Statistical Analysis for Tolerances of Noxious Weed Seeds

An analysis of the previous method for testing tolerances of noxious weed seeds was performed. Problems of the current techniques were discussed, and the solution to these problems was given. A new technique of testing through the sequential test ratio was developed, and results examined. The sequential test was found to be useful enough to include the use of it in determining tolerances for noxious weed seeds. This study did show that the use of sequential tests does have excellent potential and flexibility as a statistical tool for the tolerances of noxious weed seeds. (75 pages

On direction of dependence

Under the assumption of the existence of linear relationship between two random variables, new formulas are introduced to express the coefficient of correlation. One of these formulas, the fourth power of the correlation coefficient is used to determine the direction of dependency between two random variables. Also an interpretation of the correlation coefficient as an asymmetric function of kurtosis coefficient and skewness coefficient of dependent variable and independent variable is provided. In the absent of the intercept in linear regression, the correlation coefficient is also expressed as a ratio of coefficients of variation between independent and dependent variable

Partial quantile regression

Partial least squares regression (PLSR) is a method of finding a reliable predictor of the response variable when there are more regressors than observations. It does so by eliciting a small number of components from the regressors that are inherently informative about the response. Quantile regression (QR) estimates the quantiles of the response distribution by regression functions of the covariates, and so gives a fuller description of the response than does the usual regression for the mean value of the response. We extend QR to partial quantile regression (PQR) when there are more regressors than observations. For each percentile the method provides a low dimensional approximation to the joint distribution of the covariates and response with a given coverage probability and which, under further linearity assumptions, estimates the corresponding quantile of the conditional distribution. The methodology parallels the procedure for PLSR using a quantile covariance that is appropriate for predicting a quantile rather than the usual covariance which is appropriate for predicting a mean value. The analysis suggests a new measure of risk associated with the quantile regressions. Examples are given that illustrate the methodology and the benefits accrued, based on simulated data and the analysis of spectrometer dat

The Concise Encyclopedia of Statistics

The Concise Encyclopedia of Statistics presents the essential information about statistical tests, concepts, and analytical methods in language that is accessible to practitioners and students of the vast community using statistics in medicine, engineering, physical science, life science, social science, and business/economics. The reference is alphabetically arranged to provide quick access to the fundamental tools of statistical methodology and biographies of famous statisticians. The more than 500 entries include definitions, history, mathematical details, limitations, examples, references