Questions tagged [semiparametric]

Semiparametric probability models are a general class of models used for estimation and inference that contain a nonparametric component and a parametric component.

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Are these two estimated regression coefficient asymptotically equivalent? If not, which one is more efficient?

Suppose I have $Y=\beta_1X_1+\beta_2X_1X_2+g(X_2)+u$, where $E(u|X_1,X_2)=0$ and $S=g(X_2)+e$ with $E(e|X_2)=0$. I have a random sample $\{Y_i,X_{1i},X_{2i},S_i\}_{i=1}^n$. Suppose I first use a ...
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Semi-parameteric estimation

I am interested in the effect of certain interventions $T$ on my value of interest $Y$, my model is, $$Y = \tau f(T, X, Z) + g(X, Z), $$ where $f(T, X, Z) = T \times X + T \times Z$ , that is all the ...
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Double Machine Learning: What kind of "naive" estimator do the authors use to get such a bias?

I am reading the double-machine learning paper by Chernozhukov et al. (2018), in Example 1.1. the authors consider the partially linear model: $$Y = D \theta_0 + g_0(X) + U, E[U|X, D] = 0\\ D = m_0(X) ...
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Estimating Time-Varying Effects of Time-Invariant Covariates

In short, I have a time-invariant variable that I know has a time-varying effect on my outcomes of interest. I would like to estimate a plot this effect over time. What are some ways of going about ...
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Deriving Influence Function for variance estimator

In chapter 2 of Tsiatis (2006), the following is stated After some straightforward algebra, we can express the estimator $\hat{\sigma}_n^2$ minus the estimand as $$(\hat{\sigma}_n^2 - \sigma_0^2) = ...
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How to perform a linear regression to data which has transient behavior and saturation?

I am trying to linear-fit data in intermediate time scale (theoretically assumed to be linear) in the absence of the transient behavior in initial time and saturation after some time. For instance, ...
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Method of Sieves with Data Driven Basis Functions

Consider a nonparametric regression problem with i.i.d. sampled data $(y_1,x_1), (y_2,x_2),\ldots, (y_n,x_n)$ and regression function $$y_i = g_0(x_i) + \varepsilon_i,\quad \mathbb E[\varepsilon_i | ...
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Bandwidths in Nonparametric Estimation regarding local linear and local constant

I'm reading up on some nonparametric methods and I've gotten a bit confused regarding what will happen given a certain bandwidth. For example, if I consider the local linear least squares method and a ...
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estimation method in GAM model

I created a GAM model with semiparametric with parametric and nonparametric covariates. In the parametric regression model there is an estimation method to determine the value of the beta coefficient. ...
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Choosing variables for a semiparametric model

I am trying to create a semiparametric model for university (we were told it HAS to be semiparametric) and I have 11 response variables, some of them categorical and the rest continuous. In the simple ...
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MCMC fitting of a Dirichlet Process or Polya Tree prior to the residuals in a (simple linear regression)/(2-independent-samples) problem

Consider a simple location-shift semi-parametric model with two mutually-independent samples (here $F$ is a cumulative distribution function (CDF) on $\mathbb{ R }$, the $C_i$ and $T_j$ are real-...
David Draper's user avatar
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Efficient influence function in proportional hazards model

I was hoping someone could help me with this problem in the cox proportional hazards model. I am given the following setup. T is a non-negative random variable with continous distribution and hazard ...
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Martingale in Cox Model

Can someone help me to show that $$ \hat{A}(t, \beta_0) = \sum_{i=1}^{n} \int_0^t\frac{1}{\sum_{j}^n Y_j(s) e^{X_i^T \beta_0}} dN_i(s) $$ is a martingale. The setup is the Cox proportional hazard ...
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Local regressions with many zeroes

I want to run a nonparametric or semiparametric regression on data which I suspect to be non-linear. I'm using Stata for this. At first I thought of using LOWESS ...
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Convergence of a semiparametric estimator - a doubt

Suppose we have a parametric continuous function of $x\in\mathbb{R}$ with d-dimensional parameter $\theta$ $$g(x;\theta)$$ we also have have an n-dimensional sample if i.i.d. observations of X. With ...
Almostsurely's user avatar
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OLR with rms: proportional odds assumption

I am fitting an ordinal logistic regression model with rms package. my data involves a three-level ordered outcome (see ...
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How Semiparametric regression works?

I am working on semiparametric regression models; $$y=\beta x_1 +m(x_2)+e$$. I can understand this combination of Parametric and Nonparametric but how to estimate the responses ($\hat y$)? What is ...
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Is the Wilcoxon two-sample test maximally powered to detect proportional odds alternatives?

We know from the literature that The Wilcoxon-Mann-Whitney two-sample rank sum test is optimal for detecting simple location shifts when comparing two continuous random variables that each have a ...
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Understanding Sharpe Ratio Hypothesis Testing - Ledoit + Wolf

I've been poring over this paper written by Ledoit and Wolf regarding their approach to constructing hypothesis tests for Sharpe Ratios. In short, they see that running circular block bootstrap ...
Ringleader's user avatar
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In survival analysis, when should we use fully parametric models over semi-parametric ones?

