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Journal articles on the topic 'Optimal Sample Size'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Cressie, Noel, Jonathan Biele, and Peter B. Morgan. "Sample-size-optimal sequential testing." Journal of Statistical Planning and Inference 39, no. 2 (1994): 305–27. http://dx.doi.org/10.1016/0378-3758(94)90211-9.

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2

Müller, Peter, Giovanni Parmigiani, Christian Robert, and Judith Rousseau. "Optimal Sample Size for Multiple Testing." Journal of the American Statistical Association 99, no. 468 (2004): 990–1001. http://dx.doi.org/10.1198/016214504000001646.

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3

Stec, Daniel, Piotr Gąsiorek, Witold Morek, et al. "Estimating optimal sample size for tardigrade morphometry." Zoological Journal of the Linnean Society 178, no. 4 (2016): 776–84. http://dx.doi.org/10.1111/zoj.12404.

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4

Ito, H., W. W. Wallender, and N. S. Raghuwanshi. "Optimal Sample Size for Furrow Irrigation Design." Biosystems Engineering 91, no. 2 (2005): 229–37. http://dx.doi.org/10.1016/j.biosystemseng.2005.02.009.

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5

Schwertman, Neil C., and David K. Smith. "Optimal Sample Size for Detection of an Infestation." Journal of Agricultural, Biological, and Environmental Statistics 3, no. 4 (1998): 359. http://dx.doi.org/10.2307/1400570.

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6

Annis, Charles, Luca Gandossi, and Oliver Martin. "Optimal sample size for probability of detection curves." Nuclear Engineering and Design 262 (September 2013): 98–105. http://dx.doi.org/10.1016/j.nucengdes.2013.03.059.

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7

Barenghi, Carlo F., Amir D. Aczel, and Roger J. Best. "Determining the optimal sample size for decision making." Journal of Statistical Computation and Simulation 24, no. 2 (1986): 135–45. http://dx.doi.org/10.1080/00949658608810896.

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8

Kadane, Joseph B. "Optimal sample size for risk-compensated survey assessment." Law, Probability and Risk 16, no. 4 (2017): 151–62. http://dx.doi.org/10.1093/lpr/mgx013.

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9

Katsis, Athanassios. "CALCULATING THE OPTIMAL SAMPLE SIZE FOR BINOMIAL POPULATIONS." Communications in Statistics - Theory and Methods 30, no. 4 (2001): 665–78. http://dx.doi.org/10.1081/sta-100002143.

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10

Walter, S. D., M. Eliasziw, and A. Donner. "Sample size and optimal designs for reliability studies." Statistics in Medicine 17, no. 1 (1998): 101–10. http://dx.doi.org/10.1002/(sici)1097-0258(19980115)17:1<101::aid-sim727>3.0.co;2-e.

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11

Santis, Fulvio De, Marco Perone Pacifico, and Valeria Sambucini. "Optimal predictive sample size for case-control studies." Journal of the Royal Statistical Society: Series C (Applied Statistics) 53, no. 3 (2004): 427–41. http://dx.doi.org/10.1111/j.1467-9876.2004.0d490.x.

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12

Vagenas, Dimitrios, Nicola Pritchard, Katie Edwards, et al. "Optimal Image Sample Size for Corneal Nerve Morphometry." Optometry and Vision Science 89, no. 5 (2012): 812–17. http://dx.doi.org/10.1097/opx.0b013e31824ee8c9.

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13

Kunsch, Robert J., Erich Novak, and Daniel Rudolf. "Solvable integration problems and optimal sample size selection." Journal of Complexity 53 (August 2019): 40–67. http://dx.doi.org/10.1016/j.jco.2018.10.007.

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14

Confalonieri, R., M. Acutis, G. Bellocchi, and G. Genovese. "Resampling-based software for estimating optimal sample size." Environmental Modelling & Software 22, no. 12 (2007): 1796–800. http://dx.doi.org/10.1016/j.envsoft.2007.02.006.

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15

Zhang, Lanju, Lu Cui, and Bo Yang. "Optimal flexible sample size design with robust power." Statistics in Medicine 35, no. 19 (2016): 3385–96. http://dx.doi.org/10.1002/sim.6931.

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16

Jutkowitz, Eric, Fernando Alarid-Escudero, Karen M. Kuntz, and Hawre Jalal. "The Curve of Optimal Sample Size (COSS): A Graphical Representation of the Optimal Sample Size from a Value of Information Analysis." PharmacoEconomics 37, no. 7 (2019): 871–77. http://dx.doi.org/10.1007/s40273-019-00770-z.

