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77
Randomized Experiments from Nonrandom Selection in the U.S. House Elections
 Journal of Econometrics
, 2008
"... This paper establishes the relatively weak conditions under which causal inferences from a regressiondiscontinuity (RD) analysis can be as credible as those from a randomized experiment, and hence under which the validity of the RD design can be tested by examining whether or not there is a discont ..."
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Cited by 127 (13 self)
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This paper establishes the relatively weak conditions under which causal inferences from a regressiondiscontinuity (RD) analysis can be as credible as those from a randomized experiment, and hence under which the validity of the RD design can be tested by examining whether or not there is a discontinuity in any predetermined (or “baseline”) variables at the RD threshold. Specifically, consider a standard treatment evaluation problem in which treatment is assigned to an individual if and only if V> v0, but where v0 is a known threshold, and V is observable. V can depend on the individual’s characteristics and choices, but there is also a random chance element: for each individual, there exists a welldefined probability distribution for V. The density function – allowed to differ arbitrarily across the population – is assumed to be continuous. It is formally established that treatment status here is as good as randomized in a local neighborhood of V = v0. These ideas are illustrated in an analysis of U.S. House elections, where the inherent uncertainty in the final vote count is plausible, which would imply that the party that wins is essentially randomized among elections decided by a narrow margin. The evidence is consistent with this prediction, which is then used to generate “nearexperimental ” causal estimates of the electoral advantage to incumbency.
Modeling and Generating Random Vectors with Arbitrary Marginal Distributions and Correlation Matrix
, 1997
"... We describe a model for representing random vectors whose component random variables have arbitrary marginal distributions and correlation matrix, and describe how to generate data based upon this model for use in a stochastic simulation. The central idea is to transform a multivariate normal random ..."
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Cited by 47 (3 self)
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We describe a model for representing random vectors whose component random variables have arbitrary marginal distributions and correlation matrix, and describe how to generate data based upon this model for use in a stochastic simulation. The central idea is to transform a multivariate normal random vector into the desired random vector, so we refer to these vectors as having a NORTA (NORmal To Anything) distribution. NORTA vectors are most useful when the marginal distributions of the component random variables are neither identical nor from the same family of distributions, and they are particularly valuable when the dimension of the random vector is greater than two. Several numerical examples are provided. Keywords: simulation, random vector, input modeling, correlation matrix, copulas 1 Introduction In many stochastic simulations, simple input modelsidependent and identically distributed sequences from standard probability distributionsare not faithful representations of th...
Sojourn Time Asymptotics in the M/G/1 Processor Sharing Queue
 QUEUEING SYSTEMS
, 1998
"... We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index \Gamma , noninteger, iff the sojourn time distribution is regularly varying of index \Gamma . This result is derived from a new expression for the LaplaceStieltjes transform of the sojo ..."
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Cited by 46 (8 self)
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We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index \Gamma , noninteger, iff the sojourn time distribution is regularly varying of index \Gamma . This result is derived from a new expression for the LaplaceStieltjes transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution. We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojourn time distribution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic limiting sojourn time distribution when the service time distribution is regularly varying. Explicit formulas and multiterm expansions are provided for the case that the service time has a Pareto...
Phase Change of Limit Laws in the Quicksort Recurrence Under Varying Toll Functions
, 2001
"... We characterize all limit laws of the quicksort type random variables defined recursively by Xn = X In + X # n1In + Tn when the "toll function" Tn varies and satisfies general conditions, where (Xn ), (X # n ), (I n , Tn ) are independent, Xn . . . , n 1}. When the "toll function" Tn ..."
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Cited by 44 (18 self)
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We characterize all limit laws of the quicksort type random variables defined recursively by Xn = X In + X # n1In + Tn when the "toll function" Tn varies and satisfies general conditions, where (Xn ), (X # n ), (I n , Tn ) are independent, Xn . . . , n 1}. When the "toll function" Tn (cost needed to partition the original problem into smaller subproblems) is small (roughly lim sup n## log E(Tn )/ log n 1/2), Xn is asymptotically normally distributed; nonnormal limit laws emerge when Tn becomes larger. We give many new examples ranging from the number of exchanges in quicksort to sorting on broadcast communication model, from an insitu permutation algorithm to tree traversal algorithms, etc.
Running to Keep the Same Place: Consumer Choice as a Game of Status
 AMERICAN ECONOMIC REVIEW
, 2004
"... If individuals care about their status, defined as their rank in the distribution of consumption of one “positional ” good, then the consumer’s problem is strategic as her utility depends on the consumption choices of others. In the symmetric Nash equilibrium, each individual spends an inefficiently ..."
