forms whenever the two attributes are mutually utility independent in this paper we introduce a relaxation of utility independence and show that it too implies ordinal additivity we identify the class of utility functions that are consistent with the relaxed assumptions one member of this class z expb exp cz which we call double exponential seems particularly appealing for when b and c are positive it is increasing risk averse and decreasingly risk averse for all z the multiattribute decomposition corresponding to it expb exp cv w may be represented as ux y c expcvxwy which we call the exponential product

anchoring economic predictions in common knowledge the paper examines within a unified methodology expectational coordination in a series of economic models the methodology views the predictions associated with the rational expectations hypothesis as reasonable whenever they can be derived from the more basic common knowledge hypothesis the paper successively considers a simple nonnoisy n dimensional model standard models with intrinsic uncertainty and reference intertemporal models with infinite horizon it reviews existing results and suggests new ones it translates the formal results into looser but economically intuitive statements whose robustness in the present state of knowledge is tentatively ascertained

wild bootstrap for quantile regression the existing theory of the wild bootstrap has focused on linear estimators in this note we broaden its validity by providing a class of weight distributions that is asymptotically valid for quantile regression estimators as most weight distributions in the literature lead to biased variance estimates for nonlinear estimators of linear regression we propose a modification of the wild bootstrap that admits a broader class of weight distributions for quantile regression a simulation study on median regression is carried out to compare various bootstrap methods with a simple finite sample correction the wild bootstrap is shown to account for general forms of heteroscedasticity in a regression model with fixed design points

a smooth block bootstrap for quantile regression with time series quantile regression allows for broad conditional characterizations of a response distribution beyond conditional means and is of increasing interest in economic and financial applications because quantile regression estimators have complex limiting distributions several bootstrap methods for the independent data setting have been proposed many of which involve smoothing steps to improve bootstrap approximations currently no similar advances in smoothed bootstraps exist for quantile regression with dependent data to this end we establish a smooth tapered block bootstrap procedure for approximating the distribution of quantile regression estimators for time series this bootstrap involves two rounds of smoothing in resampling individual observations are resampled via kernel smoothing techniques and resampled data blocks are smoothed by tapering the smooth bootstrap results in performance improvements over previous unsmoothed versions of the block bootstrap as well as normal approximations based on powell s kernel variance estimator which are common in application our theoretical results correct errors in proofs for earlier and simpler versions of the unsmoothed moving blocks bootstrap for quantile regression and broaden the validity of block bootstraps for this problem under weak conditions we illustrate the smooth bootstrap through numerical studies and examples

methods one switch conditions for multiattribute utility functions we introduce a variety of new independence conditions for multiattribute utility functions that permit preference dependencies among the attributes of a decision problem the hierarchy of new conditions varies in the degree to which it specifies the functional form ranging from more general solutions with weaker constraints to more specific solutions with stronger constraints this formulation provides a wealth of new functional forms that a decision maker may use in a multiattribute decision problem in addition it may be used to tailor the utility elicitation process to the comfort level of the decision maker the new conditions and the corresponding functional forms are based on the idea of limiting the number of switches that a decision maker may make between two decision alternatives as a parameter of the problem varies we show how this formulation also relates many widely used concepts in single and multiattribute utility theory

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

a bootstrap based on the estimating equations of the linear model summary this paper presents a method of bootstrap estimation for the linear model rather than resampling from the original sample as is conventional the proposed method resamples summands in an estimating function used to produce the original estimate the method is computationally simpler then existing competitors however its main advantage lies in the robustness to heteroscedasticity of the estimators it produces these estimators are shown to have desirable asymptotic properties under fairly general conditions a simulation study provides small sample support for the new method