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17

Bevrani, H., M. Ghorbani, and M. K. Sadaghiani. "Optimal Estimator for Sample Size Using Monte-Carlo Method." Journal of Applied Sciences 8, no. 6 (2008): 1122–24. http://dx.doi.org/10.3923/jas.2008.1122.1124.

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18

Megerdichian, Aren. "Economic Analysis of Optimal Sample Size in Legal Proceedings." International Journal of Statistics and Probability 8, no. 4 (2019): 13. http://dx.doi.org/10.5539/ijsp.v8n4p13.

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In many legal settings, a statistical sample can be an effective surrogate for a larger population when adjudicating questions of causation, liability, or damages. The current paper works through salient aspects of statistical sampling and sample size determination in legal proceedings. An economic model is developed to provide insight into the behavioral decision-making about sample size choice by a party that intends to offer statistical evidence to the court. The optimal sample size is defined to be the sample size that maximizes the expected payoff of the legal case to the party conducting the analysis. Assuming a probability model that describes a hypothetical court&rsquo;s likelihood of accepting statistical evidence based on the sample size, the optimal sample size is reached at a point where the increase in the probability of the court accepting the sample from a unit increase in the chosen sample size, multiplied by the payoff from winning the case, is equal to the marginal cost of increasing the sample size.

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19

Zhang, Joanne. "Optimal Sample Size Allocation in a Thorough QTc Study." Drug Information Journal 45, no. 4 (2011): 455–68. http://dx.doi.org/10.1177/009286151104500407.

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20

Javanmard, Adel, and Andrea Montanari. "Debiasing the lasso: Optimal sample size for Gaussian designs." Annals of Statistics 46, no. 6A (2018): 2593–622. http://dx.doi.org/10.1214/17-aos1630.

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21

Wei, Bei, Stephen M. S. Lee, and Xiyuan Wu. "Stochastically optimal bootstrap sample size for shrinkage-type statistics." Statistics and Computing 26, no. 1-2 (2014): 249–62. http://dx.doi.org/10.1007/s11222-014-9493-x.

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22

Mayne, Benjamin, Oliver Berry, and Simon Jarman. "Optimal sample size for calibrating DNA methylation age estimators." Molecular Ecology Resources 21, no. 7 (2021): 2316–23. http://dx.doi.org/10.1111/1755-0998.13437.

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23

Kostic, Aleksandar, Svetlana Ilic, and Petar Milin. "Probability estimate and the optimal text size." Psihologija 41, no. 1 (2008): 35–51. http://dx.doi.org/10.2298/psi0801035k.

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Reliable language corpus implies a text sample of size n that provides stable probability distributions of linguistic phenomena. The question is what is the minimal (i.e. the optimal) text size at which probabilities of linguistic phenomena become stable. Specifically, we were interested in probabilities of grammatical forms. We started with an a priori assumption that text size of 1.000.000 words is sufficient to provide stable probability distributions. Text of this size we treated as a "quasi-population". Probability distribution derived from the "quasi-population" was then correlated with probability distribution obtained on a minimal sample size (32 items) for a given linguistic category (e.g. nouns). Correlation coefficient was treated as a measure of similarity between the two probability distributions. The minimal sample was increased by geometrical progression, up to the size where correlation between distribution derived from the quasi-population and the one derived from an increased sample reached its maximum (r=1). Optimal sample size was established for grammatical forms of nouns, adjectives and verbs. General formalism is proposed that allows estimate of an optimal sample size from minimal sample (i.e. 32 items).

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24

Barry, Graham H., William S. Castle, Frederick S. Davies, and Ramon C. Littell. "241 Estimating Optimal Sample Size for Sweet Orange Fruit Quality Experiments." HortScience 34, no. 3 (1999): 483E—484. http://dx.doi.org/10.21273/hortsci.34.3.483e.

