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1

Ludbrook, John, and Hugh Dudley. "ISSUES IN BIOMEDICAL STATISTICS: STATISTICAL INFERENCE." ANZ Journal of Surgery 64, no. 9 (September 1994): 630–36. http://dx.doi.org/10.1111/j.1445-2197.1994.tb02308.x.

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2

Loosmore, N. Bert, and E. David Ford. "STATISTICAL INFERENCE USING THEGORKPOINT PATTERN SPATIAL STATISTICS." Ecology 87, no. 8 (August 2006): 1925–31. http://dx.doi.org/10.1890/0012-9658(2006)87[1925:siutgo]2.0.co;2.

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3

Curran-Everett, Douglas. "Explorations in statistics: the bootstrap." Advances in Physiology Education 33, no. 4 (December 2009): 286–92. http://dx.doi.org/10.1152/advan.00062.2009.

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Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This fourth installment of Explorations in Statistics explores the bootstrap. The bootstrap gives us an empirical approach to estimate the theoretical variability among possible values of a sample statistic such as the sample mean. The appeal of the bootstrap is that we can use it to make an inference about some experimental result when the statistical theory is uncertain or even unknown. We can also use the bootstrap to assess how well the statistical theory holds: that is, whether an inference we make from a hypothesis test or confidence interval is justified.
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4

Barber, Stuart. "All of Statistics: a Concise Course in Statistical Inference." Journal of the Royal Statistical Society: Series A (Statistics in Society) 168, no. 1 (January 2005): 261. http://dx.doi.org/10.1111/j.1467-985x.2004.00347_18.x.

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5

Craigmile, Peter F. "All of Statistics: A Concise Course in Statistical Inference." American Statistician 59, no. 2 (May 2005): 203–4. http://dx.doi.org/10.1198/tas.2005.s30.

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6

Zhang, Jingwen, Joseph Ibrahim, Tengfei Li, and Hongtu Zhu. "A Powerful Global Test Statistic for Functional Statistical Inference." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5765–72. http://dx.doi.org/10.1609/aaai.v33i01.33015765.

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We consider the problem of performing an association test between functional data and scalar variables in a varying coefficient model setting. We propose a functional projection regression model and an associated global test statistic to aggregate relatively weak signals across the domain of functional data, while reducing the dimension. An optimal functional projection direction is selected to maximize signal-to-noise ratio with ridge penalty. Theoretically, we systematically study the asymptotic distribution of the global test statistic and provide a strategy to adaptively select the optimal tuning parameter. We use simulations to show that the proposed test outperforms all existing state-of-the-art methods in functional statistical inference. Finally, we apply the proposed testing method to the genome-wide association analysis of imaging genetic data in UK Biobank dataset.
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7

Xu, Jinfeng, Lincheng Zhao, and Chenlei Leng. "Statistical inference for induced L-statistics: a random perturbation approach." Journal of Nonparametric Statistics 21, no. 7 (October 2009): 863–76. http://dx.doi.org/10.1080/10485250902980584.

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8

Subba Rao, Suhasini. "Statistical inference for spatial statistics defined in the Fourier domain." Annals of Statistics 46, no. 2 (April 2018): 469–99. http://dx.doi.org/10.1214/17-aos1556.

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9

Rohana, Rohana, and Yunika Lestaria Ningsih. "STUDENTS’ STATISTICAL REASONING IN STATISTICS METHOD COURSE." Jurnal Pendidikan Matematika 14, no. 1 (December 31, 2019): 81–90. http://dx.doi.org/10.22342/jpm.14.1.6732.81-90.

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The role of statistics is wide and crucial in daily life, making statistics important. Many students have difficulty understanding statistics. This study aims to determine students' statistical reasoning about inference statistics, which is limited to the subject matter of the testing hypotheses about two-sample hypotheses testing. This study used descriptive research method. The subjects were 25 students of third-year Mathematics Education Departement at Universitas PGRI Palembang in the academic year 2018/2019. Data were collected through tests and interviews. Data were analyzed through descriptive quantitative. The results of data analysis showed that 32% of students had level 1 statistical reasoning (the lowest level), 20% were at level 2, 28% at level 3, 12% at level 4 and 8% at level 5 (highest level). Based on the result, it can conclude that students' statistical reasoning ability in learning statistical method is not satisfactory, students are still very lacking in reasoning.
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10

Kuchibhotla, Arun K., John E. Kolassa, and Todd A. Kuffner. "Post-Selection Inference." Annual Review of Statistics and Its Application 9, no. 1 (March 7, 2022): 505–27. http://dx.doi.org/10.1146/annurev-statistics-100421-044639.