wild residual bootstrap inference for penalized quantile regression with heteroscedastic errors summarywe consider a heteroscedastic regression model in which some of the regression coefficients are zero but it is not known which ones penalized quantile regression is a useful approach for analysing such data by allowing different covariates to be relevant for modelling conditional quantile functions at different quantile levels it provides a more complete picture of the conditional distribution of a response variable than mean regression existing work on penalized quantile regression has been mostly focused on point estimation although bootstrap procedures have recently been shown to be effective for inference for penalized mean regression they are not directly applicable to penalized quantile regression with heteroscedastic errors we prove that a wild residual bootstrap procedure for unpenalized quantile regressionis asymptotically valid for approximating the distribution of a penalized quantile regression estimator with an adaptive l 1 penalty and that a modified version can be used to approximate the distribution of a l 1 penalized quantile regression estimator the new methods do not require estimation of the unknown error density function we establish consistency demonstrate finite sample performance andillustrate the applications on a real data example

cluster robust bootstrap inference in quantile regression models abstractin this article i develop a wild bootstrap procedure for cluster robust inference in linear quantile regression models i show that the bootstrap leads to asymptotically valid inference on the entire quantile regression process in a setting with a large number of small heterogeneous clusters and provides consistent estimates of the asymptotic covariance function of that process the proposed bootstrap procedure is easy to implement and performs well even when the number of clusters is much smaller than the sample size an application to project star data is provided supplementary materials for this article are available online

correlations and copulas for decision and risk analysis the construction of a probabilistic model is a key step in most decision and risk analyses typically this is done by defining a joint distribution in terms of marginal and conditional distributions for the model s random variables we describe an alternative approach that uses a copula to construct joint distributions and pairwise correlations to incorporate dependence among the variables the approach is designed specifically to permit the use of an expert s subjective judgments of marginal distributions and correlations the copula that underlies the multivariate normal distribution provides the basis for modeling dependence but arbitrary marginals are allowed we discuss how correlations can be assessed using techniques that are familiar to decision analysts and we report the results of an empirical study of the accuracy of the assessment methods the approach is demonstrated in the context of a simple example including a study of the sensitivity of the results to the assessed correlations

period doubling and quadrupling for some second order difference schemes may exhibit stable n cycles that bifurcate into stable 2n cycles as a increases creating period doubling bifurcation sequences each beginning with a cycle of odd period these dynamics were first described by may i 21 and have since been investigated by many others see 3 61 for example a number of universal features of this bifurcation process have been observed primarily for quadratic maps 7 lo by comparison much less is known concerning the dynamics of higher order nonlinear schemes although there have been many numerical investigations of specific second order equations see i l 181 for example the full range of dynamics possible for such problems has not yet been determined in this work we investigate some general second order nonlinear difference schemes sufficient conditions are derived for the existence stability and bifurcations of periodic cycles for certain classes of such problems firstly the correspondence between periodic cycles of 1 and those of the second order problem x k l f xk l 3

multiattribute utility copulas we introduce the notion of a multiattribute utility copula that expresses any i continuous ii bounded multiattribute utility function that is iii nondecreasing with each of its arguments and iv strictly increasing with each argument for at least one reference value of the complement attributes in terms of single attribute utility assessments this formulation provides a wealth of new functional forms that can be used to model preferences over utility dependent attributes and enables sensitivity analyses to some of the widely used functional forms of utility independence we introduce a class of utility copulas called archimedean utility copulas and discuss the conditions under which it yields the additive and multiplicative forms we also discuss linear and composite transformations of utility copulas that construct utility functions with partial utility independence we conclude with the risk aversion functions that are induced by utility copula formulations and work through several examples to illustrate the approach

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

sieve instrumental variable quantile regression estimation of functional coefficient models abstract in this paper we consider sieve instrumental variable quantile regression ivqr estimation of functional coefficient models where the coefficients of endogenous regressors are unknown functions of some exogenous covariates we estimate the functional coefficients by the sieve ivqr technique and establish the uniform consistency and asymptotic normality of the estimators based on the sieve estimates we propose a nonparametric specification test for the constancy of the functional coefficients and study its asymptotic we conduct simulations to evaluate the finite sample behavior of our estimator and test statistic and apply our method to study the estimation of quantile engel curves

lack of fit tests for quantile regression models the paper novelly transforms lack of fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates accordingly by applying some successful two sample test statistics in the literature two tests are constructed to check the lack of fit for low and high dimensional quantile regression models the low dimensional test works well when the number of covariates is moderate whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size the null distribution of the high dimensional test has an explicit form and the p values or critical values can then be calculated directly the finite sample performance of the tests proposed is examined by simulation studies and their usefulness is further illustrated by two real examples