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Variability in fruit quality of citrus occurs among and within trees due to an interaction of several factors, e.g., fruit position, leaf: fruit ratio, and fruit size. By determining variability in fruit quality among i) fruit, ii) trees, iii) orchards, and iv) geographic locations where citrus is produced in Florida, optimal sample size for fruit quality experiments can be estimated. To estimate within-tree variability, five trees were randomly selected from each of three `Valencia' orange orchards in four geographic locations in Florida. Six fruit were harvested from each of two tree canopy positions, southwest top and northeast bottom; fruit were not selected or graded according to fruit size. °Brix and titratable acidity of juice samples were determined, and the °Brix: acid ratio was calculated. Statistical analysis of fruit quality variables was done using a crossed-nested design. The number of trees to sample and the number of fruit per sample were calculated. To estimate between-tree variability, 10 trees were randomly selected from each of three `Valencia' orange orchards from four geographic locations in Florida. Fifty-fruit composite samples were picked from around the tree canopy (0.9 to 1.8 m). Juice content, SSC, acid content, and ratio were determined. Using a nested design, the number of orchards and number of trees to sample were determined. There was greater variability in fruit quality among trees than within trees for a given canopy position; the optimal sample size when taking individual fruit samples from a given location and canopy position is four fruit from 20 trees. There was less variability in fruit quality when 50-fruit composite samples were used, resulting in an optimal sample size of five samples from three orchards within each location.

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25

Huang, Wensheng. "Algorithm for determination of sample size using Linex loss function." Modern Physics Letters B 31, no. 19-21 (2017): 1740060. http://dx.doi.org/10.1142/s0217984917400607.

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The sample size based on the Linex loss function and Blinex loss function is studied in this paper, and the analytical solution of the optimal sample size is deduced on the assumption that the Linex loss function and the normal distribution exist. For the Blinex loss function, an accurate algorithm was presented to obtain the optimal sample size. Furthermore, the optimal sample size is obtained, respectively, by taking Poisson distribution and normal distribution as examples. Due to the wide application of Blinex function in reality, the algorithm presented in this paper has immediate applications.

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26

Barreiro-Ures, Daniel, Ricardo Cao, and Mario Francisco-Fernández. "Bandwidth Selection in Nonparametric Regression with Large Sample Size." Proceedings 2, no. 18 (2018): 1166. http://dx.doi.org/10.3390/proceedings2181166.

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In the context of nonparametric regression estimation, the behaviour of kernel methods such as the Nadaraya-Watson or local linear estimators is heavily influenced by the value of the bandwidth parameter, which determines the trade-off between bias and variance. This clearly implies that the selection of an optimal bandwidth, in the sense of minimizing some risk function (MSE, MISE, etc.), is a crucial issue. However, the task of estimating an optimal bandwidth using the whole sample can be very expensive in terms of computing time in the context of Big Data, due to the computational complexity of some of the most used algorithms for bandwidth selection (leave-one-out cross validation, for example, has O ( n 2 ) complexity). To overcome this problem, we propose two methods that estimate the optimal bandwidth for several subsamples of our large dataset and then extrapolate the result to the original sample size making use of the asymptotic expression of the MISE bandwidth. Preliminary simulation studies show that the proposed methods lead to a drastic reduction in computing time, while the statistical precision is only slightly decreased.

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27

Cressie, Noel, and Jonathan Biele. "A Sample-Size-Optimal Bayesian Procedure for Sequential Pharmaceutical Trials." Biometrics 50, no. 3 (1994): 700. http://dx.doi.org/10.2307/2532784.

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28

Volodin, I. N. "Guaranteed statistical inference procedures (determination of the optimal sample size)." Journal of Soviet Mathematics 44, no. 5 (1989): 568–600. http://dx.doi.org/10.1007/bf01095166.

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29

Chung, Kam‐Hin, and Stephen M. S. Lee. "Optimal Bootstrap Sample Size in Construction of Percentile Confidence Bounds." Scandinavian Journal of Statistics 28, no. 1 (2001): 225–39. http://dx.doi.org/10.1111/1467-9469.00233.

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30

Rogers, Michael S., Allan M. Z. Chang, and Susan Todd. "Using group-sequential analysis to achieve the optimal sample size." BJOG: An International Journal of Obstetrics & Gynaecology 112, no. 5 (2005): 529–33. http://dx.doi.org/10.1111/j.1471-0528.2005.00479.x.

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31

Soumitri, M. Srinivas, Saptarshi Majumdar, and Kishalay Mitra. "Optimization using ANN Surrogates with Optimal Topology and Sample Size." IFAC-PapersOnLine 48, no. 8 (2015): 1168–73. http://dx.doi.org/10.1016/j.ifacol.2015.09.126.

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32

Happ, Martin, Arne C. Bathke, and Edgar Brunner. "Optimal sample size planning for the Wilcoxon-Mann-Whitney test." Statistics in Medicine 38, no. 3 (2018): 363–75. http://dx.doi.org/10.1002/sim.7983.

