Non-Parametric Signal Calibration, Orthogonal Pillar Pooling & One-Way Adversarial Veto Quorums

Q: Why do parametric sample mean and standard deviation z-scores fail on corporate filing and alternative data feeds?

Corporate event magnitudes—such as Form 4 insider purchase clusters, working-capital accrual spikes, or supply-chain revenue shocks—exhibit extreme positive skewness and heavy tails. A single outlier inflates the parametric sample standard deviation sigma, compressing subsequent informative disclosures toward zero. Starling replaces Gaussian z-scores with Out-of-Sample Blom rank quantiles on one-sided catalysts and floored Median Absolute Deviation (MAD) scaling on two-sided continuous series.

SECTION 01

Why Standard Bell-Curve Z-Scores & Simple Averages Break on Corporate Events

Once point-in-time disclosures are extracted without lookahead bias (Research Note RN-01), the next practical problem is combining them. An open-market insider purchase is measured in dollars, a cash-flow divergence is measured as a ratio of assets, and a customer-concentration shock is measured as a percentage of revenue. Before the safety layer can compare or combine those recommendations, they have to live on the same statistical scale.

Two common shortcuts cause multi-signal systems to misfire in live markets:

1. One Outlier Breaks the Bell Curve: Corporate events do not follow a neat bell curve; they are sparse and heavy-tailed. If you compute a standard Gaussian $z$-score $(x - \hat{\mu}) / \hat{\sigma}$ over a trailing window, a single massive event blows out the sample standard deviation $\hat{\sigma}$ for months—making every normal, genuinely informative filing that follows look tiny by comparison.

2. Counting the Same Filing Three Times: When a company files a 10-Q showing strong operating cash flow and falling working-capital accruals, multiple accounting scouts will fire on the exact same afternoon. If you simply add their scores together, you treat three angles on the same balance sheet as if they were three independent coin flips—inflating conviction and over-sizing the bet.

SECTION 02

Domain-Split Non-Parametric Normalization: OOS Blom Quantiles & Zero-Anchored MAD

To achieve robustness against extreme outliers without in-sample distribution leakage, Starling Quantitative partitions scout feature domains into two non-parametric normalization families evaluated strictly over prior historical observations inside $[t_0,\, t_{\text{eval}} - 12\text{d}]$:

2.1 One-Sided Catalyst Magnitudes: Out-of-Sample Blom Half-Normal Quantiles

For strictly positive catalyst magnitudes $x_{k,i,t} > 0$ (such as clustered Form 4 officer purchases, 8-K contract awards, or regulatory approvals), we compute the tie-adjusted out-of-sample mid-rank $r_{k,i,t}$ against the $N_{\text{prior}}$ strictly prior non-embargoed triggers and apply the Blom (1958) quantile transformation mapped to the folded half-normal distribution:

$$r_{k,i,t} = 1 + \sum_{m=1}^{N_{\text{prior}}} \mathbb{I}(x_m < x_{k,i,t}) + \frac{1}{2}\sum_{m=1}^{N_{\text{prior}}} \mathbb{I}(x_m = x_{k,i,t}), \qquad u_{k,i,t} = \frac{r_{k,i,t} - \frac{3}{8}}{N_{\text{prior}} + \frac{5}{4}} \in (0, 1)$$

$$q^+\!\left(u_{k,i,t}\right) = \operatorname{clip}\!\left(\Phi^{-1}\!\left(\frac{1 + u_{k,i,t}}{2}\right),\; z_{\min}^+,\; z_{\max}^+\right), \qquad 0 < z_{\min}^+ < z_{\max}^+$$

Multiplying $q^+(u_{k,i,t})$ by the deterministic thesis sign $d_{k,i,t} \in \{-1, +1\}$ and attenuating same-day multi-filing clusters of count $K_{k,i,t} \ge 1$ by a Blitzer-style square-root dampening factor $1 / \sqrt{K_{k,i,t}}$ yields a bounded, outlier-invariant directional score $z_{k,i,t}$.

2.2 Continuous Signed Series: Zero-Anchored $\operatorname{MAD}_0$ Scaling

For continuous two-sided metrics $x_{k,i,t} \in \mathbb{R}$ where $0.0$ is the natural economic origin (such as standardized unexpected earnings $\text{SUE}$, Sloan accrual ratios, or short-horizon return dislocations), we scale by the Gaussian-consistent Zero-Anchored Median Absolute Deviation ($\hat{s}_{0,k}$) floored by a fraction of the non-zero root-mean-square and a domain dispersion floor $s_{\text{floor},k} > 0$ to prevent division-by-zero explosions during low-dispersion regimes:

$$\hat{s}_{0,k} = 1.4826 \cdot \operatorname{median}_{|x_m| > 0}\!\big(|x_m|\big), \qquad s_{\text{eff},k} = \max\!\left(\hat{s}_{0,k},\;\; c_{\text{rms}}\,\operatorname{RMS}_{|x_m| > 0},\;\; s_{\text{floor},k}\right), \qquad z_{k,i,t} = \operatorname{clip}\!\left(\frac{x_{k,i,t}}{s_{\text{eff},k}},\; -z_{\max},\; +z_{\max}\right)$$