This question is the counterpoint of the other question In survival analysis, why do we use semi-parametric models (Cox proportional hazards) instead of fully parametric models? Indeed, it clearly ...
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What is the degree of freedom of semiparametric method for mixture distribution

In the semi-parametric method for density analysis, I want to compare one component semi-parametric mixture distribution and two components mixture distribution. Semi-parametric here means the shape ...
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Deconvoluting an ECDF via mixed modeling

I have data with measurement error, $W_i$, with the following structure: $$W_i = \mu + \gamma_i + U_i$$ where $U_i \sim N(0, \sigma^2_i)$, with known $\sigma^2_i$, and $U_i \; \amalg \; \gamma_i$. I ...
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Nonparametric regression on data with known noise parameterization

What's the best way to regress on data for which we don't have a parameterised generative model (e.g. an arbitrary non-smooth continuous signal, that can be regressed in model-free ways with splines, ...
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Probabilistic interpretation of Thin Plate Smoothing Splines

TLDR: Do thin plate regression splines have a probabilistic/Bayesian interpretation? Given input-output pairs $(x_i,y_i)$, $i=1,...,n$; I want to estimate a function $f(\cdot)$ as follows \begin{...
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Is quantile regression model a parametric approach?

Is quantile regression a parametric regression or it is semiparametric? If it is parametric then what are its assumptions and if semiparametric then how?
Honey's user avatar
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How general is the backfitting algorithm?

Hastie \& Tibshirani's original approach to fitting generalized additive models was the backfitting algorithm. For a model of the form $$ y = \alpha + \displaystyle\sum_k f_k(x_k) + \epsilon $$ ...
generic_user's user avatar
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How to make predictions from penalized spline model

Consider a piecewise linear function with $M$ knots: $Y_i = \beta_1 + \beta_2x_i + \beta_{21}(x_i-\kappa_1)_+ + \beta_{22}(x_i - \kappa_2)_+ + ... + \beta_{2M}(x_i-\kappa_M)_+ + e_i$ where $(x_i-\...
Adrian's user avatar
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Quadratic regressions with explanatory count variables

I am running an OLS model where my dependent variable Y is continous and among the explanatory vars I have a count variable X. I want to test if the effect of X on Y changes sing. To do so I would ...
Caserio's user avatar
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Gam with low E.D.F (estimated degrees of freedom) value in main effect, not interaction term

I have a gam model with the following structure: ...
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JuliaOpt Empirical Likelihood Estimation

I am trying to perform an empirical likelihood estimation in a regression setting using JuliaOpt (Convex or JuMP) and ran into difficulties using either API. The problem: Empirical likelihood for ...
Vincent's user avatar
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6 votes
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Understanding Big/Little $O_p$/$o_p$ Notation for Estimators

I am reading a Text about Single Index Models (SIM), where a SIM is defined as $E[Y|X=x] = G(X' \beta)$, with $G$ and $\beta$ unknown. After proposing an estimator for the function $G$, the ...
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Density Function Estimation

Given a sample of $n$ observations, which are assumed to be $i.i.d.$ and generated from a continuous probability law. Consider the question of estimating the density function $f(x)$. There are two ...
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3 votes
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Testing semi-parametric versus parametric model

I am estimating a (semi)parametric and a parametric model for a panel data set, and I want to test the functional form by applying the method proposed by Henderson et al. (2008, p.266–267). In ...
Bob's user avatar
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Generalized additive models -- who does research on them besides Simon Wood?

I use GAMs more and more. When I go to provide references for their various components (smoothing parameter selection, various spline bases, p-values of smooth terms), they are all from one ...
user59828's user avatar
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5 votes
3 answers
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Book for introductory nonparametric econometrics/statistics

My work implies a lot of econometrics, and I had a good formation about it. Nevertheless, I am regularly faced with some semi or non parametric techniques (for instance I had to use quantile ...
Anthony Martin's user avatar
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Implementation of semi parametric methods

Has anyone worked with semi parametric methods to estimate parameters with binary outcome? Examples are like Cosslett (1983) or Ichimura or Klein-Spady. In other words we are looking for semi ...
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941 views

Variance of plugin estimator

This question related to my previous question. Let $$X_1,\dots,X_n$$ are i.i.d. with distribution function $F$ and $$Y_1,\dots,Y_n$$ are i.i.d. with distribution function $G$. Suppose that there ...
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Do robust standard errors protect you from proportional odds assumptions?

Cox Proportional Hazards models are traditionally taught alongside proportional hazards assumptions. There is a corresponding test of proportionality. However, if standard errors are calculated from ...
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26 votes
5 answers
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When is quantile regression worse than OLS?

Apart from some unique circumstances where we absolutely must understand the conditional mean relationship, what are the situations where a researcher should pick OLS over Quantile Regression? I don'...
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