WeiYa's Work Yard

A dog, who fell into the ocean of statistics, tries to write down his ideas and notes to save himself.

Test of Monotonicity and Convexity by Splines

April 23, 2022

This note is for Wang, J. C., & Meyer, M. C. (2011). Testing the monotonicity or convexity of a function using regression splines. The Canadian Journal of Statistics / La Revue Canadienne de Statistique, 39(1), 89–107.

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Test of Monotonicity by U-processes

April 23, 2022

This note is for Ghosal, S., Sen, A., & van der Vaart, A. W. (2000). Testing Monotonicity of Regression. The Annals of Statistics, 28(4), 1054–1082.

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Monotonicity in Asset Returns

April 20, 2022

This note is for Patton, A. J., & Timmermann, A. (2010). Monotonicity in asset returns: New tests with applications to the term structure, the CAPM, and portfolio sorts. Journal of Financial Economics, 98(3), 605–625.

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Test of Monotonicity

April 20, 2022

This note is for Chetverikov, D. (2019). TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS. Econometric Theory, 35(4), 729–776.

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Big Data Paradox

April 07, 2022

This note is for Meng, X.-L. (2018). Statistical paradises and paradoxes in big data (I): Law of large populations, big data paradox, and the 2016 US presidential election. The Annals of Applied Statistics, 12(2).

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Adaptive Ridge Estimate

March 30, 2022

This note is for Grandvalet, Y. (1998). Least Absolute Shrinkage is Equivalent to Quadratic Penalization. In L. Niklasson, M. Bodén, & T. Ziemke (Eds.), ICANN 98 (pp. 201–206). Springer London.

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Mixture of Location-Scale Families

March 25, 2022

This note is for Chen, J., Li, P., & Liu, G. (2020). Homogeneity testing under finite location-scale mixtures. Canadian Journal of Statistics, 48(4), 670–684.

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Scale Mixture Models

March 25, 2022

This note is for scale mixture models.

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Prediction Risk for the Horseshoe Regression

March 24, 2022

The note is for Bhadra, A., Datta, J., Li, Y., Polson, N. G., & Willard, B. (2019). Prediction Risk for the Horseshoe Regression. 39.

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Estimation of Location and Scale Parameters of Continuous Density

March 22, 2022 (Update: )

This note is for Pitman, E. J. G. (1939). The Estimation of the Location and Scale Parameters of a Continuous Population of any Given Form. Biometrika, 30(3/4), 391–421. and Kagan, AM & Rukhin, AL. (1967). On the estimation of a scale parameter. Theory of Probability \& Its Applications, 12, 672–678.

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Equivariance

March 22, 2022

This post is for Chapter 3 of Lehmann, E. L., & Casella, G. (1998). Theory of point estimation (2nd ed). Springer.

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Applications with Scale Parameters

March 22, 2022

This note contains several papers related to scale parameter.

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Leave-one-out CV for Lasso

March 14, 2022

This note is for Homrighausen, D., & McDonald, D. J. (2013). Leave-one-out cross-validation is risk consistent for lasso. ArXiv:1206.6128 [Math, Stat].

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Neuronized Priors for Bayesian Sparse Linear Regression

January 16, 2022

This note is for Shin, M., & Liu, J. S. (2021). Neuronized Priors for Bayesian Sparse Linear Regression. Journal of the American Statistical Association, 1–16.

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Empirical Bayes

January 16, 2022

This note is based on Sec. 4.6 of Lehmann, E. L., & Casella, G. (1998). Theory of point estimation (2nd ed). Springer.

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Magnetic Field Orientations in Star Formation

January 12, 2022

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Generalizing Ridge Regression

December 14, 2021

This note is for Chapter 3 of van Wieringen, W. N. (2021). Lecture notes on ridge regression. ArXiv:1509.09169 [Stat].

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Gaussian Processes for Regression

December 13, 2021

This note is for Chapter 4 of Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.

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Additive Model with Linear Smoother

December 07, 2021

This note is for Buja, A., Hastie, T., & Tibshirani, R. (1989). Linear Smoothers and Additive Models. The Annals of Statistics, 17(2), 453–510. JSTOR.

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Asymptotics of Cross Validation

December 03, 2021

This note is for Austern, M., & Zhou, W. (2020). Asymptotics of Cross-Validation. ArXiv:2001.11111 [Math, Stat].

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Review on Random Matrix Theory

December 01, 2021

This note is for Paul, D., & Aue, A. (2014). Random matrix theory in statistics: A review. Journal of Statistical Planning and Inference, 150, 1–29.

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Probabilistic Principal Curves

November 22, 2021

This note is for Chang, K.-Y., & Ghosh, J. (2001). A unified model for probabilistic principal surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(1), 22–41., but only involves the principal curves.

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Regularization-Free Principal Curves

November 21, 2021

The note is for Gerber, S., & Whitaker, R. (2013). Regularization-Free Principal Curve Estimation. 18.

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Invariant Risk Minimization

November 19, 2021 0 Comments

This note is for Arjovsky, M., Bottou, L., Gulrajani, I., & Lopez-Paz, D. (2020). Invariant Risk Minimization. ArXiv:1907.02893 [Cs, Stat].

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Causal Inference by Invariant Prediction

November 19, 2021 0 Comments

This note is for Peters, J., Bühlmann, P., & Meinshausen, N. (2016). Causal inference by using invariant prediction: Identification and confidence intervals. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(5), 947–1012.

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Infinite Relational Model

November 18, 2021 (Update: ) 0 Comments

This note is based on Kemp, C., Tenenbaum, J. B., Griffiths, T. L., Yamada, T., & Ueda, N. (n.d.). Learning Systems of Concepts with an Infinite Relational Model. 8. and Saad, F. A., & Mansinghka, V. K. (2021). Hierarchical Infinite Relational Model. ArXiv:2108.07208 [Cs, Stat].

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Multidimensional Monotone Bayesian Additive Regression Tree

November 17, 2021 0 Comments

This note is for Chipman, H. A., George, E. I., McCulloch, R. E., & Shively, T. S. (2021). mBART: Multidimensional Monotone BART. ArXiv:1612.01619 [Stat].

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Debiased ML via NN for GLM

November 16, 2021 0 Comments

This is the note for Chernozhukov, V., Newey, W. K., Quintas-Martinez, V., & Syrgkanis, V. (2021). Automatic Debiased Machine Learning via Neural Nets for Generalized Linear Regression. ArXiv:2104.14737 [Econ, Math, Stat].

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Biclustering on Gene Expression Data

November 10, 2021 0 Comments

The note is based on Padilha, V. A., & Campello, R. J. G. B. (2017). A systematic comparative evaluation of biclustering techniques. BMC Bioinformatics, 18(1), 55.

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Asymptotic Properties of High-Dimensional Random Forests

November 09, 2021 0 Comments

This note is Chi, C.-M., Vossler, P., Fan, Y., & Lv, J. (2021). Asymptotic Properties of High-Dimensional Random Forests. ArXiv:2004.13953 [Math, Stat]..

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