Statistical Foundations for a Google Play User-Review Sentiment Index: Signal Fusion, Shrinkage, Distributional Validation, and Dynamic Smoothing
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Statistics > Methodology
Title:Statistical Foundations for a Google Play User-Review Sentiment Index: Signal Fusion, Shrinkage, Distributional Validation, and Dynamic Smoothing
Abstract:We develop a statistically explicit sentiment index for Google Play user reviews and establish the mathematical results supporting its construction. Normalized star ratings and text-sentiment scores are treated as noisy measures of latent review valence and fused by covariance-aware inverse-variance weighting. Review-level estimates are aggregated with bounded helpfulness and recency weights, then shrunk toward a population mean using estimated precision rather than an arbitrary review-count threshold. App-level rating histograms provide a distributional diagnostic for samples returned under different API sort orders; because star ratings are discrete, classical continuous Kolmogorov-Smirnov critical values are not used. A local-level state-space model and the Kalman filter provide a denoised temporal trend. Full proofs cover the BLUE and Gaussian maximum-likelihood result, Gaussian-conjugate shrinkage, the Glivenko-Cantelli and Donsker theorems, count transformations via the delta method, and exact Gaussian Kalman filtering. A worked three-review example shows how textual complaints can materially reduce an apparently perfect star-only score.
| Comments: | 16 pages, 2 tables, no figures |
| Subjects: | Methodology (stat.ME); Computation and Language (cs.CL); Applications (stat.AP) |
| MSC classes: | 62F10 (Primary) 62C12, 62F15, 62M20, 62P25 (Secondary) |
| ACM classes: | I.2.7; G.3 |
| Cite as: | arXiv:2609.31513 [stat.ME] |
| (or arXiv:2609.31513v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2609.31513
arXiv-issued DOI via DataCite (pending registration)
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