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33

Zanella, Pablo Giliard, Carlos Augusto Brandão de Carvalho, Everton Teixeira Ribeiro, Afrânio Silva Madeiro, and Raphael Dos Santos Gomes. "Optimal quadrat area and sample size to estimate the forage mass of stargrass." Semina: Ciências Agrárias 38, no. 5 (2017): 3165. http://dx.doi.org/10.5433/1679-0359.2017v38n5p3165.

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The objective of this study was to evaluate the sample size and area of the quadrats necessary to accurately estimate the forage mass (FM) of a fenced pasture of stargrass (Cynodon nlemfuensis cv. Florico) during the winter. Five metal quadrats were used: a 0.09 m² square (0.30 m side), a 0.25 m2 square (0.50 m side), a 0.25 m2 circle (0.28 m diameter), a 0.5 m2 rectangle (0.5 x 1.0 m), and a 1 m2 square (1.0 m side), each with eight replicates. The size and shape of the quadrats were determined based on cumulative variances to identify combinations that minimized the coefficient of variation (CV). The minimum sample size required to estimate the FM, morphological components and height was established by the CV maximum curvature method. The 0.25 m2 square quadrat (0.5 m side) presented the lowest cumulative CV in estimating the FM and the dry mass of dead material. However, for the estimation of the leaf and stem dry mass, the 1.00 m2 square quadrat (1.00 m side) presented the lowest CV. Using the 0.25 m2 square quadrat, a minimum number of six samples were required for the FM estimation, and eight samples were required for estimating the mean height of the stargrass pasture. Therefore, at least eight samples are recommended to obtain accurate results for the estimation of both variables.

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34

Tickle, Hannah, Maarten Speekenbrink, Konstantinos Tsetsos, Elizabeth Michael, and Christopher Summerfield. "Near-optimal Integration of Magnitude in the Human Parietal Cortex." Journal of Cognitive Neuroscience 28, no. 4 (2016): 589–603. http://dx.doi.org/10.1162/jocn_a_00918.

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Humans are often observed to make optimal sensorimotor decisions but to be poor judges of situations involving explicit estimation of magnitudes or numerical quantities. For example, when drawing conclusions from data, humans tend to neglect the size of the sample from which it was collected. Here, we asked whether this sample size neglect is a general property of human decisions and investigated its neural implementation. Participants viewed eight discrete visual arrays (samples) depicting variable numbers of blue and pink balls. They then judged whether the samples were being drawn from an urn in which blue or pink predominated. A participant who neglects the sample size will integrate the ratio of balls on each array, giving equal weight to each sample. However, we found that human behavior resembled that of an optimal observer, giving more credence to larger sample sizes. Recording scalp EEG signals while participants performed the task allowed us to assess the decision information that was computed during integration. We found that neural signals over the posterior cortex after each sample correlated first with the sample size and then with the difference in the number of balls in either category. Moreover, lateralized beta-band activity over motor cortex was predicted by the cumulative difference in number of balls in each category. Together, these findings suggest that humans achieve statistically near-optimal decisions by adding up the difference in evidence on each sample, and imply that sample size neglect may not be a general feature of human decision-making.

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35

Sanz-Alonso, Daniel, and Zijian Wang. "Bayesian Update with Importance Sampling: Required Sample Size." Entropy 23, no. 1 (2020): 22. http://dx.doi.org/10.3390/e23010022.

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Importance sampling is used to approximate Bayes’ rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for importance sampling in terms of the χ2-divergence between target and proposal. We illustrate through examples the roles that dimension, noise-level and other model parameters play in approximating the Bayesian update with importance sampling. Our examples also facilitate a new direct comparison of standard and optimal proposals for particle filtering.

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36

Altekruse, S. F., F. Elvinger, Y. Wang, and K. Ye. "A Model To Estimate the Optimal Sample Size for Microbiological Surveys." Applied and Environmental Microbiology 69, no. 10 (2003): 6174–78. http://dx.doi.org/10.1128/aem.69.10.6174-6178.2003.

