Density Ratio Models

Introduction to Density Ratio Models
Logistic Regression Model
Logistic Compounds of Two Distributions
Logistic Compounds of Several Distributions
Examples of Density Ratio Models
Applications of Density Ratio Models

Nonparametric and Semiparametric Likelihoods
Empirical Likelihood
Biased Sampling
Multivariate Biased Sampling
Generalized Estimating Equations
Constrained Empirical Likelihood Estimation

Nonparametric and Semiparametric Goodness-of-Fit Test Methods
Chi-Square Goodness-of-Fit Test
Generalized Chi-Square Goodness-of-Fit Test
Kolmogorov-Smirnov One-Sample Test
Kolmogorov-Smirnov Two-Sample Test
Information Matrix Test
Moments Specification Test

Semiparametric Inferences under Binary Density Ratio Models
Maximum Semiparametric Likelihood Estimation
Bias-Corrected Maximum Semiparametric Likelihood Estimation
Constrained Semiparametric Likelihood Estimation
M-Estimation
Quantile Estimation
Kernel Density Estimation
Prospective and Retrospective Analyses
Wald Test, Likelihood Ratio Test, Score Test of Odds Ratio Parameters
Testing Odds Ratio Parameters Using Entropy Distance Measures
Examples
Some Proofs

Semiparametric Goodness-of-Fit Test Methods under Binary Density Ratio Models
Kolmogorov-Smirnov-Type Test Statistic
Chi-Square-Type Test Statistic
Information-Matrix-Based Test Statistic
Moments-Specification-Type Test Statistic
Examples
Some Proofs

Multinomial Density Ratio Model
Multicategory Logistic Regression Model
Maximum Semiparametric Likelihood Estimation
Weighted Kolmogorov-Smirnov-Type Test Statistic
Examples
Some Proofs

Ordinal Density Ratio Models
Proportional Odds Model
Prospective Analysis
Semiparametric Selection Bias Model
Maximum Semiparametric Likelihood Estimation
Unbiased Estimation Equations
Weighted Kolmogorov-Smirnov-Type Test Statistic
Continuation Ratio Logistic Regression Model under Case-control Sampling Design
Examples
Some Proofs

Multiplicative-Intercept Risk Models
Binary Multiplicative-Intercept Risk Model
Maximum Semiparametric Likelihood Estimation
Weighted Kolmogorov-Smirnov-Type Test Statistic
A Bootstrap Procedure
Confidence Bands
Multivariate Multiplicative-Intercept Risk Models
Examples
Some Proofs

Finite Mixture Models
Finite Mixture Density Ratio Model
Maximum Semiparametric Likelihood Estimation
Weighted Kolmogorov-Smirnov-Type Test Statistic
Empirical Likelihood Confidence Intervals for Mixture Proportion
A Semiparametric EM Algorithm
Score Test
Partial Empirical Likelihood-Based Score Test
Some Proofs

Receiver Operating Characteristic Curve Analysis under Density Ratio Models
ROC Curve and the Area under the ROC Curve
Maximum Semiparametric Likelihood Estimation
Semiparametric Hypothesis Testing for the ROC Curve Area
Semiparametric Kernel Estimation of the ROC Curve and its AUC
Comparing Two Diagnostic Tests
Best Combination of Multiple Diagnostic Tests
ROC Surfaces for Continuous Diagnostic Tests Based on Two Test Measurements
Goodness-of-Fit Test Based on AUC
Examples
Some Proofs

Analysis with Unordered Pairs under Density Ratio Models
Introduction to the Unordered Paired Data Problem
Nonparametric Inference for Unordered Paired Data
Semiparametric Inference for Unordered Paired Data
A Semiparametric EM Algorithm
Some Proofs

One-Way Analysis of Variance under Density Ratio Models
Normal-Based One-Way Analysis of Variance
Semiparametric One-Way Analysis of Variance
Hypothesis Testing
Examples
Some Proofs

Change-Point Analysis under Density Ratio Models
Introduction to the Change-Point Problem
Nonparametric Change-Point Model
Semiparametric Change-Point Model
Examples
Some Proofs

Estimating Distributional Treatment Effect under Density Ratio Models
Instrumental Variable Approach to the Analysis of Randomized Trials with Noncompliance
Nonparametric Estimation of Causal Effects in Randomized Trials with Noncompliance
Semiparametric Estimation of Causal Effects in Randomized Trials with Noncompliance
A Semiparametric EM Algorithm
Goodness-of-Fit Test
Examples
Some Proofs