Abstract not found

Projection-based methods of inference on subsets of parameters are useful for obtaining tests that do not over-reject the true parameter values. However, they are also often criticized for being conservative. We show that the usual method of projection can be modified to obtain tests that are as powerful as the conventional tests for subsets of parameters. Like the usual projection-based methods, one can always put an upper bound to the rate at which the new method over-rejects the true value of the parameters of interest. The new method is described in the context of GMM with possibly weakly identified parameters. JEL Classification: C12; C13; C30

Diseases like chronic depression, schizophrenia, substance abuse, HIV infection, epilepsy,... are treated in multiple stages – At each stage, treatment is adapted to the available information on patient characteristics and past treatments. Information collected on patient characteristics, treatments administered, and patient outcomes together form a (short) finite horizon trajectory. Goal: To learn a “good ” treatment policy from a training dataset (batch) of finite horizon trajectories. 3 / 17 Multistage Medical Decision Making Somewhat distinct from the standard Reinforcement Learning set-up! Poorly understood system dynamics (e.g., no physical laws) Possibly high-dimensional state space, but finite action space (action = choice of treatment) Non-Markovian state transitions Very short horizon (say, 2 − 4 stages) Limited amount of data – They come from expensive and time-consuming clinical trials. We consider fitted Q-iteration (e.g., Antos et al., NIPS 2007) with linear function approximation in this context. 4 / 17

• We have discussed point estimates: – as an estimate of a success probability, – as an estimate of population mean, • These point estimates are almost never exactly equal to

Abstract not found

The definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances. Under certain conditions, the extended definition is shown to preserve a repeated

Classical confidence intervals are often misunderstood by particle physicists and the general public alike. The confusion arises from the two different definitions of probability in common use. As a result, there is general dissatisfaction when confidence intervals are empty or they exclude

We construct bootstrap confidence intervals for smoothing spline and smoothing spline ANOVA estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from exponential families. Several variations of bootstrap confidence intervals are considered and compared

Generalized Pivotal Quantities and Generalized Confidence Intervals have proved to be useful tools for making inferences in many practical problems. Although generalized confidence intervals are not guaranteed to have exact frequentist coverage, a number of published and unpublished simulation

In this short preliminary note I apply the methodology of gametheoretic probability to calculating non-asymptotic confidence intervals for the coefficient of a simple first order scalar autoregressive model. The most distinctive feature of the proposed procedure is that with high probability