Estimating population means in covariance stationary process

In simple random sampling, the basic assumption at the stage of estimating the standard error of the sample mean and constructing the corresponding confidence interval for the population mean is that the observations in the sample must be independent. In a number of cases, however, the validity of this assumption is under question, and as examples we mention the cases of generating dependent quantities in Jackknife estimation, or the evolution through time of a social quantitative indicator in longitudinal studies. For the case of covariance stationary processes, in this paper we explore the consequences of estimating the standard error of the sample mean using however the classical way based on the independence assumption. As criteria we use the degree of bias in estimating the standard error, and the actual confidence level attained by the confidence interval, that is, the actual probability the interval to contain the true mean. These two criteria are computed analytically under different sample sizes in the stationary ARMA(1,1) process, which can generate different forms of autocorrelation structure between observations at different lags.Jackknife estimation; ARMA; Longitudinal data; Actual confidence level

Confidence intervals in stationary autocorrelated time series

In this study we examine in covariance stationary time series the consequences of constructing confidence intervals for the population mean using the classical methodology based on the hypothesis of independence. As criteria we use the actual probability the confidence interval of the classical methodology to include the population mean (actual confidence level), and the ratio of the sampling error of the classical methodology over the corresponding actual one leading to equality between actual and nominal confidence levels. These criteria are computed analytically under different sample sizes, and for different autocorrelation structures. For the AR(1) case, we find significant differentiation in the values taken by the two criteria depending upon the structure and the degree of autocorrelation. In the case of MA(1), and especially for positive autocorrelation, we always find actual confidence levels lower than the corresponding nominal ones, while this differentiation between these two levels is much lower compared to the case of AR(1).Covariance stationary time series; Variance of the sample mean; Actual confidence level

Estimating population means in covariance stationary process

In simple random sampling, the basic assumption at the stage of estimating the standard error of the sample mean and constructing the corresponding confidence interval for the population mean is that the observations in the sample must be independent. In a number of cases, however, the validity of this assumption is under question, and as examples we mention the cases of generating dependent quantities in Jackknife estimation, or the evolution through time of a social quantitative indicator in longitudinal studies. For the case of covariance stationary processes, in this paper we explore the consequences of estimating the standard error of the sample mean using however the classical way based on the independence assumption. As criteria we use the degree of bias in estimating the standard error, and the actual confidence level attained by the confidence interval, that is, the actual probability the interval to contain the true mean. These two criteria are computed analytically under different sample sizes in the stationary ARMA(1,1) process, which can generate different forms of autocorrelation structure between observations at different lags

Space shuttle auxiliary propulsion system design study: Program plan

Development of design and programmatic data for space shuttle reaction control systems and integrated reaction control system/orbit maneuvering system

Estimating population means in covariance stationary process

In simple random sampling, the basic assumption at the stage of estimating the standard error of the sample mean and constructing the corresponding confidence interval for the population mean is that the observations in the sample must be independent. In a number of cases, however, the validity of this assumption is under question, and as examples we mention the cases of generating dependent quantities in Jackknife estimation, or the evolution through time of a social quantitative indicator in longitudinal studies. For the case of covariance stationary processes, in this paper we explore the consequences of estimating the standard error of the sample mean using however the classical way based on the independence assumption. As criteria we use the degree of bias in estimating the standard error, and the actual confidence level attained by the confidence interval, that is, the actual probability the interval to contain the true mean. These two criteria are computed analytically under different sample sizes in the stationary ARMA(1,1) process, which can generate different forms of autocorrelation structure between observations at different lags

Confidence intervals in stationary autocorrelated time series

In this study we examine in covariance stationary time series the consequences of constructing confidence intervals for the population mean using the classical methodology based on the hypothesis of independence. As criteria we use the actual probability the confidence interval of the classical methodology to include the population mean (actual confidence level), and the ratio of the sampling error of the classical methodology over the corresponding actual one leading to equality between actual and nominal confidence levels. These criteria are computed analytically under different sample sizes, and for different autocorrelation structures. For the AR(1) case, we find significant differentiation in the values taken by the two criteria depending upon the structure and the degree of autocorrelation. In the case of MA(1), and especially for positive autocorrelation, we always find actual confidence levels lower than the corresponding nominal ones, while this differentiation between these two levels is much lower compared to the case of AR(1)

Phase-type survival trees and mixed distribution survival trees for clustering patients' hospital length of stay

Clinical investigators, health professionals and managers are often interested in developing criteria for clustering patients into clinically meaningful groups according to their expected length of stay. In this paper, we propose two novel types of survival trees; phase-type survival trees and mixed distribution survival trees, which extend previous work on exponential survival trees. The trees are used to cluster the patients with respect to length of stay where partitioning is based on covariates such as gender, age at the time of admission and primary diagnosis code. Likelihood ratio tests are used to determine optimal partitions. The approach is illustrated using nationwide data available from the English Hospital Episode Statistics (HES) database on stroke-related patients, aged 65 years and over, who were discharged from English hospitals over a 1-year period.peer-reviewe

Torque Controlled Drive for Permanent Magnet Direct Current Brushless Motors

This thesis describes the design and implementation of a simple variable speed drive (VSD) based on a brushless direct current (BLDC) machine and discrete logic circuits. A practical VSD was built, capable of operating a BLDC machine in two quadrants, motoring and regenerative braking. The intended applications are electric scooters and electric bicycles, where the recovered energy from braking extends the range of the vehicle. A conceptual four quadrant VSD, suitable for three and four wheelers requiring reverse operation, was designed and tested in simulation. Simplicity was emphasized in this design to help achieve a robust, easy to analyse system. The versatility of multi-function gate integrated circuits (ICs) made them ideal for implementing the commutation logic and keeping the system simple. The BLDC machine has sensors with a resolution of 60 ed to determine rotor position. An electronic commutator or phase switcher module interprets the position signals and produces a switching pattern. This effectively transforms the BLDC machine into a direct current (DC) brushed machine. A synchronous step down converter controls the BLDC machine current with a tolerance band scheme. This module treats the BLDC machine as if it was a DC machine. The leakage inductance of the electric machine is used as the inductive filter element. The unipolar switching scheme used ensures that current flows out of the battery only for motoring operation and into the battery only during regeneration. The current and torque are directly related in a DC brushed machine. The action of an electronic commutator or phase switcher creates that same relationship between torque and current in a BLDC machine. Torque control is achieved in the BLDC machine using a single channel current controller. The phase switcher current is monitored and used to control the duty ratio of the synchronous converter switches. Successful operation of the practical VSD was achieved in two quadrants: forwards motoring and forwards regenerating. The maximum tested power outputs were 236W in motoring mode and 158W in regenerating mode. The output torque could be smoothly controlled from a positive to a negative value. iv v Simulation of the conceptual four quadrant design was successful in all the motoring, generating and active braking zones. The required manipulation of logic signals to achieve this type of operation was done automatically while the machine was running. The resulting output torque is smoothly controlled in all of the operating zones. Commutation at certain speeds and torques are handled better by some topologies than others. Some current sensing strategies adversely affect instantaneous phase currents under certain conditions. The final design chose the method where phase currents experience no overshoot, minimizing component stress. The battery, or energy storage system, used in verifying the operation of the VSD in the practical electric bicycle was found to be the most limiting component. In regenerating mode, the low charge acceptance rate of the battery reduced the maximum retarding torque and energy recovery rate