SECTION 03

Per-Feed Exponential Decay & Symmetric Two-Arm Concave Four-Pillar Pooling

Corporate catalysts decay at markedly different velocities depending on dissemination channel: an intraday SEC 8-K item or liquidity dislocation decays over days, whereas supply-chain footnote propagation or post-earnings drift persists over multi-week horizons. Before cross-scout aggregation, each normalized feature $z_{k,i,t}$ is attenuated by a continuous exponential kernel parameterized by its feed category’s half-life $\tau_k$ ($\lambda_k = \ln 2 / \tau_k$):

$$\tilde{z}_{k,i,t} = z_{k,i,t} \cdot \exp\!\big(-\lambda_k \Delta t_{k,i,t}\big)$$

To prevent collinear scouts from double-counting a single economic shock, every scout is mapped declaratively in our registry to one of four orthogonal causal pillars $p \in \{1, 2, 3, 4\}$:

• Pillar 1 (P1) — Accounting & Insider Forensics: Form 4 open-market officer/director purchase clusters, 8-K governance disclosures, and XBRL operating cash conversion vs. working-capital accruals.
• Pillar 2 (P2) — Physical & Regulatory Exhaust: Public federal regulatory clearances and recalls, administrative patent challenges, government procurement obligations, and product-safety telemetry.
• Pillar 3 (P3) — Positioning & Quality Rebound: Schedule 13D/13F institutional ownership shifts, solvency-screened $T+3$ stabilized liquidity rebounds, and options skew.
• Pillar 4 (P4) — Network & Macro Plumbing: Form 10-K ASC-280 customer-supplier lead-lag propagation and volatility/credit regime overlays.

Within each pillar $p$, active positive shocks $\tilde{z}_{(1)}^+ \ge \tilde{z}_{(2)}^+ \ge \dots > 0$ and negative shocks $\tilde{z}_{(1)}^- \le \tilde{z}_{(2)}^- \le \dots < 0$ are sorted by magnitude and pooled via symmetric two-arm concave summation with diminishing marginal weight $\gamma_{\text{pool}} \in (0, 1)$:

$$S_{p,i,t}^+ = \tilde{z}_{(1)}^+ + \gamma_{\text{pool}} \sum_{j \ge 2} \tilde{z}_{(j)}^+, \qquad S_{p,i,t}^- = \tilde{z}_{(1)}^- + \gamma_{\text{pool}} \sum_{j \ge 2} \tilde{z}_{(j)}^-, \qquad S_{p,i,t} = S_{p,i,t}^+ + S_{p,i,t}^-$$

Statutory restatement or delinquency filings (8-K Item 4.02, Form NT 10-K/10-Q), severe continuous distress shocks ($\tilde{z}_{k,i,t} \le -z_{\text{veto}}$), or opposing-signal collisions ($S_{p,i,t}^+ > 0 \land S_{p,i,t}^- < 0$) immediately clamp bullish conviction to $0.0$. Across the four pillars, scores are combined via Empirical-Bayes-shrunk unit-simplex weights $\boldsymbol{\omega} \in \Delta^3$ ($\sum_{p=1}^4 \omega_p = 1$, shrunk toward equal $1/4$ weights) and normalized by the uncentered arrival-event root-mean-square $\hat{\sigma}_S$ computed strictly over discrete catalyst arrivals $\mathcal{E}_{\text{active}}$:

$$Z_{i,t} = \operatorname{clip}\!\left(\frac{\sum_{p=1}^{4} \omega_p \, S_{p,i,t}}{\max(\hat{\sigma}_S,\, \epsilon_S)},\; -z_{\text{comp}},\; +z_{\text{comp}}\right)$$

SECTION 04

Zero-Skill-Null Grinold Scaling & Post-Acceptance Exhaustion Haircuts

Composite conviction $Z_{i,t}$ is mapped into an expected $H$-day idiosyncratic residual return $\hat{\alpha}_{\text{gross},i,t}$ (in basis points) via the Grinold (1989) Fundamental Law of Active Management, scaling by the stock’s clamped $H$-day residual volatility $\hat{\sigma}_{\text{resid},i,H}$ and the Empirical Bayes shrunk Information Coefficient $\operatorname{IC}_{\text{shrunk}}$:

$$\operatorname{IC}_{\text{shrunk},s} = \left(\frac{N_{\text{eff},s}}{N_{\text{eff},s} + \kappa}\right) \widehat{\operatorname{IC}}_{\text{OOS},s} + \left(\frac{\kappa}{N_{\text{eff},s} + \kappa}\right) \operatorname{IC}_0, \qquad \operatorname{IC}_0 \equiv 0.0$$

Crucially, Starling fixes the prior strictly at the zero-skill null ($\operatorname{IC}_0 = 0.0$) and applies $t$-statistic soft thresholding: any scout whose out-of-sample residual IC lacks statistical significance is shrunk directly to zero rather than buoyed by an optimistic heuristic prior.

