A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TLDR
In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.Abstract:
In many cases an optimum or computationally convenient test of a simple hypothesis $H_0$ against a simple alternative $H_1$ may be given in the following form. Reject $H_0$ if $S_n = \sum^n_{j=1} X_j \leqq k,$ where $X_1, X_2, \cdots, X_n$ are $n$ independent observations of a chance variable $X$ whose distribution depends on the true hypothesis and where $k$ is some appropriate number. In particular the likelihood ratio test for fixed sample size can be reduced to this form. It is shown that with each test of the above form there is associated an index $\rho$. If $\rho_1$ and $\rho_2$ are the indices corresponding to two alternative tests $e = \log \rho_1/\log \rho_2$ measures the relative efficiency of these tests in the following sense. For large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample of size $en$ with the second test. To obtain the above result, use is made of the fact that $P(S_n \leqq na)$ behaves roughly like $m^n$ where $m$ is the minimum value assumed by the moment generating function of $X - a$. It is shown that if $H_0$ and $H_1$ specify probability distributions of $X$ which are very close to each other, one may approximate $\rho$ by assuming that $X$ is normally distributed.read more
Citations
More filters
Journal ArticleDOI
On Optimizing Overlay Topologies for Search in Unstructured Peer-to-Peer Networks
Hung-Chang Hsiao,Hong-Wei Su +1 more
TL;DR: A novel overlay formation algorithm for unstructured P2P networks based on the file sharing pattern exhibiting the power-law property is proposed, which clearly outperforms the competing algorithms in terms of the hop count of routing a query message, the successful ratio of resolving a query, the number of messages required for resolving a queries, and the message overhead for maintaining and formatting the overlay.
Journal ArticleDOI
Performance Analysis of Optical Receivers by the Saddlepoint Approximation
TL;DR: A saddlepoint method is described for both setting the decision level and approximating the error probability on the basis of the probability generating function of the p k 's of a binary communication receiver embodying a photoelectric detector.
Proceedings ArticleDOI
General dynamic routing with per-packet delay guarantees of O(distance+1/session rate)
TL;DR: This work addresses the problem of scheduling the sessions at each switch, so as to minimize worst-case packet delay and queue buildup at the switches, and presents an asymptotically-optimal schedule that achieves a delay bound of O(1/r/ sub i/+d/sub i/) with only constant-size queues at the switch.
Journal ArticleDOI
Estimates of Location: A Large Deviation Comparison
TL;DR: In this paper, the authors consider the estimation of a location parameter in a one-sample problem and show that the asymptotic performance of a sequence of estimates is measured by the exponential rate of convergence to 0.
Journal ArticleDOI
Higher key rate of measurement-device-independent quantum key distribution through joint data processing
TL;DR: Numerical results show that the double-scanning method can improve the key rate of measurement-device-independent quantum key distribution drastically and the optimization of MDI-QKD protocol with all parameters including the source parameters and failure probability parameters, over symmetric channel or asymmetric channel.
References
More filters