Mathematical Programming for Statistical Inference

The study is concerned with the transforming theoretical Mathematical models into applied Mathematical programming models that are easy to handle and use. These Mathematical programming models can be applied and used in statistical inference, which used in many applied fields, for example, quality control and its application. The aim of this paper is to suggest two mathematical programming models for hypotheses tests, which make a balance between the high power (1-β), and the probability of a type I error, significance (), of the test. The paper introduces a simulation study to evaluate the performance of the two suggested mathematical programming models for tests hypotheses. The two suggested mathematical programming models solved with different sample sizes and different level of significance. The suggested models calculate the critical values which determine the rejection region exactly and the results are easy to interpret clearly. Then the conclusion for the suggested mathematical programming models makes balance between the power and the significance.

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Mathematical Programming Models for Environmental Quality Control

Operations Research ◽

10.1287/opre.43.4.578 ◽

1995 ◽

Vol 43 (4) ◽

pp. 578-622 ◽

Cited By ~ 39

Author(s):

Harvey J. Greenberg

Keyword(s):

Quality Control ◽

Mathematical Programming ◽

Environmental Quality ◽

Programming Models ◽

Mathematical Programming Models

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Assessing Person Fit With the Information Matrix Test

Methodology ◽

10.1027/1614-2241/a000085 ◽

2015 ◽

Vol 11 (1) ◽

pp. 3-12 ◽

Cited By ~ 2

Author(s):

Jochen Ranger ◽

Jörg-Tobias Kuhn

Keyword(s):

Simulation Study ◽

Type I Error ◽

Information Matrix ◽

Small Samples ◽

Type I ◽

Person Fit ◽

Power Of The Test ◽

Order Expansion ◽

Trait Stability ◽

Information Matrix Test

In this manuscript, a new approach to the analysis of person fit is presented that is based on the information matrix test of White (1982) . This test can be interpreted as a test of trait stability during the measurement situation. The test follows approximately a χ2-distribution. In small samples, the approximation can be improved by a higher-order expansion. The performance of the test is explored in a simulation study. This simulation study suggests that the test adheres to the nominal Type-I error rate well, although it tends to be conservative in very short scales. The power of the test is compared to the power of four alternative tests of person fit. This comparison corroborates that the power of the information matrix test is similar to the power of the alternative tests. Advantages and areas of application of the information matrix test are discussed.

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Correction: “Influence of Selection Bias on the Test Decision – A Simulation Study”

Methods of Information in Medicine ◽

10.3414/me11-01-0043e ◽

2014 ◽

Vol 53 (05) ◽

pp. 343-343

Keyword(s):

Selection Bias ◽

Simulation Study ◽

Error Rate ◽

Type I Error ◽

Block Size ◽

Error Rates ◽

Type I ◽

Type I Error Rate ◽

Representation Error ◽

Numeric Representation

We have to report marginal changes in the empirical type I error rates for the cut-offs 2/3 and 4/7 of Table 4, Table 5 and Table 6 of the paper “Influence of Selection Bias on the Test Decision – A Simulation Study” by M. Tamm, E. Cramer, L. N. Kennes, N. Heussen (Methods Inf Med 2012; 51: 138 –143). In a small number of cases the kind of representation of numeric values in SAS has resulted in wrong categorization due to a numeric representation error of differences. We corrected the simulation by using the round function of SAS in the calculation process with the same seeds as before. For Table 4 the value for the cut-off 2/3 changes from 0.180323 to 0.153494. For Table 5 the value for the cut-off 4/7 changes from 0.144729 to 0.139626 and the value for the cut-off 2/3 changes from 0.114885 to 0.101773. For Table 6 the value for the cut-off 4/7 changes from 0.125528 to 0.122144 and the value for the cut-off 2/3 changes from 0.099488 to 0.090828. The sentence on p. 141 “E.g. for block size 4 and q = 2/3 the type I error rate is 18% (Table 4).” has to be replaced by “E.g. for block size 4 and q = 2/3 the type I error rate is 15.3% (Table 4).”. There were only minor changes smaller than 0.03. These changes do not affect the interpretation of the results or our recommendations.

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