conditional quantile regression models of melanoma tumor growth curves for assessing treatment effect in small sample studies tumor growth curves provide a simple way to understand how tumors change over time the traditional approach to fitting such curves to empirical data has been to estimate conditional mean regression functions which describe the average effect of covariates on growth however this method ignores the possibility that tumor growth dynamics are different for different quantiles of the possible distribution of growth patterns furthermore typical individual preclinical cancer drug study designs have very small sample sizes and can have lower power to detect a statistically significant difference in tumor volume between treatment groups in our work we begin to address these issues by combining several independent small sample studies of an experimental cancer treatment with differing study designs to construct quantile tumor growth curves for modeling we use a penalized fixed effects quantile regression with added study effects to control for study differences we demonstrate this approach using data from a series of small sample studies that investigated the effect of a naturally derived biological peptide p28 on tumor volumes in mice grafted with human melanoma cells we find a statistically significant quantile treatment effect on tumor volume trajectories and baseline values in particular the experimental treatment and a corresponding conventional chemotherapy had different effects on tumor growth by quantile the conventional treatment dacarbazine dtic tended to inhibit growth for smaller quantiles while the experimental treatment p28 produced slower rates of growth in the upper quantiles especially in the 95th quantile copyright 2014 john wiley sons ltd

quantile correlations and quantile autoregressive modeling in this article we propose two important measures quantile correlation qcor and quantile partial correlation qpcor we then apply them to quantile autoregressive qar models and introduce two valuable quantities the quantile autocorrelation function qacf and the quantile partial autocorrelation function qpacf this allows us to extend the box jenkins three stage procedure model identification model parameter estimation and model diagnostic checking from classical autoregressive models to quantile autoregressive models specifically the qpacf of an observed time series can be employed to identify the autoregressive order while the qacf of residuals obtained from the fitted model can be used to assess the model adequacy we not only demonstrate the asymptotic properties of qcor and qpcor but also show the large sample results of qacf qpacf and the quantile version of the box pierce test moreover we obtain the bootstrap approximations to the distributions of parameter estimators and p

an assumption free exact test for fixed design linear models with exchangeable errors we propose the cyclic permutation test cpt to test general linear hypotheses for linear models this test is non randomized and valid in finite samples with exact type i error alpha for an arbitrary fixed design matrix and arbitrary exchangeable errors whenever 1 alpha is an integer and n p ge 1 alpha 1 the test involves applying the marginal rank test to 1 alpha linear statistics of the outcome vector where the coefficient vectors are determined by solving a linear system such that the joint distribution of the linear statistics is invariant with respect to a non standard cyclic permutation group under the null hypothesis the power can be further enhanced by solving a secondary non linear travelling salesman problem for which the genetic algorithm can find a reasonably good solution extensive simulation studies show that the cpt has comparable power to existing tests when testing for a single contrast of coefficients an exact confidence interval can be obtained by inverting the test furthermore we provide a selective yet extensive literature review of the century long efforts on this problem highlighting the novelty of our test

quantile regression inference with adaptive control of size abstractregression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors this article develops a new estimate of the asymptotic var

multiattribute utility functions satisfying mutual preferential independence the construction of a multiattribute utility function is an important step in decision analysis one of the most widely used conditions for constructing the utility function is the assumption of mutual preferential independence where trade offs among any subset of the attributes do not depend on the instantiations of the remaining attributes mutual preferential independence asserts that ordinal preferences can be represented by an additive function of the attributes this paper derives the most general form of a multiattribute utility function that i exhibits mutual preferential independence and ii is strictly increasing with each argument at the maximum value of the complement attributes we show that a multiattribute utility function satisfies these two conditions if and only if it is an archimedean combination of univariate utility assessments this result enables the construction of multiattribute utility functions that satisfy additive ordinal preferences using univariate utility assessments and

