
On the Relationship Between Measures of Relative Efficiency for Random Signal Detection
Relative efficiency (RE), the Pitman asymptotic relative efficiency (ARE...
read it

Empirical or Invariant Risk Minimization? A Sample Complexity Perspective
Recently, invariant risk minimization (IRM) was proposed as a promising ...
read it

Bootstrap pvalues reduce type 1 error of the robust rankorder test of difference in medians
The robust rankorder test (Fligner and Policello, 1981) was designed as...
read it

Bounds for the asymptotic distribution of the likelihood ratio
In this paper we give an explicit bound on the distance to chisquare for...
read it

Tstatistic for Autoregressive process
In this paper, we discuss the distribution of the tstatistic under the ...
read it

Rakingratio empirical process with auxiliary information learning
The rakingratio method is a statistical and computational method which ...
read it

Connecting Sharpe ratio and Student tstatistic, and beyond
Sharpe ratio is widely used in asset management to compare and benchmark...
read it
On Asymptotic Standard Normality of the Two Sample Pivot
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test statistic being asymptotically standard Normal, which is known to happen if the two samples are independent and the ratio of the sample sizes converges to a finite positive number. This restriction on the asymptotic behavior of the ratio of the sample sizes carries the risk of rendering the asymptotic justification of the finite sample approximation invalid. It turns out that neither the restriction on the asymptotic behavior of the ratio of the sample sizes nor the assumption of cross sample independence is necessary for the pivotal convergence in question to take place. If the joint distribution of the standardized sample means converges to a spherically symmetric distribution, then that distribution must be bivariate standard Normal (which can happen without the assumption of cross sample independence), and the aforesaid pivotal convergence holds.
READ FULL TEXT
Comments
There are no comments yet.