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We discuss inference after data exploration, with a particular focus on inference after model or variable selection. We review three popular approaches to this problem: sample splitting, simultaneous inference, and conditional selective inference. We explain how each approach works and highlight its advantages and disadvantages. We also provide an illustration of these post-selection inference approaches.
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11

Nordhausen, Klaus, and Hannu Oja. "Robust Nonparametric Inference." Annual Review of Statistics and Its Application 5, no. 1 (March 7, 2018): 473–500. http://dx.doi.org/10.1146/annurev-statistics-031017-100247.

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12

Mayo-Wilson, Conor. "Statistical Inference as Severe Testing: How to Get beyond the Statistics." Philosophical Review 130, no. 1 (January 1, 2021): 185–89. http://dx.doi.org/10.1215/00318108-8699656.

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13

Frühwirth-Schnatter, Sylvia. "On statistical inference for fuzzy data with applications to descriptive statistics." Fuzzy Sets and Systems 50, no. 2 (September 1992): 143–65. http://dx.doi.org/10.1016/0165-0114(92)90213-n.

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14

Baggio, Hugo C., Alexandra Abos, Barbara Segura, Anna Campabadal, Anna Garcia‐Diaz, Carme Uribe, Yaroslau Compta, Maria Jose Marti, Francesc Valldeoriola, and Carme Junque. "Statistical inference in brain graphs using threshold‐free network‐based statistics." Human Brain Mapping 39, no. 6 (February 15, 2018): 2289–302. http://dx.doi.org/10.1002/hbm.24007.

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15

Rennolls, Keith, P. H. Garthwaite, I. T. Jolliffe, and B. Jones. "Statistical Inference." Journal of the Royal Statistical Society. Series A (Statistics in Society) 159, no. 3 (1996): 622. http://dx.doi.org/10.2307/2983341.

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16

Crowder, Martin, P. H. Garthwaite, I. T. Jolliffe, and B. Jones. "Statistical Inference." Statistician 45, no. 3 (1996): 386. http://dx.doi.org/10.2307/2988478.

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17

Brunson, Barry W., and Vijay K. Rohatgi. "Statistical Inference." American Mathematical Monthly 94, no. 2 (February 1987): 210. http://dx.doi.org/10.2307/2322441.

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18

Lindley, D. V., and Vijay K. Rohatgi. "Statistical Inference." Mathematical Gazette 69, no. 447 (March 1985): 63. http://dx.doi.org/10.2307/3616474.

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19

Rohatgi, V. K. "Statistical Inference." Biometrics 41, no. 4 (December 1985): 1102. http://dx.doi.org/10.2307/2530991.

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20

Ghosh, Malay, George Casella, and Roger L. Berger. "Statistical Inference." Journal of the American Statistical Association 89, no. 426 (June 1994): 712. http://dx.doi.org/10.2307/2290879.

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21

Casella, G., and R. L. Berger. "Statistical Inference." Biometrics 49, no. 1 (March 1993): 320. http://dx.doi.org/10.2307/2532634.

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22

Ziegel, Eric R. "Statistical Inference." Technometrics 44, no. 4 (November 2002): 407–8. http://dx.doi.org/10.1198/tech.2002.s94.

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23

Angus, John E. "Statistical Inference." Technometrics 33, no. 4 (November 1991): 493. http://dx.doi.org/10.1080/00401706.1991.10484898.

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24

Randles, Ronald H., and Vijay K. Rohatgi. "Statistical Inference." Journal of the American Statistical Association 81, no. 393 (March 1986): 258. http://dx.doi.org/10.2307/2288010.

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25

Roberts, Rosemary A., and J. G. Kalbfleisch. "Probability and Statistical Inference, Volume 2: Statistical Inference." Journal of the American Statistical Association 84, no. 407 (September 1989): 842. http://dx.doi.org/10.2307/2289686.

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26

Yun-Shan Sun, Yun-Shan Sun, Hong-Yan Xu Yun-Shan Sun, and Yan-Qin Li Hong-Yan Xu. "Missing Data Interpolation with Variational Bayesian Inference for Socio-economic Statistics Applications." 電腦學刊 33, no. 2 (April 2022): 169–76. http://dx.doi.org/10.53106/199115992022043302015.

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<p>The information integrity is needed to solving socio-economic statistical problems. However, the information integrity is destroyed by missing data which is caused by various subjective and objective reasons. So the missing data interpolation is used to supplement missing data. In this paper, missing data interpolation with variational Bayesian inference is proposed. This method is combined with Gaussian model to approximate the posterior distribution to obtain complete data. The experiments include two datasets (artificial dataset and actual dataset) based on three missing ratios separately. The missing data interpolation performance of variational Bayesian method is compared with that which is obtained by mean interpolation and K-nearest neighbor interpolation methods separately in MSE (Mean Square Error) and MAPE (Mean Absolute Percentage Error). The experimental results show that the proposed variational Bayesian method is better in MSE and MAPE.</p> <p>&nbsp;</p>
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27

Yun-Shan Sun, Yun-Shan Sun, Hong-Yan Xu Yun-Shan Sun, and Yan-Qin Li Hong-Yan Xu. "Missing Data Interpolation with Variational Bayesian Inference for Socio-economic Statistics Applications." 電腦學刊 33, no. 2 (April 2022): 169–76. http://dx.doi.org/10.53106/199115992022043302015.

