Open research questions in Statistical Methods and Inference
186 gap statements mined from Statistical Methods and Inference papers in our 4.5M-paper local library, which holds 1,610 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
What the literature leaves open
The continuous dynamics presented in Algorithm 2 is not suitable for practical simulations. The simulation is performed with a limited number of numerical integration steps.
Future studies could investigate the performance of different methods in other types of regression models. Future studies could explore the use of other prior distributions for Bayesian model averaging methods. Future studies could investigate the impact of model uncertainty on the results of logistic regression analyses.
The assumption of normal distribution for error terms in regression models may not be well-justified. Bridge regression can address overfitting, but existing methods may not be flexible or adaptable enough. There is a need for a more flexible and adaptable approach to nonparametric regression analysis.
The calculation of model degrees of freedom is not straightforward in complex models, such as tree-structured varying coefficient models. There is a need for a new method to calculate the degrees of freedom in these models.
A tool to determine the degrees of freedom in tree-structured varying coefficient models · 2026Standard survival analysis models are limited in their ability to account for sequences of intermediate events. Competing risk models consider experiments with multiple events, but are limited in their ability to model complex systems.
Multi-state model with temporal-consistent survival analysis for homogeneous Markov chains · 2026There is a need to extend structural nested mean models to modified treatment policies. There is a need to enable characterization of time-varying heterogeneity of MTP effects.
The paper notes that the performance of the new estimator is somewhat disappointing. The paper also notes that caveats concerning automatic bandwidth selection remain in place. The simulations are limited to a set of ten known densities.
The gap is that existing estimators do not achieve their desired properties theoretically. The paper aims to fill this gap by proposing a new estimator that combines two existing methods.
The existing methods do not promote sparsity and select variables specific to each event. The proposed method aims to fill this gap.
Variable selection with broken adaptive ridge regression for interval-censored competing risks data · 2026 · DOIFuture research can investigate the application of the proposed method to other domains, such as genetics and engineering. Future research can compare the proposed method with other methods for stability selection.
To apply the proposed method to other large-scale registries where event times are recorded on a discrete scale.
Gradient boosting-based discrete failure time model for selecting time-varying effects and interactions · 2026 · DOIThe existing methods do not efficiently identify both time-varying and time-independent effects, while preserving interpretability.
Gradient boosting-based discrete failure time model for selecting time-varying effects and interactions · 2026 · DOIThe paper focuses on a binary treatment scenario. The method may not be applicable to multiple treatment options. The approach requires further extension to longitudinal studies and survival data.
Existing methods require parametric or semiparametric modeling of the relationship between the time-dependent covariate and the survival outcome.
The paper notes that previous results do not provide any immediate guidance on whether preserving the linear relationship requires all variables to be conditioned on all other variables.
The paper focuses on comparing two population-level categorical Gini correlations. We develop a formal test to assess whether a significant difference exists between them. The proposed test statistic is derived, and its asymptotic distribution is studied under both the null and alternative hypotheses.
Comparing Two Categorical Gini Correlations with Applications to Classification Problems · 2026To further investigate the properties of the kernel-based estimator.
Multi-state model with temporal-consistent survival analysis for homogeneous Markov chains · 2026The instability of the Lasso algorithm in the presence of correlated variables is a major concern. Previous research has not provided a satisfactory solution to this problem.
The literature focuses on the situation in which the model errors are stationary, and that the only non-stationarity in the data arises from change points in the linear model parameters.
CONFIDENCE INTERVALS FOR MULTIPLE CHANGE POINTS IN LINEAR MODELS WITH HETEROSCEDASTIC ERRORS · 2026 · DOITo apply the CVN model to more real-world data sets. To develop more efficient algorithms to solve the optimization problem.
Extending the proposed method to multiple treatment options. Applying the approach to longitudinal studies and survival data. Investigating the use of other machine learning techniques for estimating quantile OTRs.
The application of the DHMC method to other fields, such as machine learning. The development of more efficient algorithms for transdimensional sampling.
Investigate the performance of the JREL function in scenarios where the standard normal distribution is inadequate, - Explore the application of the Bridge model to other…
Further evaluation of the proposed formula in different scenarios. Application of the formula to other complex modeling approaches. Development of new methods for calculating the degrees of freedom in complex models.
A tool to determine the degrees of freedom in tree-structured varying coefficient models · 2026In contrast, no standard method has yet emerged for automatic nonparametric spectral density estimation, and there seems to be little willingness to weigh the advantages and disadvantages of different risk functions and the various methods for estimating them on a case-by-case basis, particularly because it is unclear whether the effort is even worthwhile without concrete prior information about the unknown spectral…
Bandwidth selection with a frequency-domain version of the AIC · 2026
Most-cited papers in Statistical Methods and Inference
- Multimodel Inference · Sociological Methods & Research · 2004 · 10,358 citations
- An Introduction to Kernel and Nearest-Neighbor Nonparametric Regression · The American Statistician · 1992 · 9,382 citations
- A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation · The American Statistician · 1983 · 5,908 citations
- Quantile Regression · The Journal of Economic Perspectives · 2001 · 4,274 citations
- Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy · Statistical Science · 1986 · 3,631 citations
- Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions · Psychometrika · 1987 · 3,606 citations
- Matching As An Econometric Evaluation Estimator · The Review of Economic Studies · 1998 · 2,478 citations
- Approximately normal tests for equal predictive accuracy in nested models · Journal of Econometrics · 2006 · 2,232 citations
- A statistical model for the analysis of ordinal level dependent variables · Journal of Mathematical Sociology · 1975 · 1,734 citations
- Optimal Bandwidth Choice for the Regression Discontinuity Estimator · The Review of Economic Studies · 2011 · 1,617 citations
Most recent work
- On multiplicative bias correction in kernel density estimation · Open Research Online (The Open University) · 2026
- Robust Bayesian high-dimensional variable selection and inference with the horseshoe family of priors · Computational Statistics & Data Analysis · 2026
- A unified framework for complex survival data: accounting for clustering, cure fractions, and competing risks · BMC Medical Research Methodology · 2026
- A New Family of Error Distributions for Bayesian Quantile Regression · Bayesian Analysis · 2026
- Consistency, distributional convergence, and optimality of time-varying parameters in score-driven models · Journal of Econometrics · 2026
- Assessing the impact of variance heterogeneity and misspecification in mixed-effects location-scale models · BMC Medical Research Methodology · 2026
- Sex-specific allometric modeling and regression–residual normalization for size-adjusted strength assessment · European Journal of Applied Physiology · 2026
- Bayesian stability selection and inference on selection probabilities · Statistics and Computing · 2026
- Empirical likelihood for partially linear functional-coefficient autoregressive errors-in-variables models · Statistics and Computing · 2026
- A Ranked Sparsity Extension to the Bayesian Information Criterion: A Tool for Selecting Variables from Multiple Data Modalities · Entropy · 2026
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