Introduction to Hoeffding (1948) A Class of Statistics with Asymptotically Normal Distribution

1992 ◽  
pp. 299-307 ◽  
Author(s):  
P. K. Sen
Keyword(s):  
Normal Distribution ◽  
Asymptotically Normal

scholarly journals Better Coverage Intervals for Estimators from a Complex Sample Survey

2020 ◽  
Author(s):  
Phillip S. Kott
Keyword(s):  
Normal Distribution ◽  
Parameter Estimate ◽  
Regression Coefficients ◽  
Sample Survey ◽  
Complex Survey ◽  
Asymptotically Normal ◽  
Complex Survey Data ◽  
Complex Sample ◽  
Chi Squared ◽  
Coverage Interval

Coverage intervals for a parameter estimate computed using complex survey data are often constructed by assuming the parameter estimate has an asymptotically normal distribution and the measure of the estimator’s variance is roughly chi-squared. The size of the sample and the nature of the parameter being estimated render this conventional “Wald” methodology dubious in many applications. I developed a revised method of coverage-interval construction that “speeds up the asymptotics” by incorporating an estimated measure of skewness. I discuss how skewness-adjusted intervals can be computed for ratios, differences between domain means, and regression coefficients.

scholarly journals Mean and variance of balanced Pólya urns

2020 ◽  
Vol 52 (4) ◽  
pp. 1224-1248
Author(s):  
Svante Janson
Keyword(s):  
Normal Distribution ◽  
Covariance Matrix ◽  
Largest Eigenvalue ◽  
Asymptotically Normal ◽  
Pólya Urn ◽  
Polya Urn ◽  
Mean And Variance ◽  
The Mean ◽  
The Largest Eigenvalue

AbstractIt is well-known that in a small Pólya urn, i.e., an urn where the second largest real part of an eigenvalue is at most half the largest eigenvalue, the distribution of the numbers of balls of different colours in the urn is asymptotically normal under weak additional conditions. We consider the balanced case, and then give asymptotics of the mean and the covariance matrix, showing that after appropriate normalization, the mean and covariance matrix converge to the mean and covariance matrix of the limiting normal distribution.

scholarly journals Estimation and testing for panel data partially linear single-index models with errors correlated in space and time

2019 ◽  
Vol 09 (02) ◽  
pp. 2150005
Author(s):  
Jian-Qiang Zhao ◽  
Yan-Yong Zhao ◽  
Jin-Guan Lin ◽  
Zhang-Xiao Miao ◽  
Waled Khaled
Keyword(s):  
Panel Data ◽  
Normal Distribution ◽  
Test Method ◽  
Link Function ◽  
Single Index ◽  
Asymptotically Normal ◽  
Space And Time ◽  
Partially Linear ◽  
Single Index Models ◽  
Unknown Link

We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.

scholarly journals The Inversion Number and the Major Index are Asymptotically Jointly Normally Distributed on Words

2016 ◽  
Vol 25 (3) ◽  
pp. 470-483
Author(s):  
MARKO THIEL
Keyword(s):  
Normal Distribution ◽  
Joint Distribution ◽  
Bivariate Normal Distribution ◽  
Bivariate Normal ◽  
Asymptotically Normal ◽  
Major Index ◽  
Inversion Number ◽  
Mahonian Statistics ◽  
Normally Distributed

In a recent paper, Baxter and Zeilberger showed that the two most important Mahonian statistics, the inversion number and the major index, are asymptotically independently normally distributed on permutations. In another recent paper, Canfield, Janson and Zeilberger proved the result, already known to statisticians, that the Mahonian distribution is asymptotically normal on words. This leaves one question unanswered: What, asymptotically, is the joint distribution of the inversion number and the major index on words? We answer this question by establishing convergence to a bivariate normal distribution.

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