2,353 research outputs found
Improving Point and Interval Estimates of Monotone Functions by Rearrangement
Suppose that a target function is monotonic, namely, weakly increasing, and
an available original estimate of this target function is not weakly
increasing. Rearrangements, univariate and multivariate, transform the original
estimate to a monotonic estimate that always lies closer in common metrics to
the target function. Furthermore, suppose an original simultaneous confidence
interval, which covers the target function with probability at least
, is defined by an upper and lower end-point functions that are not
weakly increasing. Then the rearranged confidence interval, defined by the
rearranged upper and lower end-point functions, is shorter in length in common
norms than the original interval and also covers the target function with
probability at least . We demonstrate the utility of the improved
point and interval estimates with an age-height growth chart example.Comment: 24 pages, 4 figures, 3 table
Testing for the Monotone Likelihood Ratio Assumption
Monotonicity of the likelihood ratio for conditioned densities is a common technical assumption in economic models. But we have found no empirical tests for its plausibility. This paper develops such a test based on the theory of order-restricted inference, which is robust with respect to the correlation structure of the distributions being compared. We apply the test to study the technology revealed by agricultural production experiments. For the data under scrutiny, the results support the assumption of the monotone likelihood ratio. In a second application, we find some support for the assumption of affiliation among bids cast in a multiple-round Vickrey auction for a consumption good. Keywords: affiliation, auction, likelihood ratio, order-restricted inference, stochastic order.
Formal and Informal Model Selection with Incomplete Data
Model selection and assessment with incomplete data pose challenges in
addition to the ones encountered with complete data. There are two main reasons
for this. First, many models describe characteristics of the complete data, in
spite of the fact that only an incomplete subset is observed. Direct comparison
between model and data is then less than straightforward. Second, many commonly
used models are more sensitive to assumptions than in the complete-data
situation and some of their properties vanish when they are fitted to
incomplete, unbalanced data. These and other issues are brought forward using
two key examples, one of a continuous and one of a categorical nature. We argue
that model assessment ought to consist of two parts: (i) assessment of a
model's fit to the observed data and (ii) assessment of the sensitivity of
inferences to unverifiable assumptions, that is, to how a model described the
unobserved data given the observed ones.Comment: Published in at http://dx.doi.org/10.1214/07-STS253 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version
This paper studies the inference of interaction effects, i.e., the impacts of players' actions on each other's payoffs, in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in the presence of multiple equilibria, and, as a by-product of our approach, we propose a formal test for multiple equilibria in the data-generating process. We provide Monte Carlo evidence of the test's good performance infinite samples. We also implement the test to infer the direction of interaction effects in couples' joint retirement decisions using data from the Health and Retirement Study.identification, inference, multiple equilibria, incomplete information games
Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version
This paper studies the inference of interaction effects (impacts of players' actions on each other's payoffs) in discrete simultaneous games with incomplete information. We propose an easily implementable test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in (but does not rely on) the presence of multiple equilibria in the data-generating process (DGP). As a by-product, we propose a formal test for multiple equilibria in the DGP. We also show how to extend our arguments to identify signs of interaction effects when private signals are correlated. We provide Monte Carlo evidence of the test's good performance in finite samples. We then implement the test using data on radio programming of commercial breaks in the U.S., and infer stations' incentives to synchronize their commercial breaks. Our results support the earlier finding by Sweeting (2009) that stations have stronger incentives.identification, inference, multiple equilibria, incomplete information games
- …