Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. The term "mathematical statistics" is closely related to the term "statistical theory" but also embraces modelling for actuarial science and non-statistical probability theory, particularly in Scandinavia.

Excerpt: The traditional literature on seasonality has mainly focused attention on various statistical procedures for obtaining a seasonally adjusted time series from an observed time series that exhibits seasonal variation. Many of these procedures rely on the no ...

By: Food and Agriculture Organization of the United Nations

Nutrition Reference Publication

Excerpt: As indicated in the previous chapter (from page 59 onwards) querying of data grids in GIS can give you a first indication of relations between different factors. To get a more precise idea you have to carry out a statistical analysis on the available data. Regression analysis is a simple statistical tool to look at correlations between two or more types of data and is the most commonly used statistical technique in fisheries biology. First a refresher of the bas...

Introduction: In the National Crime Survey (NCS) conducted by the Bureau of the Census for the Bureau of Justice Statistics, a sampled household is interviewed every six months for three years. The first of the seven interviews, the bounding interview, is used only to set a time frame in order to avoid duplicating reported crimes on subsequent visits. The estimated crime levels and rates that are computed from the NCS are based on the last six interviews only. For furthe...

Excerpt: This appendix provides guidance on the statistical analysis of waste testing and environmental monitoring data. You should select the statistical test during the Data Quality Assessment (DQA) phase after you review the data quality objectives, the sampling design, and the characteristics of the data set. See guidance provided in Section 8. The statistical methods in this appendix are appropriate for use in evaluating sample analysis results when comparing consti...

Excerpt: It is demonstrated that any two backshift operator polynomials which transform a given non-stationary time series into stationary series with continuous spectral distributions must have a common divisor which has this property. It follows that the lowest-degree polynomial with this property is unique to within a constant multiple. Using this result some derivations are given, under varying assumptions, of a transformation formula used in non-stationary signal ex...

Excerpt: The ASA Fellowship presented a unique opportunity for the author to work on - the topic ?Data Analysis of Time Series.? This report is an attempt to summarize the author?s work on the ASA Special Project for Time Series methods development at the Bureau of the Census. This report consists of four main parts. The first two deal with Seasonal Adjustment and Forecasting quantitative series, based mainly on nonmetric filters. Analysis and Prediction by various types...

Introduction: Fertility projections often involve the forecasting of age-specific fertility rates. This may be done to take advantage of the tiown age stnure of the existing female population in using the cohort-component approach to fertility projection, or because age-specific fertility is itself of interest. If rates for single years of age are used, this creates a forecasting problem of large dimension, with fertility rates for 30 or more ages to forecast. If long-te...

Introduction: Census taking is both a civic ceremony and a scientific undertaking. Statistical science is used throughout the process to provide the most accurate measures of the population possible under the law and within the constraints of time, financial resources, and respondent burden. The use of statistical methods has grown steadily during the past seven censuses. While there may be limits to the role statistics can play in our civic ceremony, the available evide...

Excerpt: The analysis of- the components of time series has a long history (discussed in Nerlove, Grether, and Carvalho 1979), going back to work in astronomy, meteorology, and economics in the 17th through 19th centuries, and to early seasonal analysis by Buys-Ballot (1847). Empirical methods of seasonal adjustment were developed in the early part of this century leading utlimately to the development of the well-known X-11 method in 1967. As discussed in Bell and Hillme...

By: Food and Agriculture Organization of the United Nations

Nutrition Reference Publication

Excerpt: This chapter contains a brief description of some statistical methods in common use in tropical fishery biology and introduces the statistical notation adopted in the manual. It serves as a refresher and reference point, but is not intended as a textbook in its own right. The amount of literature on statistical methods is staggering, so there is no problem if you want to do further studies in biostatistics. Only two references are given here. The book ?Biometry?...

Description: If a drive system with unknown parameters represents “reality” and the response system a “computational model,” the unidirectional coupling can be used to change model parameters, as well as the model state, such that both systems synchronize with each other and model parameters coincide with their true values of “reality.” Such a parameter identification method is called adaptive synchronization (also autosynchronization) method and is widely used in the li...

Introduction: This paper is addressed to the problem of modeling and smoothing of time series with trend and seasonal mean value functions and stationary covariances. A modeling approach is taken. We were motivated by the Shiller-Akaike ?smoothness priors? solution to the smoothing problem originally posed by Whittaker in 1919. (Our earlier work is in Kitagawa (1981) and Brotherton and Gersch (19811.) Consider the smoothing problem: Let the observations of a discrete tim...

Excerpt: Time series containing abrupt structural shifts or outliers or both are considered. Techniques are developed for handling these using mixtures of densities, one component of which is a Gaussian density with a large variance. State space models are fitted to the series. The state vectors are estimated by the mode of their posterior density given the observations. The mode is found by Gauss-Newton iteration using Kalman filtering and smoothing. Three approximation...

Excerpt: Census taking is both a civic ceremony and a scientific undertaking. Statistical science is used throughout the process to provide the most accurate measures of the population possible under the law and within the constraints of time, financial resources, and respondent burden. The use of statistical methods has grown steadily during the past seven censuses. While there may be limits to the role statistics can play in our civic ceremony, the available evidence i...

Excerpt: The Environmental Public Health Tracking Network (EPHTN) proposes to link environmental hazards and exposures to health outcomes. Statistical methods used in case?control and cohort studies to link health outcomes to individual exposure estimates are well developed. However, reliable exposure estimates for many contaminants are not available at the individual level. In these cases, exposure/hazard data are often aggregated over a geographic area, and ecologic mo...

Excerpt: Preterm delivery can lead to serious infant health outcomes, including death and lifelong disability. Small increases in preterm delivery risk in relation to spatial gradients of air pollution have been reported, but previous studies may have controlled inadequately for individual factors. Using a time-series analysis, which eliminates potential confounding by individual risk factors that do not change over short periods of time, we investigated the effect of am...

Supplemental catalog subcollection information: NASA Publication Collection; Astrophysics and Technical Documents; Statistical theory of critical point and application of theory to phase changes in systems