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Cited by 44 (6 self)
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If individuals care about their status, defined as their rank in the distribution of consumption of one “positional ” good, then the consumer’s problem is strategic as her utility depends on the consumption choices of others. In the symmetric Nash equilibrium, each individual spends an inefficientlyhighamountonthe status good. Using techniques from auction theory, we analyze the effects of exogenous changes in the distribution of income. In a richer society, almost all individuals spend more on conspicuous consumption, and individual utility is lower at each income level. In a more equal society, the poor are worse off.
CLT for Linear Spectral Statistics of Large Dimensional Sample Covariance Matrices
, 2003
"... This paper shows their of rate of convergence to be 1/n by proving, after proper scaling, they form a tight sequence. Moreover, if EX 11 =0andEX11 =2, or if X11 and T n are real and EX 11 = 3, they are shown to have Gaussian limits ..."
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Cited by 37 (0 self)
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This paper shows their of rate of convergence to be 1/n by proving, after proper scaling, they form a tight sequence. Moreover, if EX 11 =0andEX11 =2, or if X11 and T n are real and EX 11 = 3, they are shown to have Gaussian limits
Less hashing, same performance: Building a better bloom filter
 In Proc. the 14th Annual European Symposium on Algorithms (ESA 2006
, 2006
"... ABSTRACT: A standard technique from the hashing literature is to use two hash functions h1(x) and h2(x) to simulate additional hash functions of the form gi(x) = h1(x) + ih2(x). We demonstrate that this technique can be usefully applied to Bloom filters and related data structures. Specifically, on ..."
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Cited by 28 (3 self)
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ABSTRACT: A standard technique from the hashing literature is to use two hash functions h1(x) and h2(x) to simulate additional hash functions of the form gi(x) = h1(x) + ih2(x). We demonstrate that this technique can be usefully applied to Bloom filters and related data structures. Specifically, only two hash functions are necessary to effectively implement a Bloom filter without any loss in the asymptotic false positive probability. This leads to less computation and potentially less need for
An asymptotic theory for CauchyEuler differential equations with applications to the analysis of algorithms
, 2002
"... CauchyEuler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We ..."
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Cited by 22 (10 self)
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CauchyEuler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We study in this paper the most general framework for CauchyEuler equations and propose an asymptotic theory that covers almost all applications where CauchyEuler equations appear. Our approach is very general and requires almost no background on differential equations. Indeed the whole theory can be stated in terms of recurrences instead of functions. Old and new applications of the theory are given. New phase changes of limit laws of new variations of quicksort are systematically derived. We apply our theory to about a dozen of diverse examples in quicksort, binary search trees, urn models, increasing trees, etc.
2010), "Nonparametric estimation in random coefficients binary choice models," Unpublished manuscript
"... This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an illposed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizi ..."
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Cited by 14 (1 self)
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This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an illposed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier–Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields a simple plugin procedure requiring no numerical optimization. The new estimator, therefore, is easy to implement in empirical applications, while being flexible about the treatment of unobserved heterogeneity. Extensions including treatments of nonrandom coefficients and models with endogeneity are discussed.
Modeling and Simulating Poisson Processes Having Trends or Nontrigonometric Cyclic Effects
 European Journal of Operational Research
, 1999
"... : We formulate a nonparametric technique for estimating the meanvalue function of a nonhomogeneous Poisson process having a longterm trend or some cyclic e#ect(s) that may lack familiar trigonometric characteristics such as symmetry over the corresponding cycle(s). This multiresolution procedure b ..."
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Cited by 11 (8 self)
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: We formulate a nonparametric technique for estimating the meanvalue function of a nonhomogeneous Poisson process having a longterm trend or some cyclic e#ect(s) that may lack familiar trigonometric characteristics such as symmetry over the corresponding cycle(s). This multiresolution procedure begins at the lowest level of resolution by estimating any longterm trend in the target counting process; then at progressively higher levels of resolution, the procedure yields estimates of the cyclic behavior associated with progressively smaller cycle lengths. We also formulate an e#cient algorithm for generating realizations of such counting processes. Keywords: Counting processes; Multiresolution estimation procedure; Simulation 1 Introduction In many simulation studies, we encounter arrival processes having a longterm trend or multiply periodic behavior. A prominent recent example is found in a largescale simulation model of the organ procurement and transplantation network of the Un...