### Table 2: Conditional and marginal distributions

### Table 3 ML estimates of the marginal distribution of Nl (mixture model)

in Auctions with Discrete Increments: a Structural Econometric Approach Based on Dominated Strategies

### Table 1: Summary of the marginal prior distributions of

"... In PAGE 3: ... Example Again consider the example introduced in Section 1. Table1 summarizes the marginal prior distributions based on an objective Bayesian analysis (using WinBUGS) of the original thermostat data using only a randomly selected subset of 3 lifetimes in each of the 12 runs. In this case, 5 out of the 36 lifetimes were found to be censored.... ..."

### Table 2 A marginal probability distribution

### Table 2: Selected quantiles of model parameters apos; marginal posterior distributions

1997

"... In PAGE 11: ... The number of initial #5Cwarm-up quot; runs were chosen to be 500,000, and one set of samples of parameters were then taken in every 100 it- erations to avoid serial correlation. The distributions of the six parameters of the piecewise linear model are shown in Figures 3a to 3f, and Table2 shows selected quantiles of these distributions. The mode and the mean of the marginal posterior distribution of #0C 1 are very close to 0, which further elaborated the mechanism hypothesized in the conceptual model.... ..."

Cited by 5

### Table 5. Marginal Z Distributions for State-Based Models

"... In PAGE 6: ...6 conditional distributions on Z for all states other than a1b0 are as similar as possible, subject to satisfaction of the AB and Z constraints. This is illustrated in Table5 for four different state-based models, including the AB:Z:a0b1Z model.... ..."

### Table 5. Marginal Z Distributions for State-Based Models

"... In PAGE 6: ... This relaxation procedure has the effect that, in the model, the conditional distributions on Z for all states other than a 1 b 0 are as similar as possible, subject to satisfaction of the AB and Z constraints. This is illustrated in Table5 for four different state-based models, including the AB :Z:a 0 b 1 Z model. data AB:Z:a0b0Z AB:Z:a0b1Z AB:Z:a1b0Z AB:Z:a1b1Z p(z0) p(z1) p(z0) p(z1) p(z0) p(z1) p(z0) p(z1) p(z0) p(z1) a0b0 0.... ..."

### Table 3: Quantiles for the studentized statistic Z from the bootstrap and the two methods for the saddlepoint approximations to marginal distributions.

1997

"... In PAGE 6: ... The only other quantities that are required are the derivatives of a(z; s; rj) with respect to z and s and its second deriva- tive with respect to s, which can easily be obtained from (9). As Table3 shows, this method does rather better than that based on the approximate cumulant generat- ing function particularly in the tails of the distribution. 5 Conclusion This paper has outlined a simple and generally e cient way to implement saddlepoint approximations in boot- strap applications.... ..."

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