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.

Supplemental catalog subcollection information: NASA Publication Collection; Astrophysics and Technical Documents; Bayesian estimation, decision theory, least squares method, maximum likelihood, and other mathematical techniques of statistical inference t

Supplemental catalog subcollection information: NASA Publication Collection; Astrophysics and Technical Documents; The results of an effort performed by Sperry Systems Management Division for AMRL in applying time series analysis as a tool for modeling th

Excerpt: 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.) ...

Excerpt: Economic, environmental and engineering data are often collected at equally spaced time intervals. In many problems such time series may be available from several related variables. It is of interest to model and analyze such series jointly to understand the dynamic relationships among them and to enhance the accuracy of forecasts.

Excerpt: Let Yt be a discrete time series following a stochastic difference equation model of the form ? In this paper we concentrate on unit roots of +l.

Excerpt: As in all recent censuses, the U.S. Census Bureau used statistical methods in the 2000 Census to account for missing or contradictory information concerning the number of people living in some identified housing units. These statistically corrected counts ...

Excerpt: Proposals are made for more comprehensive historic and current analysis of the periodic, systematic, and event-conditioned components in economic time series. The effects of unusual events U are distinguished from regular seasonality sand other periodic ...

Excerpt: It is frequently desired to obtain certain derived quantities from economic time series. These include smoothed values, deseasonalized values, forecasts, trend estimates and measurements of intervention effects. The form that these derived quantities ...

Excerpt: Procedures for the optimal seasonal adjustment of economic time series and their aggregation are derived, given a criterion suitable for the adjustment of data used in political or journalistic contexts. It is shown that data should be adjusted jointly an ...

Excerpt: Given a basic stochastic seasonal time series model, developed by Box and Jenkins, the corresponding model for temporal aggregates is derived. Insofar as forecasting future aggregates is concerned, the loss in information due to aggregation is substantial ...

Excerpt: Trading-day effects reflect variations in monthly time series due to the changing composition of months with respect to the numbers of times each day of the week occurs in the month. A relevant question regarding trading-day effects is whether they remain ...

Excerpt: Methods are developed for estimating trends in time series subject to level shifts. The approach is based on specifying stochastic models for breaks as part of the model structure, using heavy-tailed densities to allow for a positive probability of such a ...

Mathematics document containing theorems and formulas.

Excerpt: Mathematical Preliminaries: This chapter collects some fundamental mathematical concepts that we will use in our study of probability and statistics. Most of these concepts should seem familiar, although our presentation of them may be a bit more formal than you have previously encountered. This formalism will be quite useful as we study probability, but it will tend to recede into the background as we progress to the study of statistics.

Introduction: The Population Division of the Bureau of the Census periodically publishes projections of the number of households and families. In 1979 the Population Division issued the report f?Projections of the Number of Households and Families: 1979 to 1995? (Series P-25, No. 8051, and this year (1986) they released ?Projections of the Number of Households and Families: 1986 to 2000? (Series P-25, No. 986). In this paper we describe the time series methodology used i...

Excerpt: The Population Division of the Bureau of the Census periodically publishes projections of the number of households and families. In 1979 the Population Division issued the report f?Projections of the Number of Households and Families: 1979 to 1995? (Series P-25, No. 8051, and this year (1986) they released ?Projections of the Number of Households and Families: 1986 to 2000? (Series P-25, No. 986). In this paper we describe the time series methodology used in the...

Description: A general statistical theory of the intermittency in turbulence based on short-lived coherent structures (instantons) is presented. The probability density functions (PDFs) of the flux R are shown to have an exponential scaling P(R)∝exp(−cRs) in the tails, with the exponent s = (n+1)/m. Here, n and m are the order of the highest nonlinear interaction term and moments for which the PDFs are computed, respectively; c is constant depending on spatial profile of...

Introduction: Let Yt be a discrete time series following a stochastic difference equation model of the form (l-a 1 B- l .* -ap+d BP+d)(Yt-p) = (1-elB- ?* -eqBq)et (1.1) where B is the backshift operator (BYt = YtB1); et is a series of independent, identically distributed random shocks with mean 0 and variance ~2; and al, l *?) ap+d? h el? and u are parameters. Now let z denote a complex variable and consider the function a(Z) = (l-alz- l ** -ap+dZp*d). The behavior of th...

Excerpt: 1. OUTLINE OF PROBLEM It is often taken for granted that modification of outliers improves the forecasting performance of a time series model, because: 1. It is believed that outliers occur at places where the process generating the series has temporarily broken down, so that modification of outliers is needed to compensate for this in the forecasts calculations. 2. If so, modification should bring the parameter estimates closer to their true values, resulting i...

Excerpt: 1. Introduct ion Three common approaches to evaluating (Gaussian) likelihoods and doing other computations with time series models might be called the classical approach, the Kalmau filter approach, and the matrix approach. The classical approach works directly with difference equation forms of models (particularly for autoregressive - integrated - moving average (ARIMA) models) and such things as covariance generating functions and spectral densities. This appr...

Excerpt: It is often taken for granted that modification of outliers improves the forecasting performance of a time series model, because: 1. It is believed that outliers occur at places where the process generating the series has temporarily broken down, so that modification of outliers is needed to compensate for this in the forecasts calculations. 2. If so, modification should bring the parameter estimates closer to their true values, resulting in improved forecasts. ...