Several new asymptotic estimates (with precise error bounds) are derived for Poisson and binomial distributions as the parameters tend to infinity. The analytic methods used are also applicable to other discrete distribution functions.

We examine the effect of regularly scheduled macroeconomic announcements on the beliefs and preferences of participants in the U.S. Treasury market by comparing the option-implied state-price density (SPD) of bond prices shortly before and after the announcements. We find that the announcements reduce the uncertainty implicit in the second moment of the SPD regardless of the content of the news. The changes in the higher-order moments, in contrast, depend on whether the news is good or bad for economic prospects. Using a standard model for interest rates to disentangle changes in beliefs and changes in preferences, we demonstrate that our results are consistent with time-varying risk aversion in the spirit of habit formation. We thank Tim Bollerslev, Jun Cai, and Frank Song for providing the announcements data and Nick

This note (1) provides references to recent work that applies computer algebra (CA) to the life sciences, (2) cites literature that explains the biological background of each application, (3) states the mathematical methods that are used, (4) mentions the benefits of CA, and (5) suggests some topics for future work.

In this article, we derive an explicit formula for computing confidence interval for the mean of a bounded random variable. Moreover, we have developed multistage point estimation methods for estimating the mean value with prescribed precision and confidence level based on the proposed confidence interval. 1

Abstract—This paper presents a computationally simple and accurate method to compute the error probabilities in decentralized detection in sensor networks. The cost of the direct computation of these probabilities—e.g., the probability of false alarm, the probability of a miss, or the average error probability—is combinatorial in the number of sensors and becomes infeasible even with small size networks. The method is based on the theory of large deviations, in particular, the saddlepoint approximation and applies to generic parallel fusion sensor networks, including networks with nonidentical sensors, nonidentical observations, and unreliable communication links. The paper demonstrates with parallel fusion sensor network problems the accuracy of the saddlepoint methodology: 1) computing the detection performance for a variety of small and large sensor network scenarios; and 2) designing the local detection thresholds. Elsewhere, we have used the saddlepoint approximation to study tradeoffs among parameters for networks of arbitrary size. Index Terms—Decentralized detection, Lugannani-Rice approximation, parallel fusion, quantization, saddlepoint approximation,

In time series regression with nonparametrically autocorrelated errors, it is now standard empirical practice to construct con…dence intervals for regression coe ¢ cients on the basis of nonparametrically studentized t-statistics. The standard error used in the studentization is typically estimated by a kernel method that involves some smoothing process over the sample autocovariances. The underlying parameter (M) that controls this tuning process is a bandwidth or truncation lag and it plays a key role in the …nite sample properties of tests and the actual coverage properties of the associated con…dence intervals. The present paper develops a bandwidth choice rule for M that optimizes the coverage accuracy of interval estimators in the context of linear GMM regression. The optimal bandwidth balances the asymptotic variance with the asymptotic bias of the robust standard error estimator. This approach contrasts with the conventional bandwidth choice rule for nonparametric estimation where the focus is the nonparametric quantity itself and the choice rule balances asymptotic variance with squared asymptotic bias. It turns out that the optimal bandwidth for interval estimation has a di¤erent expansion rate and is typically substantially larger

(1) The sequence fb kn g = f1; b 1n ; b 2n ; . . .g determines the asymptotic behavior of the expansion: in particular how the re-expression approximates the original function. Usual choices of fb kn g are f1; n \Gamma1=2 ; n \Gamma1 ; . . .g or f1; n \Gamma1 ; n \Gamma2 ; . . .g; in any case it is required that b kn = o(b k\Gamma1;n ) as n !1. For sequences of constants fa n g, fb n g, we write a n =<F13.5

Estimation of Autoregressive Processes with Heterogenous Persistence We propose a semi-nonparametric method of identification and estimation for a gaussian autoregressive process with stochastic autoregressive coefficient. The autoregressive coefficient is considered as a latent process with either a moving average, or regime switching representation. We develop a consistent estimator of the distribution of the autoregressive coefficient based on nonlinear canonical analysis of the observed process. The approach is illustrated by simulation results. Keywords: Canonical analysis, stochastic parameter, time deformation, identification, nonparametric method JEL : C32, C14 THIS VERSION: March 7, 2000 0 R'esum'e Estimation de Processus Autoregressifs avec Heterogeneit'e Persistante Nous proposons une m'ethode d'identification et d'estimation semi-nonparam'etrique pour un processus autor'egressif gaussien avec coefficient autor'egressif stochastique. Le coefficient autor'egressif constitu...

In time series regression with nonparametrically autocorrelated errors, it is now standard empirical practice to construct confidence intervals for regression coefficients on the basis of nonparametrically studentized t-statistics. The standard error used in the studentization is typically estimated by a kernel method that involves some smoothing process over the sample autocovariances. The underlying parameter (M) that controls this tuning process is a bandwidth or truncation lag and it plays a key role in the finite sample properties of tests and the actual coverage properties of the associated confidence intervals. The present paper develops a bandwidth choice rule for M that optimizes the coverage accuracy of interval estimators in the context of linear GMM regression. The optimal bandwidth balances theasymptoticvariancewiththeasymptoticbias of the robust standard error estimator. This approach contrasts with the conventional bandwidth choice rule for nonparametric estimation where the focus is the nonparametric quantity itself and the choice rule balances asymptotic variance with squared asymptotic bias. It turns out that the optimal bandwidth for interval estimation has a different expansion rate and is typically substantially larger