Conditional Mode Estimation Research Articles

Some asymptotic results of a kNN conditional mode estimator for functional stationary ergodic data

. This article investigates the conditional mode estimation of a univariate response variable given a functional random covariate (i.e., valued in some infinite-dimensional space) whenever a stationary ergodic data are considered. We construct a new estimator of the conditional mode which is constructed by a kNN approach. Under less restrictive conditions, we show the strong consistency of the proposed estimator. To assess the efficiency of the developed estimator, empirical analysis as well as real data analyses are performed.

On non parametric kernel estimation of the mode of the regression function in the strong mixing random design model with censored data

. This study delves into the conditional mode estimation of a randomly censored scalar response variable operating within the framework of strong mixing conditions. We introduce a kernel-based estimator for the conditional mode function. The principal contribution of this investigation lies in the derivation of the asymptotic distribution and the strong rate of convergence of the newly proposed estimators. These findings are established under a set of fairly comprehensive structural assumptions governing the underlying models. Additionally, we conduct a series of simulation studies to showcase the finite sample performance characteristics of the proposed estimator.

Kernel conditional density and mode estimation for psi-weakly dependent observations

In practical problems connected with forecasting, it sometimes happens that the classical regression estimation is not informative enough to make good predictions of a response variable. This occurs typically when multi-modality, asymmetry, or heteroscedastic noise characterizes the underlying distribution function. In this situation, conditional mode estimation may constitute an alternative method to prediction, because conditional density is more adequate to describe the association between an explanatory data vector and a target variable. In this paper we derive rates of convergence for kernel conditional density and mode functions estimators under psi-weak dependence condition. The asymptotic distribution of the mode function estimator is established and the accuracy of the proposed estimators is illustrated via a simulation study.

On the local linear modelization of the conditional density for functional and ergodic data

In this paper, we estimate the conditional density function using the local linear approach. We treat the case when the regressor is valued in a semi-metric space, the response is a scalar and the data are observed as ergodic functional times series. Under this dependence structure, we state the almost complete consistency (a.co.) with rates of the constructed estimator. Moreover, the usefulness of our results is illustrated through their application to the conditional mode estimation.

Asymptotic normality of conditional mode estimation for functional dependent data

Based on the local polynomial smoother idea, we construct a local linear estimator of the conditional mode for dependent functional covariables. Precisely, observations are assumed to be a sequence of stationary α-mixing random variables. Then, we establish the asymptotic normality of the constructed estimator.

Quantile regression approach to conditional mode estimation

In this paper, we consider estimation of the conditional mode of an outcome variable given regressors. To this end, we propose and analyze a computationally scalable estimator derived from a linear quantile regression model and develop asymptotic distributional theory for the estimator. Specifically, we find that the pointwise limiting distribution is a scale transformation of Chernoff’s distribution despite the presence of regressors. In addition, we consider analytical and subsampling-based confidence intervals for the proposed estimator. We also conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimator together with the analytical and subsampling confidence intervals. Finally, we apply the proposed estimator to predicting the net hourly electrical energy output using Combined Cycle Power Plant Data.

Berry–Esseen type bound of conditional mode estimation under truncation and strong mixing assumptions

ABSTRACTIn order to investigate the convergence rate of the asymptotic normality for the estimator of the conditional mode function for the left-truncation model, we derive a Berry–Esseen type bound of the estimator when the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The finite sample performance of the estimator of the conditional mode function is explored through simulations.

Estimation of conditional mode with truncated, censored, and dependent data

ABSTRACTIn this paper, we studied the uniform convergence with rates for the kernel estimator of the conditional mode function for a left truncated and right censored model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. Also, the asymptotic normality of the estimator is established.

Strong consistency result of a non parametric conditional mode estimator under random censorship for functional regressors

Let (T, C, X) be a vector of random variables (rvs) where T, C, and X are the interest variable, a right censoring rv, and a covariate, respectively. In this paper, we study the kernel conditional mode estimation when the covariate takes values in an infinite dimensional space and is α-mixing. Under some regularity conditions, the almost complete convergence of the estimate with rates is established.

Conditional mode estimation for functional stationary ergodic data with responses missing at random

In this paper, we investigate the asymptotic properties of a non-parametric conditional mode estimation given a functional explanatory variable, when functional stationary ergodic data and missing at random responses are observed. First of all, we establish asymptotic properties for a conditional density estimator from which we derive almost sure convergence (with rate) and asymptotic normality of a conditional mode estimator. This new estimate take into account missing data, and a simulation study is performed to illustrate how this fact allows to get higher predictive performances than those obtained with standard estimates.

