Related papers: Conditional regression for single-index models
Theoretically, the conditional expectation of a square-integrable random variable $Y$ given a $d$-dimensional random vector $X$ can be obtained by minimizing the mean squared distance between $Y$ and $f(X)$ over all Borel measurable…
Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods for…
The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion…
Conditional forecasts, i.e. projections of a set of variables of interest on the future paths of some other variables, are used routinely by empirical macroeconomists in a number of applied settings. In spite of this, the existing…
Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…
We introduce a new class of conditional autoregressive models for spatially dependent functional data, formulated through conditional means given neighboring functional observations and characterized by a covariance operator and a spatial…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of…
We consider the complex data modeling problem motivated by the zero-inflated and overdispersed data from microbiome studies. Analyzing how microbiome abundance is associated with human biological features, such as BMI, is of great…
In this paper, we consider a single-index mixed model with longitudinal data. A new set of estimating equations is proposed to estimate the single-index coefficient. The link function is estimated by using the local linear smoothing.…
Consider a stationary real-valued time series $\{X_n\}_{n=0}^{\infty}$ with a priori unknown distribution. The goal is to estimate the conditional expectation $E(X_{n+1}|X_0,..., X_n)$ based on the observations $(X_0,..., X_n)$ in a…
We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for…
Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However (partially) linear models for example, which would deliver these, may fit poorly to the data. On the other hand, an…
We propose new parametric frameworks of regression analysis with the conditional mode of a bounded response as the focal point of interest. Covariate effects estimation and prediction based on the maximum likelihood method under two new…
This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…
We introduce a new family of one factor distributions for high-dimensional binary data. The model provides an explicit probability for each event, thus avoiding the numeric approximations often made by existing methods. Model interpretation…
This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional…
In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric…
A typical desideratum for quantifying the uncertainty from a classification model as a prediction set is class-conditional singleton set calibration. That is, such sets should map to the output of well-calibrated selective classifiers,…
This paper investigates a new approach to estimate the gradient of the conditional probability given the covariates in the binary classification framework. The proposed approach consists in fitting a localized nearest-neighbor logistic…