This paper considers a decision-maker who prefers to make a point decision when the object of interest is interval-identified with regular bounds. When the bounds are just identified along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an efficient lower bound estimator plus the half of the known interval length. However, when the interval length or any nontrivial upper bound for the length is not known, the minimax approach suffers from triviality because the maximal risk is associated with infinitely long identified intervals. In this case, this paper proposes a local asymptotic minimax regret approach and shows that the midpoint between semiparametrically efficient bound estimators is optimal.

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This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of Lp-type functionals of kernel estimators (1 ≤ p < ∞). Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. In particular, the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives. Furthermore, we establish conditions under which the tests have nontrivial local power against Pitman local alternatives. Some results from Monte Carlo simulations are presented.

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Given a class  of real functions and a twice differentiable real-valued map 'on R, let be an R-valued functional on  of form : 7! E[Z
'(E [Y j(X)])], where Z and Y are random variables and X is a random vector. This paper calls a conditional expectation functional. Conditional expectation functionals often arise in semiparametric models. The main contribution of this paper is that it provides nontrivial conditions under which has a uniform modulus of continuity with order 2. Hence under these conditions, the functional becomes very smooth.

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One of the approaches to compare forecasting methods is to test whether the risk from a benchmark prediction is smaller than the others. The test can be embedded into a general problem of testing inequality constraints using a one-sided sup functional. Hansen (2005) showed that such tests suffer from asymptotic bias. This paper generalizes this observation, and proposes a hybrid method to robustify the power properties by coupling a one-sided sup test with a complementary test. The method can also be applied to testing stochastic dominance or moment inequalities. Simulation studies demonstrate that the new test performs well relative to the existing methods. For illustration, the new test was applied to analyze the forecastability of stock returns using technical indicators employed in White (2000).

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We develop a methodology for the empirical study of the markets for services. These markets are typically organized as multi-attribute auctions in which buyers take into account seller's price as well as his various characteristics, including quality. Our identification strategy exploits observed buyer and seller decisions to recover the distribution of seller quality conditional on observable characteristics, the distribution of seller's costs conditional on the full vector of characteristics including quality, and the distribution of buyers' tastes. These objects are central to understanding the functioning of these markets, their efficiency, and their optimal design. We propose an implementable econometric procedure based on our identication strategy and apply it to an on-line market for programming services. Our empirical results conrm that quality plays a central role in this market: for example, the variation in quality among the providers and the willingness of buyers to pay for quality account for over 50% of the variation in buyer choices, while the observable characteristics account for less than 20%.

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When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable. However, when the nondifferentiable transform is a known composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map, this paper demonstrates that it is possible to define a notion of asymptotic optimality of an estimator as an extension of the classical local asymptotic minimax estimation. This paper establishes a local asymptotic risk bound and proposes a general method to construct a local asymptotic minimax decision.

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In many semiparametric models, the parameter of interest is identified through conditional expectations, where the conditioning variable involves a single-index that is estimated in the first step. Among the examples are sample selection models and propensity score matching estimators. When the first-step estimator follows cube-root asymptotics, no method of analyzing the asymptotic variance of the second step estimator exists in the literature. This paper provides nontrivial suffiient conditions under which the asymptotic variance is not affected by the first step single index estimator regardless of whether it is root-n or cube-root consistent. The finding opens a way to simple inference procedures in these models. Results from Monte Carlo simulations show that the procedures perform well in finite samples.

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Many existing methods of simulated likelihood for discrete choice models require additive errors that have normal or extreme value distributions, with the prominent exception of the original simulated frequency method of Lerman and Manski (1981). This paper proposes a new method of simulated likelihood that is free from simulation bias for each finite number of simulation, and yet flexible enough to accommodate various model specifications beyond those of additive normal or logit errors. The method is flexible in the sense that it applies to almost any discrete choice model where individual choices can be simulated. The method begins with the likelihood function involving simulated frequencies and finds a transform of the likelihood function that identifies the true parameter for each finite simulation number. The transform is explicit, containing no unknowns that demand an additional step of estimation. The estimator achieves the efficiency of MLE as the simulation number increases fast enough. This paper presents and discusses results from Monte Carlo simulation studies of the new method.

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