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Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations

Yata, Kazuyoshi; Aoshima, Makoto - In: Journal of Multivariate Analysis 105 (2012) 1, pp. 193-215

In this article, we propose a new estimation methodology to deal with PCA for high-dimension, low-sample-size (HDLSS …) data. We first show that HDLSS datasets have different geometric representations depending on whether a ρ …-mixing-type dependency appears in variables or not. When the ρ-mixing-type dependency appears in variables, the HDLSS data converge to an n …

Persistent link: https://www.econbiz.de/10011041986

Eigenvectors of some large sample covariance matrices ensembles

Ledoit, Olivier; Péché, Sandrine - Institut für Volkswirtschaftslehre, … - 2009

We consider sample covariance matrices constructed from real or complex i.i.d. variates with finite 12th moment. We assume that the population covariance matrix is positive definite and its spectral measure almost surely converges to some limiting probability distribution as the number of...

Persistent link: https://www.econbiz.de/10005627835

A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data

Aoshima, Makoto; Yata, Kazuyoshi - In: Annals of the Institute of Statistical Mathematics 66 (2014) 5, pp. 983-1010

In this paper, we consider a scale adjusted-type distance-based classifier for high-dimensional data. We first give such a classifier that can ensure high accuracy in misclassification rates for two-class classification. We show that the classifier is not only consistent but also asymptotically...

Persistent link: https://www.econbiz.de/10010950414

Bivariate high-level exceedance and the Chen–Stein theorem in genomics multiple hypothesis testing perspectives

Sen, Pranab K.; Kang, Moonsu - In: Statistics & Probability Letters 83 (2013) 7, pp. 1725-1730

In genomic studies, generally the genes are neither independent nor marginally identically distributed, though in microarray studies and DNA/RNA SNP models, often they are assumed to be independent and identically distributed. A version of the Chen–Stein theorem on Poisson approximation for...

Persistent link: https://www.econbiz.de/10010665605

PCA consistency for the power spiked model in high-dimensional settings

Yata, Kazuyoshi; Aoshima, Makoto - In: Journal of Multivariate Analysis 122 (2013) C, pp. 334-354

In this paper, we propose a general spiked model called the power spiked model in high-dimensional settings. We derive relations among the data dimension, the sample size and the high-dimensional noise structure. We first consider asymptotic properties of the conventional estimator of...

Persistent link: https://www.econbiz.de/10010702809

Correlation tests for high-dimensional data using extended cross-data-matrix methodology

Yata, Kazuyoshi; Aoshima, Makoto - In: Journal of Multivariate Analysis 117 (2013) C, pp. 313-331

In this paper, we consider tests of correlation when the sample size is much lower than the dimension. We propose a new estimation methodology called the extended cross-data-matrix methodology. By applying the method, we give a new test statistic for high-dimensional correlations. We show that...

Persistent link: https://www.econbiz.de/10011042082

Bienenfeld’s approximation of production prices and eigenvalue distribution: some more evidence from five European economies

Iliadi, Fotoula; Mariolis, Theodore; Soklis, George; … - Volkswirtschaftliche Fakultät, … - 2012

This paper tests Bienenfeld’s polynomial approximation of production prices using data from ten symmetric input-output tables of five European economies. The empirical results show that the quadratic formula works extremely well and its accuracy is connected to the actual distribution of the...

Persistent link: https://www.econbiz.de/10009647410

ON BRODY’S CONJECTURE: FACTS AND FIGURES FROM THE US ECONOMY

Mariolis, Theodore; Tsoulfidis, Lefteris - 2012

Brody’s conjecture is submitted to an empirical test using input-output flow data of varying size for the US economy for the benchmark years 1997 and 2002, as well as for the period 1998-2010. The results suggest that the ratio of the modulus of the subdominant eigenvalue to the dominant one...

Persistent link: https://www.econbiz.de/10010729122

On Bródy’s conjecture: facts and figures from the US economy

Mariolis, Theodore; Tsoulfidis, Lefteris - Volkswirtschaftliche Fakultät, … - 2012

Bródy’s conjecture is submitted to an empirical test using input-output flow data of varying size for the US economy for the benchmark years 1997 and 2002, as well as for the period 1998-2010. The results suggest that the ratio of the modulus of the subdominant eigenvalue to the dominant one...

Persistent link: https://www.econbiz.de/10011110770

Eigenvalue distribution and the production price-profit rate relationship in linear single-product systems: theory and empirical evidence

Mariolis, Theodore; Tsoulfidis, Lefteris - Volkswirtschaftliche Fakultät, … - 2010

A typical finding in many empirical studies is that the production price-profit rate relationship is, by and large, monotonic. This paper derives, in terms of the usual single-product model, the spectral conditions that make possible the appearance of such monotonicity. Furthermore, using data...

Persistent link: https://www.econbiz.de/10011110823

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