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<p>The information integrity is needed to solving socio-economic statistical problems. However, the information integrity is destroyed by missing data which is caused by various subjective and objective reasons. So the missing data interpolation is used to supplement missing data. In this paper, missing data interpolation with variational Bayesian inference is proposed. This method is combined with Gaussian model to approximate the posterior distribution to obtain complete data. The experiments include two datasets (artificial dataset and actual dataset) based on three missing ratios separately. The missing data interpolation performance of variational Bayesian method is compared with that which is obtained by mean interpolation and K-nearest neighbor interpolation methods separately in MSE (Mean Square Error) and MAPE (Mean Absolute Percentage Error). The experimental results show that the proposed variational Bayesian method is better in MSE and MAPE.</p> <p>&nbsp;</p>
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28

Wasserman, Larry, Aaditya Ramdas, and Sivaraman Balakrishnan. "Universal inference." Proceedings of the National Academy of Sciences 117, no. 29 (July 6, 2020): 16880–90. http://dx.doi.org/10.1073/pnas.1922664117.

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We propose a general method for constructing confidence sets and hypothesis tests that have finite-sample guarantees without regularity conditions. We refer to such procedures as “universal.” The method is very simple and is based on a modified version of the usual likelihood-ratio statistic that we call “the split likelihood-ratio test” (split LRT) statistic. The (limiting) null distribution of the classical likelihood-ratio statistic is often intractable when used to test composite null hypotheses in irregular statistical models. Our method is especially appealing for statistical inference in these complex setups. The method we suggest works for any parametric model and also for some nonparametric models, as long as computing a maximum-likelihood estimator (MLE) is feasible under the null. Canonical examples arise in mixture modeling and shape-constrained inference, for which constructing tests and confidence sets has been notoriously difficult. We also develop various extensions of our basic methods. We show that in settings when computing the MLE is hard, for the purpose of constructing valid tests and intervals, it is sufficient to upper bound the maximum likelihood. We investigate some conditions under which our methods yield valid inferences under model misspecification. Further, the split LRT can be used with profile likelihoods to deal with nuisance parameters, and it can also be run sequentially to yield anytime-valid P values and confidence sequences. Finally, when combined with the method of sieves, it can be used to perform model selection with nested model classes.
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29

Bowers, Jake, Mark M. Fredrickson, and Peter M. Aronow. "Research Note: A More Powerful Test Statistic for Reasoning about Interference between Units." Political Analysis 24, no. 3 (2016): 395–403. http://dx.doi.org/10.1093/pan/mpw018.

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Bowers, Fredrickson, and Panagopoulos (2013, Reasoning about interference between units: A general framework, Political Analysis 21(1):97–124; henceforth BFP) showed that one could use Fisher's randomization-based hypothesis testing framework to assess counterfactual causal models of treatment propagation and spillover across social networks. This research note improves the statistical inference presented in BFP (2013) by substituting a test statistic based on a sum of squared residuals and incorporating information about the fixed network for the simple Kolmogorov–Smirnov test statistic (Hollander 1999, section 5.4) they used. This note incrementally improves the application of BFP's “reasoning about interference” approach. We do not offer general results about test statistics for multi-parameter causal models on social networks here, but instead hope to stimulate further, and deeper, work on test statistics and sharp hypothesis testing.
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30

KYBURG, HENRY E., and CHOH MAN TENG. "STATISTICAL INFERENCE AS DEFAULT REASONING." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 02 (March 1999): 267–83. http://dx.doi.org/10.1142/s021800149900015x.

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Classical statistical inference is nonmonotonic in nature. We show how it can be formalized in the default logic framework. The structure of statistical inference is the same as that represented by default rules. In particular, the prerequisite corresponds to the sample statistics, the justifications require that we do not have any reason to believe that the sample is misleading, and the consequence corresponds to the conclusion sanctioned by the statistical test.
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31

El-Din, M. M. Mohie, Nahed S. A. Ali, M. M. Amein, and M. S. Mohamed. "Statistical Inference of Concomitants Based on Morgenstern Family under Generalized Order Statistics." Mathematical Sciences Letters 5, no. 3 (September 1, 2016): 243–54. http://dx.doi.org/10.18576/msl/050305.