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ABSTRACT Estimating optimal sample size for microbiological surveys is a challenge for laboratory managers. When insufficient sampling is conducted, biased inferences are likely; however, when excessive sampling is conducted valuable laboratory resources are wasted. This report presents a statistical model for the estimation of the sample size appropriate for the accurate identification of the bacterial subtypes of interest in a specimen. This applied model for microbiology laboratory use is based on a Bayesian mode of inference, which combines two inputs: (ii) a prespecified estimate, or prior distribution statement, based on available scientific knowledge and (ii) observed data. The specific inputs for the model are a prior distribution statement of the number of strains per specimen provided by an informed microbiologist and data from a microbiological survey indicating the number of strains per specimen. The model output is an updated probability distribution of strains per specimen, which can be used to estimate the probability of observing all strains present according to the number of colonies that are sampled. In this report two scenarios that illustrate the use of the model to estimate bacterial colony sample size requirements are presented. In the first scenario, bacterial colony sample size is estimated to correctly identify Campylobacter amplified restriction fragment length polymorphism types on broiler carcasses. The second scenario estimates bacterial colony sample size to correctly identify Salmonella enterica serotype Enteritidis phage types in fecal drag swabs from egg-laying poultry flocks. An advantage of the model is that as updated inputs from ongoing surveys are incorporated into the model, increasingly precise sample size estimates are likely to be made.

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37

Khaw, Khai Wah, XinYing Chew, Sin Yin Teh, and Wai Chung Yeong. "Optimal Variable Sample Size and Sampling Interval Control Chart for the Process Mean based on Expected Average Time to Signal." International Journal of Machine Learning and Computing 9, no. 6 (2019): 880–85. http://dx.doi.org/10.18178/ijmlc.2019.9.6.887.

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38

Martínez-Muñoz, Gonzalo, and Alberto Suárez. "Out-of-bag estimation of the optimal sample size in bagging." Pattern Recognition 43, no. 1 (2010): 143–52. http://dx.doi.org/10.1016/j.patcog.2009.05.010.

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39

Pérez-Llorca, Marina, Erola Fenollosa, Roberto Salguero-Gómez, and Sergi Munné-Bosch. "What Is the Minimal Optimal Sample Size for Plant Ecophysiological Studies?" Plant Physiology 178, no. 3 (2018): 953–55. http://dx.doi.org/10.1104/pp.18.01001.

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40

Lane, Adam, and Nancy Flournoy. "Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size." Journal of Probability and Statistics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/436239.

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In adaptive optimal procedures, the design at each stage is an estimate of the optimal design based on all previous data. Asymptotics for regular models with fixed number of stages are straightforward if one assumes the sample size of each stage goes to infinity with the overall sample size. However, it is not uncommon for a small pilot study of fixed size to be followed by a much larger experiment. We study the large sample behavior of such studies. For simplicity, we assume a nonlinear regression model with normal errors. We show that the distribution of the maximum likelihood estimates converges to a scale mixture family of normal random variables. Then, for a one parameter exponential mean function we derive the asymptotic distribution of the maximum likelihood estimate explicitly and present a simulation to compare the characteristics of this asymptotic distribution with some commonly used alternatives.

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41

HANCOCK, W., D. LUNDBERG, D. KELTON, and D. BLSCHAK. "Economically optimal sample size, frequency and capability indices using X¯ charts." International Journal of Production Research 25, no. 7 (1987): 967–77. http://dx.doi.org/10.1080/00207548708919889.

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42

Demidenko, Eugene. "Sample size and optimal design for logistic regression with binary interaction." Statistics in Medicine 27, no. 1 (2007): 36–46. http://dx.doi.org/10.1002/sim.2980.

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43

Yang, Chih-Ching, and Su-Fen Yang. "Optimal variable sample size and sampling interval ‘mean squared error’ chart." Service Industries Journal 33, no. 6 (2013): 652–65. http://dx.doi.org/10.1080/02642069.2011.614345.

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44

Gabler, Siegfried, Matthias Ganninger, and Ralf Münnich. "Optimal allocation of the sample size to strata under box constraints." Metrika 75, no. 2 (2010): 151–61. http://dx.doi.org/10.1007/s00184-010-0319-3.

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45

Jain, R. K. "Unequal sample size allocation to optimal design for binomial logistic models." Statistische Hefte 28, no. 1 (1987): 285–90. http://dx.doi.org/10.1007/bf02932608.

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46

Stallard, Nigel, Frank Miller, Simon Day, et al. "Determination of the optimal sample size for a clinical trial accounting for the population size." Biometrical Journal 59, no. 4 (2016): 609–25. http://dx.doi.org/10.1002/bimj.201500228.

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47

Dimitrijevic, Strahinja, Aleksandar Kostic, and Petar Milin. "Stability of the syntagmatic probability distributions." Psihologija 42, no. 1 (2009): 107–20. http://dx.doi.org/10.2298/psi0901107d.

