Hypothesis Testing for Dependent Variables with Unbalanced Data

Implements hierarchical Bayesian inference, robust frequentist inference, and distribution-free inference for dependent and unbalanced data under strong-mixing conditions. Supports triangular-array, weighted-sum and mixingale convergence regimes with Whittle and composite likelihoods, heteroskedasticity-and-autocorrelation-consistent variance estimation, block bootstrap with automatic block length, fixed-bandwidth HAR inference, adaptive conformal prediction, Bayesian decision under Region of Practical Equivalence, bridge-sampling Bayes factors, and predictive comparison via the Widely Applicable Information Criterion and leave-future-out cross-validation. Methods follow Andrews (1991) , Kiefer and Vogelsang (2005) , Patton, Politis and White (2009) , Vehtari, Gelman and Gabry (2017) , Kruschke (2018) , and Gibbs and Candes (2021) .

HTDV

Hypothesis Testing for Dependent Variables with Unbalanced Data.

HTDV provides a unified R toolkit for inference on dependent, unbalanced data under strong-mixing conditions, combining hierarchical Bayesian estimation via Hamiltonian Monte Carlo with frequentist and distribution-free robustness anchors (fixed-b HAR, block bootstrap, adaptive conformal).

Validation card

The framework is shipped with two pre-registered validation studies, both reproducible end-to-end and with their summary tables exposed as package datasets. See vignette("HTDV-validation").

Factorial Monte Carlo (htdv_sim_summary). 1024-cell design crossing sample size, AR(1) coefficient, innovation tail, imbalance ratio and location shift; 500 replications per cell × 3 inferential layers; 31 hours of wall-clock on 16 cores. The Bayesian envelope holds nominal size (mean 0.0556, sd 0.013) and nominal coverage (mean 0.944) across the entire grid; HAR and bootstrap inflate to empirical size 0.60 and coverage 0.29 in the worst corners under strong persistence. The asymptotic gap that motivates the framework is visible in the data.
External benchmarks (htdv_empirical_benchmarks). Three public datasets compared against published references:
- FRED-MD post-1984 CPI inflation against Stock and Watson (2007).
- Shiller log-CAPE against Campbell and Shiller (1998).
- US-Canada 10-year yield differential against the iid Welch baseline.
All three layers reproduce all three references with agreement in every case. The 95% interval widths scale monotonically with the series persistence: at $\widehat\phi\approx 0.45$ Bayes is 0.81× HAR; at $\widehat\phi\approx 0.97$ it is 2.80× HAR; at near-unit-root ($\widehat\phi\approx 0.99$) it is 15.0× HAR. The framework's value is the visibility of this gradient.

library(HTDV)
data(htdv_sim_summary)         # simulation summary, 3069 rows
data(htdv_empirical_benchmarks) # three-dataset external validation
vignette("HTDV-validation")    # full narrative

Installation

remotes::install_github("IsadoreNabi/HTDV")

rstan is required. Optional backends: bridgesampling (Bayes factors), loo (WAIC / PSIS-LOO), posterior (draws utilities), bayesplot (visualization), readxl (vignette).

Core API

Function	Purpose
`htdv_fit()`	Hierarchical Bayesian HMC fit.
`htdv_envelope()`	Berger-robust envelope across models.
`htdv_lrv()`	HAC long-run variance (Andrews bandwidth).
`htdv_fixedb()`	Fixed-bandwidth HAR Wald test.
`htdv_boot()`	Block bootstrap with automatic block length.
`htdv_conformal()`	Adaptive conformal inference.
`htdv_rope()`	ROPE-based posterior decision.
`htdv_bf()`	Bridge-sampling Bayes factor.
`htdv_waic_lfo()`	WAIC and leave-future-out CV.
`htdv_stack()`	Predictive stacking.
`htdv_diagnostics()`	MCMC diagnostics.
`htdv_ppc()`	Posterior-predictive checks on dependence statistics.
`htdv_equivalence_constants()`	Explicit TAC/WSC/MPC constants.
`htdv_simstudy()`	Factorial Monte Carlo study (Section 12-bis).
`htdv_simstudy_summary()`	Aggregate per-cell results.
`htdv_simstudy_warnings()`	Flag cells in the limit-of-identification zone.