Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA two parameter ratio-product-ratio estimator using auxiliary information
183
0
0.0
(
0
)
Added by
Bernd Sing
Publication date
2012
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We propose a two parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in Ray and Sahai (1980), Sahai and Ray (1980), Sahai and Sahai (1985) and Singh and Ruiz Espejo (2003). The bias and mean square error of our proposed estimator are obtained to the first degree of approximation. We derive conditions for the parameters under which the proposed estimator has smaller mean square error than the sample mean, ratio and product estimators. We carry out an application showing that the proposed estimator outperforms the traditional estimators using groundwater data taken from a geological site in the state of Florida.
rate research
Read More
Hotellings T-squared test is a classical tool to test if the normal mean of a multivariate normal distribution is a specified one or the means of two multivariate normal means are equal. When the population dimension is higher than the sample size, the test is no longer applicable. Under this situation, in this paper we revisit the tests proposed by Srivastava and Du (2008), who revise the Hotellings statistics by replacing Wishart matrices with their diagonal matrices. They show the revised statistics are asymptotically normal. We use the random matrix theory to examine their statistics again and find that their discovery is just part of the big picture. In fact, we prove that their statistics, decided by the Euclidean norm of the population correlation matrix, can go to normal, mixing chi-squared distributions and a convolution of both. Examples are provided to show the phase transition phenomenon between the normal and mixing chi-squared distributions. The second contribution of ours is a rigorous derivation of an asymptotic ratio-unbiased-estimator of the squared Euclidean norm of the correlation matrix.
The odds ratio measure is used in health and social surveys where the odds of a certain event is to be compared between two populations. It is defined using logistic regression, and requires that data from surveys are accompanied by their weights. A nonparametric estimation method that incorporates survey weights and auxiliary information may improve the precision of the odds ratio estimator. It consists in $B$-spline calibration which can handle the nonlinear structure of the parameter. The variance is estimated through linearization. Implementation is possible through standard survey softwares. The gain in precision depends on the data as shown on two examples.
We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the ratio and show that its cumulative distribution function can be expressed in terms of the hypergeometric function 2F1 of a matrix argument. Then we apply the holonomic gradient method for numerical evaluation of the hypergeometric function. This approach enables us to compute the power function of Roys maximum root test for testing the equality of two covariance matrices.
Let $b(x)$ be the probability that a sum of independent Bernoulli random variables with parameters $p_1, p_2, p_3, ldots in [0,1)$ equals $x$, where $lambda := p_1 + p_2 + p_3 + cdots$ is finite. We prove two inequalities for the maximal ratio $b(x)/pi_lambda(x)$, where $pi_lambda$ is the weight function of the Poisson distribution with parameter $lambda$.
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the response data is large compared to the sample size, the classical chi-square approximation of the likelihood ratio test statistic often fails. Theoretically, it has been an open problem when such a phenomenon happens as the dimension of data increases; practically, the effect of high dimensionality is less examined in exploratory factor analysis, and there lacks a clear statistical guideline on the validity of the conventional chi-square approximation. To address this problem, we investigate the failure of the chi-square approximation of the likelihood ratio test in high-dimensional exploratory factor analysis, and derive the necessary and sufficient condition to ensure the validity of the chi-square approximation. The results yield simple quantitative guidelines to check in practice and would also provide useful statistical insights into the practice of exploratory factor analysis.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