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32

El-Deen, M. "Statistical Inference for Kumaraswamy Distribution Based on Generalized Order Statistics with Applications." British Journal of Mathematics & Computer Science 4, no. 12 (January 10, 2014): 1710–43. http://dx.doi.org/10.9734/bjmcs/2014/9193.

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33

Beutner, E., and U. Kamps. "Order restricted statistical inference for scale parameters based on sequential order statistics." Journal of Statistical Planning and Inference 139, no. 9 (September 2009): 2963–69. http://dx.doi.org/10.1016/j.jspi.2009.01.017.

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34

Chen, E. Jack. "Order Statistics and Clinical-Practice Studies." International Journal of Computers in Clinical Practice 3, no. 2 (July 2018): 13–30. http://dx.doi.org/10.4018/ijccp.2018070102.

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Statistics are essential tools in scientific studies and facilitate various hypothesis tests, such as test administration, response scoring, data analysis, and test interpretation. Order statistics refer to the collection of sample observations sorted in ascending order and are among the most fundamental tools in non-parametric statistics and inference. Statistical inference established based on order statistics assumes nothing stronger than continuity of the cumulative distribution function of the population and is simple and broadly applicable. The authors discuss how order statistics are applied in statistical analysis, e.g., tests of independence, tests of goodness of fit, hypothesis tests of equivalence of means, ranking and selection, and quantile estimation. These order-statistics techniques are key components of many clinical studies.
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35

Schafer, Chad M. "A Framework for Statistical Inference in Astrophysics." Annual Review of Statistics and Its Application 2, no. 1 (April 10, 2015): 141–62. http://dx.doi.org/10.1146/annurev-statistics-022513-115538.

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36

Low, Mark, Axel Munk, and Alexandre Tsybakov. "Adaptive Statistical Inference." Oberwolfach Reports 11, no. 1 (2014): 721–79. http://dx.doi.org/10.4171/owr/2014/13.

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37

Randles, Ronald H., and Jean Dickinson Gibbons. "Nonparametric Statistical Inference." Technometrics 28, no. 3 (August 1986): 275. http://dx.doi.org/10.2307/1269084.

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38

Ziegel, Eric R., and Vic Barnett. "Comparative Statistical Inference." Technometrics 42, no. 4 (November 2000): 442. http://dx.doi.org/10.2307/1270977.

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39

Schabes, Yves. "Statistical grammar inference." Journal of the Acoustical Society of America 92, no. 4 (October 1992): 2368. http://dx.doi.org/10.1121/1.404865.

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40

Shalabh. "Nonparametric Statistical Inference." Journal of the Royal Statistical Society: Series A (Statistics in Society) 174, no. 2 (March 14, 2011): 508–9. http://dx.doi.org/10.1111/j.1467-985x.2010.00681_6.x.

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41

Katsaounis, T. I. "Introductory Statistical Inference." Technometrics 50, no. 1 (February 2008): 89–90. http://dx.doi.org/10.1198/tech.2008.s529.

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42

Banerjee, Tathagata. "Introductory Statistical Inference." Journal of the American Statistical Association 102, no. 480 (December 2007): 1474. http://dx.doi.org/10.1198/jasa.2007.s231.

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43

Ziegel, Eric. "Nonparametric Statistical Inference." Technometrics 30, no. 4 (November 1988): 457. http://dx.doi.org/10.1080/00401706.1988.10488449.

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44

Ziegel, Eric R. "Nonparametric Statistical Inference." Technometrics 35, no. 2 (May 1993): 239–40. http://dx.doi.org/10.1080/00401706.1993.10485070.

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45

Shanmugam, Ram. "Parametric Statistical Inference." Technometrics 40, no. 2 (May 1998): 161. http://dx.doi.org/10.1080/00401706.1998.10485208.

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46

Barnett, Vic. "Comparative Statistical Inference." Technometrics 42, no. 4 (November 2000): 442. http://dx.doi.org/10.1080/00401706.2000.10485741.

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47

Periwal, Vipul. "Geometric statistical inference." Nuclear Physics B 554, no. 3 (August 1999): 719–30. http://dx.doi.org/10.1016/s0550-3213(99)00278-3.

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48

Malley, James D., and John Hornstein. "Quantum Statistical Inference." Statistical Science 8, no. 4 (November 1993): 433–57. http://dx.doi.org/10.1214/ss/1177010787.

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49

Anscombe, F. J., and Rupert G. Miller. "Simultaneous Statistical Inference." Journal of the American Statistical Association 80, no. 389 (March 1985): 250. http://dx.doi.org/10.2307/2288100.

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50

Sukhatme, Shashikala, and Jean Dickinson Gibbons. "Nonparametric Statistical Inference." Journal of the American Statistical Association 82, no. 399 (September 1987): 953. http://dx.doi.org/10.2307/2288823.

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