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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Panel regression with an added smooth function

I would like to estimate the following regression model $$\log p_{it} = x_{it}^\top\beta + \mu_{m(i,t),t} + \epsilon_{it}$$ where the dependent variable is log housing prices and $x_{it}$ are housing ...
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Local Data Generating Process in Semiparametric Statistics

I am a bit confused about the LDGP assumption that is mentioned in books on semiparametric statistics. For example, in Semiparametric Theory and Missing Data by Tsiatis, the LDGP is defined as follows:...
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47 views

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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28 views

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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INLA in R for fitting parametric and semiparametric (Cox-like) survival models with frailties

I am exploring different methods of fitting survival models in R. One method of interest utilizes INLA for fitting Cox-type semi-parametric survival models. I would like to compare fits from INLA to ...
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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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92 views

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 ...
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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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375 views

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 ...
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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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505 views

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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445 views

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?
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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 $$ y = \alpha + \displaystyle\sum_k f_k(x_k) + \epsilon $$ ...
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132 views

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-\...
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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 ...
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4k views

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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259 views

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 ...
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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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96 views

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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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.267). In particular, ...
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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 ...
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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 ...
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102 views

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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828 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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551 views

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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11k views

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'...