Sparse principal component analysis with measurement errors

• The sparse principal component analysis is introduced for data with measurement errors.
• Efficient algorithms are designed to implement the procedures.
• Numerical studies show the finite sample performance of the proposed methods is satisfying.

Traditional principal component analysis often produces non-zero loadings, which makes it hard to interpret the principal components. This drawback can be overcome by the sparse principal component analysis procedures developed in the past decade. However, similar work has not been done when the random variables or vectors are contaminated with measurement errors. Simply applying the existing sparse principal component analysis procedure to the error-contaminated data might lead to biased loadings. This paper tries to modify an existing sparse principal component procedure to accommodate the measurement error setup. Similar to error-free cases, we show that the sparse principal component for the latent variables can be formulated as a bias-corrected lasso (elastic net) regression problem based on the observed surrogates, efficient algorithms are also developed to implement the procedure. Numerical simulation studies are conducted to illustrate the finite sample performance of the proposed method.