Survey of Estimability Criteria, Connected Design and Testing Testable Hypotheses in Unbalanced Design
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Abstract
In the linear model Y = Xβ+ε with X having a full column rank, all β parameters can be estimated and the estimates are unique. However, in cases where X does not have a full column rank, not all β parameters can be estimated. In this paper, the problem to be discussed is how to determine parameters or parameter functions that are estimable and testable. Applications to the case of unbalanced data will be presented.
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[1] RC Bose. The Fundamental Theorem of Linear Estimation. In Proc. 31???????? Indian Scientific Congress (1944), pages 2–3, 1944
[2] George A Milliken and Dallas E Johnson. Analysis of Messy Data, Volume I: Designed Experiments. Taylor & Francis, 2001
[3] George A Milliken. New Criteria for Estimability for Linear Models. The Annals of Mathematical Statistics, 42(5):1588–1594, 1971
[4] Shayle Robert Searle, Charles E McCulloch, and John M Neuhaus. Generalized, Linear and Mixed Models. Wiley Hoboken, NJ, USA, 2001
[5] George Seber. The Linear Model and Hypothesis. Springer, 2015
[6] Andre I Khuri. Linear Model Methodology. Chapman and Hall/CRC, 2009
[7] IS Alalouf and George PH Styan. Characterizations of Estimability in the General Linear Model. The Annals of Statistics, 7(1):194–200, 1979
[8] Jan R Magnus and Heinz Neudecker. Matrix Differential Calculus with Applications in Statistics and Econometrics. John Wiley & Sons, 2019
[9] Mustofa Usman. Testing Hypothesis in Split Plot Design When Some Observations Are Missing. PhD thesis, Kansas State University, 1985. Unpublished Dissertation
[10] Franklin A Graybill. Theory and Application of the Linear Model. 1976
[11] Shayle Robert Searle. Linear Models. John Wiley and Sons, New York, 1971
[12] NR Mohan Madhyastha, Sreenivasan Ravi, and AS Praveena. A First Course in Linear Models and Design of Experiments. Springer, 2020
[13] Jerzy K Baksalary and R Kala. Extensions of Milliken’s estimability criterion. The Annals of Statistics, 4(3):639–641, 1976
[14] RK Elswick Jr, Chris Gennings, Vernon M Chinchilli, and Kathryn S Dawson. A Simple Approach for Finding Estimable Functions in Linear Models. The American Statistician, 45(1):51–53, 1991
[15] Justus Seely. Estimability and Linear Hypotheses. The American Statistician, 31(3):121–123, 1977
[16] Shayle R Searle, F Michael Speed, and George A Milliken. Population Marginal Means in the Linear Model: An Alternative to Least Squares Means. The American Statistician, 34(4):216–221, 1980
[17] Saang-Yoon Hyun and Kyuhan Kim. An Evaluation of Estimability of Parameters in the State-Space Non-Linear Logistic Production Model. Fisheries Research, 245:106135, 2022
[18] Yunxiao Chen, Xiaoou Li, and Siliang Zhang. Structured Latent Factor Analysis for Large-Scale Data: Identifiability, Estimability, and Their Implications. Journal of the American Statistical Association, 115(532):1756–1770, 2020
[19] A Khodabandeh and PJG Teunissen. Integer Estimability in GNSS Networks. Journal of Geodesy, 93(9):1805–1819, 2019
[20] Iman Moshiritabrizi, Kaveh Abdi, Jonathan P McMullen, Brian M Wyvratt, and Kimberley B McAuley. Parameter Estimation and Estimability Analysis in Pharmaceutical Models with Uncertain Inputs. AIChE Journal, 70(1):e18168, 2024
[21] Ravindra B Bapat. Linear Algebra and Linear Models. Springer, 2000
[22] Alan Agresti. Foundations of Linear and Generalized Linear Models. John Wiley & Sons, 2015