This thesis proposes alternative estimation methods for two separate frameworks. These

are presented in two main chapters, namely, “Quasi-likelihood inference for binary dyadic

regression” and “Penalized quantile regression based on moments”.

In the first chapter we focus on the case of binary dyadic outcomes, which has recently

attracted much attention in the context of network formation models. Dyadic

data is known to exhibit a distinctive form of correlation known as dyadic clustering. We

propose a quasi-likelihood procedure constructed from the first two data moments that

accounts this correlation. Our method avoids strong assumptions on the specification of

latent components, and through simulation work, we find efficiency gains when compared

with common alternatives, returning less scattered estimates and shorter confidence intervals.

Empirical applications based on advice and trade networks are provided.

The second chapter studies quantile regression under high-dimensionality and sparsity.

Specifically, we present a penalized estimator which selects predictors affecting

the location and scale of a response variable, and estimates conditional quantiles. To

achieve this, we augment the procedure in Machado & Santos Silva (2019) by including

a penalty term allowing the shrinkage of coefficients. This approach benefits from the

use of methods specific to the estimation of conditional means, which particularly aids

in computational simplicity and in difficult estimation settings for quantile regression.

Simulation work indicates that our proposal selects all relevant predictors affecting the

location and scale of the response variable, given a sufficiently large sample size, and

delivers adequate quantile prediction. To demonstrate the proposed estimator, we show

an illustrative application based on the Corrected Boston House Price Data.