  Transfer learning has emerged as a highly sought-after and actively pursued
research area within the statistical community. The core concept of transfer
learning involves leveraging insights and information from auxiliary datasets
to enhance the analysis of the primary dataset of interest. In this paper, our
focus is on datasets originating from distinct yet interconnected
distributions. We assume that the training data conforms to a standard
generalized linear model, while the testing data exhibit a connection to the
training data based on a prior probability shift assumption. Ultimately, we
discover that the two-sample conditional means are interrelated through an
unknown, nondecreasing function. We integrate the power of generalized
estimating equations with the shape-restricted score function, creating a
robust framework for improved inference regarding the underlying parameters. We
theoretically establish the asymptotic properties of our estimator and
demonstrate, through simulation studies, that our method yields more accurate
parameter estimates compared to those based solely on the testing or training
data. Finally, we apply our method to a real-world example.