Finally, because a filing accepted at $\tau_{\text{accept}}$ may already be partially priced by the market before batch order routing at $t_{\text{exec}}$, we deduct a one-way post-acceptance price-exhaustion haircut whenever the stock has already moved in the signal’s direction between $\tau_{\text{accept}}$ and $t_{\text{exec}}$:

$$\hat{\alpha}_{\text{rem},i,t} = \hat{\alpha}_{\text{gross},i,t} \cdot \max\!\left(0,\;\; 1 - \frac{\max\!\big(0,\, d_{i,t} \cdot r_{i,\, \tau_{\text{accept}} \to t_{\text{exec}}}\big)}{\gamma_{\text{exh}} \, \hat{\sigma}_{\text{resid},i,1\text{d}}}\right)$$

An order is eligible for routing only if the remaining unpriced alpha clears expected round-trip execution friction by a strict safety multiple $\eta_{\text{cost}} > 1$: $\hat{\alpha}_{\text{rem},i,t} \ge \eta_{\text{cost}} \cdot \operatorname{ExpectedRoundTripCost}_{i,t}$.

SECTION 05

The One-Way Adversarial Audit Gate

Quantitative parsers excel at structured XBRL and numerical time series, but footnotes occasionally conceal qualitative structural traps—such as toxic convertible-debt resets, off-balance-sheet litigation contingencies, or going-concern language. Starling incorporates a sandboxed qualitative audit gate strictly downstream of deterministic calibration under a non-negotiable one-way veto invariant:

$$w_{i,t}^{\text{final}} = \mathbb{I}_{\text{pass\_audit}}(i,t) \cdot w_{i,t}^{\text{quant}}, \qquad \mathbb{I}_{\text{pass\_audit}}(i,t) \in \{0, 1\}$$

The qualitative audit gate can only multiply a candidate’s quantitative weight by $0$ (vetoing a flawed setup to NO_TRADE) or $1$ (allowing the deterministic weight through unchanged). It possesses zero authority to originate trade ideas, override a failed quantitative screen, or increase position size.

SECTION 06

Selected References & Technical FAQ

• Blom, G. (1958). Statistical Estimates and Transformed Beta-Variables. John Wiley & Sons.
• Grinold, R. C. (1989). The fundamental law of active management. Journal of Portfolio Management, 15(3), 30–37.
• Grinold, R. C., & Kahn, R. N. (1999). Active Portfolio Management: A Quantitative Approach for Providing Superior Returns and Controlling Risk (2nd ed.). McGraw-Hill.
• Huber, P. J. (1981). Robust Statistics. John Wiley & Sons.

Why do parametric sample mean and standard deviation z-scores fail on corporate filing and alternative data feeds?

Corporate event magnitudes exhibit extreme positive skewness and heavy tails. A single outlier inflates the parametric sample standard deviation $\hat{\sigma}$, compressing subsequent informative disclosures toward zero. Starling replaces Gaussian $z$-scores with Out-of-Sample Blom rank quantiles on one-sided catalysts and floored Median Absolute Deviation ($\text{MAD}_0$) scaling on two-sided continuous series.

How does concave 4-pillar pooling prevent correlated scouts from double-counting the same event?

When multiple scouts within the same economic domain trigger on a single corporate filing, linear summation overstates conviction. Starling groups its scouts into four orthogonal causal pillars (P1–P4) and applies symmetric two-arm sorted concave pooling ($\tilde{z}_{(1)} + \gamma_{\text{pool}} \sum_{j \ge 2} \tilde{z}_{(j)}$) inside each pillar before combining across pillars via Empirical-Bayes-shrunk unit-simplex weights normalized by arrival-event RMS.

Why does Starling shrink scout Information Coefficients toward a zero-skill prior ($\operatorname{IC}_0 = 0.0$)?

Shrinking noisy small-sample Information Coefficients toward a positive heuristic baseline manufactures positive expected alpha out of uninformative series. Starling shrinks every scout’s empirical residual IC strictly toward zero ($\operatorname{IC}_0 = 0.0$) with $t$-statistic soft thresholding so any signal lacking statistically significant out-of-sample predictability collapses to zero expected alpha.

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Non-Parametric Signal Calibration, Orthogonal Pillar Pooling &
One-Way Adversarial Veto Quorums.