Spatial modelization: Local linear estimation of the conditional distribution for functional data

The main purpose of this paper is to estimate nonparametrically some characteristics of spatial models related to the conditional cumulative distribution of a scalar response given functional random variables by the local linear approach. Specifically, the local linear estimators of the conditional cumulative distribution function and of the successive derivatives of the conditional density are constructed. Then, the asymptotic properties of these estimators, in terms of the almost-complete convergence with rates, are stated. Moreover, the usefulness of our results is illustrated through their application (a) to the spatial conditional mode estimation and (b) to the soil chemistry properties data.

On the iterated forms of Kalman filters using statistical linearization

The extended Kalman filter (EKF) is a suboptimal estimator of the conditional mean and covariance for nonlinear state estimation. It is based on first order Taylor series approximation of nonlinear state functions. The unscented Kalman filter (UKF) and the ensemble Kalman filter (EnKF) are suboptimal estimators that are termed as Jacobian free because they do not require the existence of the Jacobian of the nonlinearity. The iterated form of EKF is an estimator of the conditional mode that employs an approximate Newton–Raphson iterative scheme to solve the maximization of the conditional probability density function. In this paper, the iterated forms of UKF and EnKF are presented that perform Newton–Raphson iteration without explicitly differentiating the nonlinear functions. The use of statistical linearization in iterated UKF and EnKF is a nondifferentiable optimization method when the measurement function is nonsmooth or discontinuous. All three iterated forms can be shown to be conditional mean estimators after the first iteration. A simple numerical example involving continuous and discontinuous measurment functions is included to evaluate the performance of the algorithms for the estimation of conditional mean, covariance and mode. A batch reactor simulation is shown for estimating both the states and unknown parameters.

On Semiparametric Mode Regression Estimation

It has been found that, for a variety of probability distributions, there is a surprising linear relation between mode, mean, and median. In this article, the relation between mode, mean, and median regression functions is assumed to follow a simple parametric model. We propose a semiparametric conditional mode (mode regression) estimation for an unknown (unimodal) conditional distribution function in the context of regression model, so that any m-step-ahead mean and median forecasts can then be substituted into the resultant model to deliver m-step-ahead mode prediction. In the semiparametric model, Least Squared Estimator (LSEs) for the model parameters and the simultaneous estimation of the unknown mean and median regression functions by the local linear kernel method are combined to infer about the parametric and nonparametric components of the proposed model. The asymptotic normality of these estimators is derived, and the asymptotic distribution of the parameter estimates is also given and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model. These results are applied to obtain a data-based test for the dependence of mode regression over mean and median regression under a regression model.

Asymptotic normality for estimator of conditional mode under left-truncated and dependent observations

In this paper, we establish asymptotic normality of a new kernel estimator of the conditional mode function introduced by Ould-Said and Tatachak (C R Acad Sci Paris Ser I 344:651–656, 2007) for the left-truncation model when the data exhibit some kind of dependence. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence.

Dynamic Factor Analysis with Non-Linear Temporal Aggregation Constraints

Summary The paper estimates an index of coincident economic indicators for the US economy by using time series with different frequencies of observation (monthly and quarterly, possibly with missing values). The model that is considered is the dynamic factor model that was proposed by Stock and Watson, specified in the logarithms of the original variables and at the monthly frequency, which poses a problem of temporal aggregation with a non-linear observational constraint when quarterly time series are included. Our main methodological contribution is to provide an exact solution to this problem that hinges on conditional mode estimation by iteration of the extended Kalman filtering and smoothing equations. On the empirical side the contribution of the paper is to provide monthly estimates of quarterly indicators, among which is the gross domestic product, that are consistent with the quarterly totals. Two applications are considered: the first dealing with the construction of a coincident index for the US economy, whereas the second does the same with reference to the euro area.

Functional time series prediction via conditional mode estimation

This Note focuses on an estimator of the conditional mode of a scalar response Y given a functional random variable X. We start by building a kernel estimator of the conditional density of Y given X; the conditional mode is defined as the value which maximizes this conditional density. We establish the almost complete convergence for this estimate under α-mixing assumption. To cite this article: F. Ferraty et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).