A Robust Model for Estimating and Testing for Means in Single Subject Experiments

1978 ◽  
Vol 20 (6) ◽  
pp. 717-724 ◽  
Author(s):  
James J. Higgins
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Autoregressive Model ◽  
Error Term ◽  
Behavioral Research ◽  
Single Subject ◽  
First Order ◽  
Normal Approximations ◽  
Robust Model ◽  
Tests Of Hypotheses

The first order autoregressive model is proposed as a robust model for estimating and testing for means in single subject experiments. It has the advantage of mathematical simplicity, and it provides good approximations to a number of other models of the type typically encountered in behavioral research. Practical considerations on the use of the model are considered including: tests of hypotheses and confidence intervals, sample size requirements, normal approximations, and advantages of the model over the independent error term model. Inferences for means and differences of means are considered.

scholarly journals Double sampling control chart for a first order autoregressive process

2008 ◽  
Vol 28 (3) ◽  
pp. 545-562 ◽  
Author(s):  
Fernando A. E. Claro ◽  
Antonio F. B. Costa ◽  
Marcela A. G. Machado
Keyword(s):  
Sample Size ◽  
Closed Form ◽  
Control Chart ◽  
Autoregressive Model ◽  
Average Run Length ◽  
Autoregressive Process ◽  
Double Sampling ◽  
First Order ◽  
Shewhart Chart ◽  
Sampling Intervals

In this paper we propose the Double Sampling control chart for monitoring processes in which the observations follow a first order autoregressive model. We consider sampling intervals that are sufficiently long to meet the rational subgroup concept. The Double Sampling chart is substantially more efficient than the Shewhart chart and the Variable Sample Size chart. To study the properties of these charts we derived closed-form expressions for the average run length (ARL) taking into account the within-subgroup correlation. Numerical results show that this correlation has a significant impact on the chart properties.

scholarly journals Functional effectiveness of a myo-electric prosthesis compared with a functional split-hook prosthesis: A single subject experiment

1981 ◽  
Vol 5 (2) ◽  
pp. 92-96 ◽  
Author(s):  
P. J. Agnew
Keyword(s):  
Autoregressive Model ◽  
Sensory Feedback ◽  
Clinical Evidence ◽  
Hand Function ◽  
Single Subject ◽  
Myoelectric Prosthesis ◽  
First Order ◽  
Independent Observations ◽  
New Ideas ◽  
Subject Experiment

The functional effectiveness of a myo-electric prosthesis with sensory feedback compared with that of a split-hook is described. Thirty independent observations were made on a single subject with a right below-elbow amputation wearing the myo-electric prosthesis and the split-hook prosthesis. Using a first order autoregressive model for making inferences about the two sets of data, the split-hook was found to be functionally better (p<0-001) than the myo-electric prosthesis. Functional effectiveness was defined operationally as scores on the Minnesota Rate of Manipulation Placing Test and the Smith Test of Hand Function. No predictions are made regarding the use of either prosthesis for other amputees. However clinical evidence suggested suitability of the myoelectric prosthesis with sensory feedback for some other functional tasks. It is difficult to add new ideas or to be critical concerning the projects proposed by McCoIIough in the April, 1981 issue of Prosthetics and Orthotics International, and therefore, for the most part, this presentation is restricted to amplification of the ideas set forth in that article.

Inference for treatment effect parameters in potentially misspecified high-dimensional models

Biometrika ◽  
2020 ◽  
Author(s):  
Oliver Dukes ◽  
Stijn Vansteelandt
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Treatment Effect ◽  
Observational Studies ◽  
Treatment Effects ◽  
Treatment Selection ◽  
High Dimensional ◽  
Selection Mechanism ◽  
Dimensional Models ◽  
Effect Parameter

Summary Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators, such as the lasso, or other regularization approaches. Naïve use of such estimators yields confidence intervals for the conditional treatment effect parameter that are not uniformly valid. Moreover, as the number of covariates grows with the sample size, correctly specifying a model for the outcome is nontrivial. In this article we deal with both of these concerns simultaneously, obtaining confidence intervals for conditional treatment effects that are uniformly valid, regardless of whether the outcome model is correct. This is done by incorporating an additional model for the treatment selection mechanism. When both models are correctly specified, we can weaken the standard conditions on model sparsity. Our procedure extends to multivariate treatment effect parameters and complex longitudinal settings.

SMALL SAMPLE SIZE SCIENTIST

PEDIATRICS ◽  
1989 ◽  
Vol 83 (3) ◽  
pp. A72-A72
Author(s):  
Student
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Causal Explanation ◽  
Small Sample Size ◽  
Small Sample ◽  
Small Samples ◽  
High Expectations ◽  
Sampling Variation ◽  
The Law ◽  
The Stability

The believer in the law of small numbers practices science as follows: 1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power. 2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance. 3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals. 4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.

PATH INTEGRAL METHOD FOR LIMITING DISTRIBUTION OF AN ESTIMATOR ARISING FROM AN AR(1)-PROCESS WITH A UNIT ROOT

2013 ◽  
Vol 16 (04) ◽  
pp. 1350029
Author(s):  
SHIH-FENG HUANG ◽  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
Characteristic Function ◽  
Path Integral ◽  
Unit Root ◽  
Autoregressive Model ◽  
Integral Method ◽  
Unit Root Test ◽  
Random Variable ◽  
Limiting Distribution ◽  
First Order ◽  
Path Integral Method

We propose the path-integral technique to derive the characteristic function of the limiting distribution of the unit root test in a first order autoregressive model. Our results provide a new and useful approach to obtain the closed form of the characteristic function of a random variable associated with the limiting distribution, which is realized as a ratio of Brownian functionals on the classical Wiener space.

Sign in / Sign up

Export Citation Format

Share Document