A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
Reads0
Chats0
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
Small domain randomization: same privacy, more utility
Rhonda Chaytor,Ke Wang +1 more
TL;DR: An alternative way to randomize sensitive values, called small domain randomization, is proposed, which partitions the given table into sub-tables that have smaller domains of sensitive values and randomizes the sensitive values within each sub-table independently.
Journal ArticleDOI
Optimal query complexity bounds for finding graphs
Sung-Soon Choi,Jeong Han Kim +1 more
TL;DR: It is shown that O(mlognlogm) queries are enough provided m>=(logn)^@a for a sufficiently large constant @a, which is best possible up to a constant factor if m=0.
Journal ArticleDOI
The Commitment Capacity of the Gaussian Channel Is Infinite
TL;DR: It is proved that the commitment capacity of the power-constrained Gaussian channel, i.e., the optimal rate at which this channel can be used for implementing commitment schemes, is infinite.
Book
Handling experimental data
TL;DR: Plans and records errors graphs distributions reporting data units dimensions are presented, and logarithms are presented for the first time.
Journal ArticleDOI
A Formal Approach to Physics-based Attacks in Cyber-physical Systems
TL;DR: A hybrid process calculus is defined to model both CPSs and physics-based attacks and how to estimate the impact of a successful attack on a CPS and investigate possible quantifications of the success chances of an attack.
References
More filters