local indirect least squares and average marginal effects in nonseparable structural systems we study the scope of local indirect least squares lils methods for nonparametrically estimating average marginal effects of an endogenous cause x on a response y in triangular structural systems that need not exhibit linearity separability or monotonicity in scalar unobservables one main finding is negative in the fully nonseparable case lils methods cannot recover the average marginal effect lils methods can nevertheless test the hypothesis of no effect in the general nonseparable case we provide new nonparametric asymptotic theory treating both the traditional case of observed exogenous instruments z and the case where one observes only error laden proxies for z

bootstrap and wild bootstrap for high dimensional linear models in this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of f test statistics in high dimensional linear models an asymptotic approach will be chosen where the dimension p of the model may increase for sample size n rightarrow infty the range of validity will be compared for the normal approximation and for the bootstrap procedures furthermore it will be argued that the rates of convergence are different for the bootstrap procedures in this asymptotic framework this is in contrast to the usual asymptotic approach where p is fixed

convergence results for patchwork copulas abstract we present a general construction that allows to extend a given subcopula to a copula in such a way that the extension is affine on some specific segments of the copula domain this construction is hence applied to provide convergence theorems for approximating a copula in strong convergence and in d 1 metric related to the markov kernel representation of a copula

elicitation of multiattribute value functions through high dimensional model representations monotonicity and interactions abstract this work addresses the early phases of the elicitation of multiattribute value functions proposing a practical method for assessing interactions and monotonicity we exploit the link between multiattribute value functions and the theory of high dimensional model representations the resulting elicitation method does not state any a priori assumption on an individual s preference structure we test the approach via an experiment in a riskless context in which subjects are asked to evaluate mobile phone packages that differ on three attributes

a note on markov perfect equilibria in a class of non stationary stochastic bequest games abstract in this note we prove the existence of a markov perfect equilibrium in a non stationary version of a paternalistic bequest game the method we advocate is general and allows to study models with unbounded state space and unbounded utility functions we cover both the stochastic and deterministic cases we provide a characterization of the set of all markov perfect equilibria by means of a set valued recursive equation involving the best response operator in the stationary case we show that there exists a set of strategies that is invariant under the best response mapping

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

monotone comparative statics the authors derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem in addition they develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm the monopolist the bertrand oligopolist consumer and growth theory game theory and general equilibrium analysis copyright 1994 by the econometric society

continuous measures in one dimension families of unimodal maps satisfying 1 t 1 1 1 1 witht 1 1 and t 1 1 2 t x isc2 inx2 and and symmetric inx 3 t0 0 0 t1 0 1 with frac d d lambda t 0 0 are considered the results of guckenheimer 1982 are extended to show that there is a positive measure of for whicht has a finite absolutely continuous invariant measure

estimation and testing of varying coefficients in quantile regression in this article we establish a novel connection between the null hypothesis h0 on the coefficients and a rank reducible form of the varying coefficient model in quantile regression we use b splines to approximate the varying coefficients in the rank reducible model and make use of the fact that the null hypothesis h0 implies a unidimensional structure of a transformed coefficient matrix for the b spline basis functions by evaluating the unidimensional structure we alleviate the difficulty of testing such hypotheses commonly considered in varying coefficient quantile models we demonstrate through numerical studies that the proposed method can be much more powerful than the rank score test which is widely used in the quantile regression literature supplementary materials for this article are available online

on the existence of monotone pure strategy equilibria in bayesian games we extend and strengthen both athey s 2001 and mcadams 2003 results on the existence of monotone pure strategy equilibria in bayesian games we allow action spaces to be compact locally complete metrizable semilatttices and can handle both a weaker form of quasisupermodularity than is employed by mcadams and a weaker single crossing property than is required by both athey and mcadams our proof which is based upon contractibility rather than convexity of best reply sets demonstrates that the only role of single crossing is to help ensure the existence of monotone best replies finally we do not require the milgrom weber 1985 absolute continuity condition on the joint distribution of types

ordinal one switch utility functions we study the problem of finding ordinal utility functions to rank the outcomes of a decision when preference independence between the attributes is not present we propose that the next level of complexity is to assume that preferences over one attribute can switch at most once as another attribute varies from low to high we refer to this property as ordinal one switch independence we present both necessary and sufficient conditions for this ordinal property to hold and provide families of functions that satisfy this new property