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The aim of the present study is to establish criteria for the optimal size of a corpus that can provide stable conditional probabilities of morphological and/or syntagmatic types. The optimality of corpus size is defined in terms of the smallest sample that generates probability distribution equal to distribution derived from the large sample that generates stable probabilities. The latter distribution we refer to as 'target distribution'. In order to establish the above criteria we varied the sample size, the word sequence size (bigrams and trigrams), sampling procedure (randomly chosen words and continuous text) and position of the target word in a sequence. The obtained distributions of conditional probabilities derived from smaller samples have been correlated with target distributions. Sample size at which probability distribution reaches maximal correlation (r=1) with the target distribution was taken as being optimal. The research was done on Corpus of Serbian language. In case of bigrams the optimal sample size for random word selection is 65.000 words, and 281.000 words for trigrams. In contrast, continuous text sampling requires much larger samples to reach stability: 810.000 words for bigrams and 868.000 words for trigrams. The factors that caused these differences remain unclear and need additional empirical investigation.

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48

Tyzhnenko, A. G., and Y. V. Ryeznik. "Practical Treatment of the Multicollinearity: The Optimal Ridge Method and the Modified OLS." PROBLEMS OF ECONOMY 1, no. 47 (2021): 155–68. http://dx.doi.org/10.32983/2222-0712-2021-1-155-168.

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The paper discusses the applicability of the two main methods for solving the linear regression (LR) problem in the presence of multicollinearity – the OLS and the ridge methods. We compare the solutions obtained by these methods with the solution calculated by the Modified OLS (MOLS) [1; 2]. Like the ridge, the MOLS provides a stable solution for any level of data collinearity. We compare three approaches by using the Monte Carlo simulations, and the data used is generated by the Artificial Data Generator (ADG) [1; 2]. The ADG produces linear and nonlinear data samples of arbitrary size, which allows the investigation of the OLS equation's regularization problem. Two possible regularization versions are the COV version considered in [1; 2] and the ST version commonly used in the literature and practice. The performed investigations reveal that the ridge method in the COV version has an approximately constant optimal regularizer (?_ridge^((opt))?0.1) for any sample size and collinearity level. The MOLS method in this version also has an approximately constant optimal regularizer, but its value is significantly smaller (?_MOLS^((opt))?0.001). On the contrary, the ridge method in the ST version has the optimal regularizer, which is not a constant but depends on the sample size. In this case, its value needs to be set to ?_ridge^((opt))?0.1(n-1). With such a value of the ridge parameter, the obtained solution is strictly the same as one obtained with the COV version but with the optimal regularizer ?_ridge^((opt))?0.1 [1; 2]. With such a choice of the regularizer, one can use any implementation of the ridge method in all known statistical software by setting the regularization parameter ?_ridge^((opt))?0.1(n-1) without extra tuning process regardless of the sample size and the collinearity level. Also, it is shown that such an optimal ridge(0.1) solution is close to the population solution for a sample size large enough, but, at the same time, it has some limitations. It is well known that the ridge(0.1) solution is biased. However, as it has been shown in the paper, the bias is economically insignificant. The more critical drawback, which is revealed, is the smoothing of the population solution – the ridge method significantly reduces the difference between the population regression coefficients. The ridge(0.1) method can result in a solution, which is economically correct, i.e., the regression coefficients have correct signs, but this solution might be inadequate to a certain extent. The more significant the difference between the regression coefficients in the population, the more inadequate is the ridge(0.1) method. As for the MOLS, it does not possess this disadvantage. Since its regularization constant is much smaller than the corresponding ridge regularizer (0.001 versus 0.1), the MOLS method suffers little from both the bias and smoothing of its solutions. From a practical point of view, both the ridge(0.1) and the MOLS methods result in close stable solutions to the LR problem for any sample size and collinearity level. With the sample size increasing, both solutions approach the population solution. We also demonstrate that for a small sample size of less than 40, the ridge(0.1) method is preferable, as it is more stable. When the sample size is medium or large, it is preferable to use the MOLS as it is more accurate yet has approximately the same stability.

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SUN, Qing-wen, Hai-ying TENG, Mao-hai SONG, and Ying FANG. "Optimal pool size and pooled sample size for hypothesis test of critical threshold of infection rates based on fixed sample size and pooled sampling method." Academic Journal of Second Military Medical University 31, no. 12 (2012): 1353–56. http://dx.doi.org/10.3724/sp.j.1008.2011.01353.

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Yao, Tzy-Jyun, Colin B. Begg, and Philip O. Livingston. "Optimal Sample Size for a Series of Pilot Trials of New Agents." Biometrics 52, no. 3 (1996): 992. http://dx.doi.org/10.2307/2533060.

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