Projected principal component analysis in factor models

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are related to the projected linear space. When the dimensionality is large, the factors can be estimated accurately even when the sample size is finite. We propose a flexible semiparametric factor model, which decomposes the factor loading matrix into the component that can be explained by subject-specific covariates and the orthogonal residual component. The covariates' effects on the factor loadings are further modeled by the additive model via sieve approximations. By using the newly proposed Projected-PCA, the rates of convergence of the smooth factor loading matrices are obtained, which are much faster than those of the conventional factor analysis. The convergence is achieved even when the sample size is finite and is particularly appealing in the high-dimension-low-sample-size situation. This leads us to developing nonparametric tests on whether observed covariates have explaining powers on the loadings and whether they fully explain the loadings. The proposed method is illustrated by both simulated data and the returns of the components of the S&P 500 index.Comment: Published at http://dx.doi.org/10.1214/15-AOS1364 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ambidexterity in the Cellphone Industry: An Empirical Study of Asian Firms

Leveraging a hybrid research approach between quantitative and qualitative methods, the present research project intended to investigate 1)in the Chinese cellphone market, the difference in level of organizational ambidexterity exhibited by East Asian and Non-East Asian manufacturers, and 2)whether there exists a positive correlation between cellphone manufacturers’ market performance and organizational ambidexterity. This study drew from He & Wong’s (2004) framework of a dual-dimensioned organizational ambidexterity which includes the Balance Dimension (BD) that describes a balanced effort in organizational exploitation and exploration, and the Combined Dimension (CD) that describes the totality of effort devoted to exploitation and exploration activities. The present study proposes a positive correlation in the Chinese cellphone market between a cellphone manufacturer’s sales growth rate and 1a)BD, 1b)CD, and the simultaneous pursuit of 1c)BD & CD. The study also proposes that East Asian firms would exhibit a higher level of organizational ambidexterity in both 2a)BD and 2b)CD based on my discussion of cultural and institutional factors. The analytical results indicated that East Asian cellphone firms indeed demonstrated a higher level of organizational ambidexterity across both dimensions compared to their Non-East Asian counterparts. Mixed findings were obtained concerning organizational ambidexterity’s impact on organizational performance. The results partially supported that BD ambidexterity has a positive correlation with organizational performance. Contrary to expectations, the findings revealed a negative effect of CD ambidexterity on organizational performance. In addition, no significant relationship was detected between the simultaneous pursuit of BD & CD ambidexterity and organizational performance. Overall, the results support Raisch & Birkinshaw’s (2008) findings that the relationship between organizational ambidexterity and organizational performance is complex. The present study contributes to the literature by providing empirical evidence to the presence of a complex relationship between organizational ambidexterity and performance using the BD & CD framework. Discussion of the findings also offers insights into business practices in the consumer electronics industry. Keywords: organizational ambidexterity, exploration, exploitation, innovation, cellphone, mobile phone, Chinese market, East Asia

Network-based group variable selection for detecting expression quantitative trait loci (eQTL)

<p>Abstract</p> <p>Background</p> <p>Analysis of expression quantitative trait loci (eQTL) aims to identify the genetic loci associated with the expression level of genes. Penalized regression with a proper penalty is suitable for the high-dimensional biological data. Its performance should be enhanced when we incorporate biological knowledge of gene expression network and linkage disequilibrium (LD) structure between loci in high-noise background.</p> <p>Results</p> <p>We propose a network-based group variable selection (NGVS) method for QTL detection. Our method simultaneously maps highly correlated expression traits sharing the same biological function to marker sets formed by LD. By grouping markers, complex joint activity of multiple SNPs can be considered and the dimensionality of eQTL problem is reduced dramatically. In order to demonstrate the power and flexibility of our method, we used it to analyze two simulations and a mouse obesity and diabetes dataset. We considered the gene co-expression network, grouped markers into marker sets and treated the additive and dominant effect of each locus as a group: as a consequence, we were able to replicate results previously obtained on the mouse linkage dataset. Furthermore, we observed several possible sex-dependent loci and interactions of multiple SNPs.</p> <p>Conclusions</p> <p>The proposed NGVS method is appropriate for problems with high-dimensional data and high-noise background. On eQTL problem it outperforms the classical Lasso method, which does not consider biological knowledge. Introduction of proper gene expression and loci correlation information makes detecting causal markers more accurate. With reasonable model settings, NGVS can lead to novel biological findings.</p