Errors, Theory of ; Probabilities

- Academic Research Collections
- Statistics
- Mathematical Statistics

### Mathematical Statistics (2,118 Books)

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. |

### The State of Mining in the Kimberley District : The Probability of...

##### By: Robert Neil Smith

### An Essay on the Probability of Sensation in Vegetables : With Addi...

##### By: James Perchard Tupper

### The Theory of Human Progression, And Natural Probability of a Reig...

##### By: Patrick Edward Dove

### The Theory of Human Progression, And Natural Probability of a Reig...

##### By: Patrick Edward Dove

### The Prediction of Time Series with Trends and Seasonalities

##### By: Will Gersch

Statistical Reference Document

Introduction: In this paper we consider the optimal smoothing and forecasting of nonstationary time series with trend and seasonal mean value components with stationary covariance. Two classes of smoothness priors trend models are considered. In one the trend is modeled as a stochastically perturbed local polynomial function of time. In the other, the trend is assumed to consist of both the stocchastically perturbed local polynomial component plus a ?global? stationary t...

### Modeling Time Series Subject to Sampling Error

##### By: William R. Bell

Statistical Reference Document

Introduction: Papers by Scott and Smith (1974), and Scott, Smith, and Jones (1977) suggested the use of signal extraction results from time series analysis to improve estimates in periodic surveys. Given models for the true unobserved time series (population quantities) and the sampling errors, these results produce estimates of the population quantities that have minimum mean squared error among estimates that are linear functions of the observed time series of survey e...

### Time Series Methods for Survey Estimation

##### By: William R. Bell

Statistical Reference Document

Introduction: Papers by Scott and Smith (1974) and Scott, Smith, and Jones (1977), hereafter SSJ, suggested the use of signal extraction results from time series analysis to improve estimates in periodic surveys. If the covariance structure of the usual survey estimators (Y,) and their sampling errors (et> for a set of time points is known, these results produce the linear functions of the available Yt?s that have minimum mean squared error as estimators of the populatio...

### Initializing the Kalman Filter for Nonstationary Time Series Models

##### By: William R. Bell

Statistical Reference Document

Introduction: The Kalman filter and variations of it have been widely advocated in recent years for time series filtering, prediction, interpolation, signal extraction, and likelihood evaluation. The algorithms requ re two things: (1) a known state-space model suitable for the problem, and (2) an estimate of the initial state vector and the variance of the error n this estimate. For stationary time series models the usual initialization uses the unconditional mean and va...

### Alternative Approaches to the Analysis of Time Series Components

##### By: William R. Bell

Statistical Reference Document

Introduction: 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 H...

### Empirical Comparisons of Seasonal Arima and Arima Component (Struc...

##### By: William R. Bell

Statistical Reference Document

Introduction: Two popular models for seasonal time series are multiplicative seasonal ARIMA (autoregressive-integrated-moving average) models (Box and Jenkins 1970) and ARIMA component (structural) models (Harvey 1989). Despite the rising popularity of ARIMA component models in the time series literature of recent years, empirical studies comparing these models with seasonal ARIMA models have been relatively rare. One exception is Bell and Pugh (1990), hereafter BP, whic...

### Time Series Methods for Survey Estimation

##### By: William Bell

Statistical Reference Document

Excerpt: Papers by Scott and Smith (1974) and Scott, Smith, and Jones (1977), hereafter SSJ, suggested the use of signal extraction results from time series analysis to improve estimates in periodic surveys. If the covariance structure of the usual survey estimators (Y,) and their sampling errors (et> for a set of time points is known, these results produce the linear functions of the available Yt?s that have minimum mean squared error as estimators of the population val...

### Empirical Comparisons of Seasonal Arima and Arima Component (Struc...

##### By: William R. Bell

Statistical Reference Document

Excerpt: Two popular models for seasonal time series are multiplicative seasonal ARIMA (autoregressive-integrated-moving average) models (Box and Jenkins 1970) and ARIMA component (structural) models (Harvey 1989). Despite the rising popularity of ARIMA component models in the time series literature of recent years, empirical studies comparing these models with seasonal ARIMA models have been relatively rare. One exception is Bell and Pugh (1990), hereafter BP, which com...

### Preliminary Estimates for the National Crime Survey Using Regzessi...

##### By: Paul G. Wakim

Statistical Reference Document

Excerpt: 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 further det...

### Probability Theory: The Logic of Science

##### By: E.T. Jaynes

Mathematics document containing theorems and formulas.

Excerpt: Obability Theory; The Logic Of Science; Long Contents; Principles And Elementary Applications; Plausible Reasoning Deductive And Plausible Reasoning; and Analogies With Physical Theories.

### Final Report to Asa/Census Special Program for Time Series Methods...

##### By: Adi Raveh

Statistical Reference Document

Excerpt: This report deals with data analysis of empirical series. The main concept in such data analysis is the concept of order among the observations. An important special case of these series are the Time Series in which the order is determined by Time. Indeed, most of the examples included in this work are (economic) Time Series, but not exclusively. We are concerned with relationships between the values of the observations and their order, namely, the behavior of observations over time.

### Initializing the Kalman Filter for Nonstationary Time Series Models

##### By: William Bell

Statistical Reference Document

Excerpt: The Kalman filter and variations of it have been widely advocated in recent years for time series filtering, prediction, interpolation, signal extraction, and likelihood evaluation. The algorithms requ re two things: (1) a known state-space model suitable for the problem, and (2) an estimate of the initial state vector and the variance of the error n this estimate. For stationary time series models the usual initialization uses the unconditional mean and varianc...