testing for marginal linear effects in quantile regression this paper develops a new marginal testing procedure to detect the presence of significant predictors associated with the conditional quantiles of a scalar response the idea is to fit the marginal quantile regression on each predictor one at a time and then base the test on the t statistics associated with the most predictive predictors a resampling method is devised to calibrate this test statistic which has non regular limiting behavior due to the selection of the most predictive variables asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified even though a fixed dimension is assumed to derive the asymptotic results the proposed test is applicable and computationally feasible for large dimensional predictors the method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response the approach is illustrated using an application to an hiv drug resistance dataset

utility copula functions matching all boundary assessments the construction of a multiattribute utility function is an important step in decision analysis and can be a challenging task unless some decomposition of the utility function is performed when every attribute is utility independent of its complement the utility elicitation task is significantly simplified because the functional form of the utility function requires only one conditional utility function for each attribute and some normalizing constants when utility independence conditions do not hold the conditional utility function of an attribute may vary across the domain of the complement attributes and therefore a single conditional utility assessment for each attribute may not be sufficient to capture the decision maker s preferences this paper proposes a method to construct utility functions that have the flexibility to match the variations in the conditional utility function across the domain of the attributes using univariate utility assessments at the boundary values the approach incor

a simple proof for persistence of snap back repellers abstract in this article we show that if f has a snap back repeller then any small c 1 perturbation of f has a snap back repeller and hence has li yorke chaos and positive topological entropy by simply using the implicit function theorem we also give some examples

the wild bootstrap tamed at last the wild bootstrap is studied in the context of regression models with heteroskedastic disturbances we show that in one very specific case perfect bootstrap inference is possible and a substantial reduction in the error in the rejection probability of a bootstrap test is available much more generally however the version of the wild bootstrap with this desirable property is without the skewness correction afforded by the currently most popular version of the wild bootstrap simulation experiments show that this does not prevent the preferred version from having the smallest error in rejection probability in small and medium sized samples

bootstrap procedures under some non i i d models it is shown in this article that the classical i i d bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location as long as the random observations are independently drawn from distributions with essentially a common location this may be viewed as a robust property of the classical i i d bootstrap also included is a study of the second order properties of a different bootstrap procedure proposed by wu in the context of heteroscedasticity in regression

adaptive l estimation for linear models asymptotically efficient adaptive estimators for the slope parameters of the linear regression model are constructed based upon the regression quantile statistics suggested by koenker and bassett the estimators are natural analogues of the adaptive l estimators of location of sacks but employ kernel density type estimators of the optimal l estimator weight function

isotone equilibrium in games of incomplete information an isotone pure strategy equilibrium exists in any game of incomplete information in which each player s action set is a finite sublattice of multidimensional euclidean space types are multidimensional and atomless and each player s interim expected payoff function satisfies two nonprimitive conditions whenever others adopt isotone pure strategies i single crossing in own action and type and ii quasi supermodularity in own action conditions i ii are satisfied in supermodular and log supermodular games given affiliated types and in games with independent types in which each player s ex post payoff satisfies supermodularity in own action and nondecreasing differences in own action and type this result is applied to provide the first proof of pure strategy equilibrium existence in the uniform price auction when bidders have multi unit demand nonprivate values and independent types

bifurcation to infinitely many sinks this paper considers one parameter families of diffeomorphisms ft in two dimensions which have a curve of dissipative saddle periodic pointspt i e ftn pt pt and detdftn pt 1 the family is also assumed to create new homoclinic intersections of the stable and unstable manifolds ofpt as the parameter varies throught0 gavirlov and silnikov proved that if the new homoclinic intersections are created nondegenerately att0 then there is an infinite cascade of periodic sinks i e there are parameter valuestn accumulating att0 for which there is a sink of periodn gs2 sect 4 we show that this result is true for real analytic diffeomorphisms even if the homoclinic intersection is created degenerately we give computer evidence to show that this latter result is probably applicable to the henon map fora near 1 392 andb equal 0 3