Asymptotic properties of correlation-based principal component analysis

Choi, Jungjun; Yang, Xiye

doi:10.1016/j.jeconom.2021.08.003

Cited by 5 publications

(3 citation statements)

References 49 publications

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“…Principal component analysis (PCA) : Because the soil had too many influencing components, PCA was adopted to cut down the number of dependent variables into a smaller group of basic ones based on a correlation model, entailing the first principal component (PC1) and the second component (PC2) [ 28 ]. Thereby, the importance of each influencing soil component and its relationships with others would be revealed.…”

Section: Methodsmentioning

confidence: 99%

Yield gap reduction of pineapple (Ananas comosus L.) by site-specific nutrient management

Khuong,

Phung,

Quang

et al. 2024

Heliyon

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Section: Methodsmentioning

confidence: 99%

Yield gap reduction of pineapple (Ananas comosus L.) by site-specific nutrient management

Khuong,

Phung,

Quang

et al. 2024

Heliyon

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“…This R package is named PCAtest and is available for download from . Eigenvalues and eigenvector loadings are calculated from a standardized (centered and scaled) multivariate matrix (variables in columns and observations in rows) with the stats : prcomp function, which performs a singular value decomposition of the correlation matrix ( Choi & Yang, in press ). Observed eigenvalues are used to calculate empirical ψ and φ values, percentages of explained variance for each PC axis (rank-of-roots statistic; ter Braak, 1988 ), and the indexes of the loadings of each variable on each PC axis ( Vieira, 2012 ).…”

Section: Methodsmentioning

confidence: 99%

PCAtest: testing the statistical significance of Principal Component Analysis in R

Camargo¹

2022

PeerJ

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Principal Component Analysis (PCA) is one of the most broadly used statistical methods for the ordination and dimensionality-reduction of multivariate datasets across many scientific disciplines. Trivial PCs can be estimated from data sets without any correlational structure among the original variables, and traditional criteria for selecting non-trivial PC axes are difficult to implement, partially subjective or based on ad hoc thresholds. PCAtest is an R package that implements permutation-based statistical tests to evaluate the overall significance of a PCA, the significance of each PC axis, and of contributions of each observed variable to the significant axes. Based on simulation and empirical results, I encourage R users to routinely apply PCAtest to test the significance of their PCA before proceeding with the direct interpretation of PC axes and/or the utilization of PC scores in subsequent evolutionary and ecological analyses.

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“…The quality of the PCA method can be evaluated using cross-validation techniques, such as the bootstrap and the jackknife (see, e.g., Choi and Yang, 2021). Furthermore, PCA can be generalized both as correspondence analysis to handle qualitative variables and as multifactorial analysis (see, e.g., Kreinin et al, 1998;Murakami, 2020) to examine heterogeneous sets of variables.…”

Section: On the Tracking Error For Portfolio Optimizationmentioning

confidence: 99%

Straightening skewed markets with an index tracking optimizationless portfolio

Bufalo¹,

Bufalo²,

Cesarone³

et al. 2022

Preprint

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Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent decades to offer returns close to benchmarks at a lower cost. In this article, we first refine the existing results on the theoretical properties of oblique Brownian motion. Then, assuming that the returns follow skew geometric Brownian motions and that they are correlated, we describe some statistical properties for the ex-post, the ex-ante tracking errors, and the forecasted tracking portfolio. To this end, we develop an innovative statistical methodology, based on a benchmark-asset principal component factorization, to determine a tracking portfolio that replicates the performance of a benchmark by investing in a subset of the investable universe. This strategy, named hybrid Principal Component Analysis (hPCA), is applied both on normal and skew distributions. In the case of skew-normal returns, we propose a framework for calibrating the model parameters, based on the maximum likelihood estimation method. For testing and validation, we compare four alternative models for index tracking. The first two are based on the hPCA when returns are assumed to be normal or skew-normal. The third model adopts a standard optimizationbased approach and the last one is used in the financial sector by some practitioners. For validation and testing, we present a thorough comparison of these strategies on real-world data, both in terms of performance and computational efficiency. A noticeable result is that, not only, the suggested lean PCA-based portfolio selection approach compares well versus cumbersome algorithms for optimization-based portfolios, but, also, it could provide a better service to the asset management industry.

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Asymptotic properties of correlation-based principal component analysis

Cited by 5 publications

References 49 publications

Yield gap reduction of pineapple (Ananas comosus L.) by site-specific nutrient management

Yield gap reduction of pineapple (Ananas comosus L.) by site-specific nutrient management

PCAtest: testing the statistical significance of Principal Component Analysis in R

Straightening skewed markets with an index tracking optimizationless portfolio

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