NONPARAMETRIC ESTIMATION WITH AGGREGATED DATA

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

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Statistically Efficient Construction of α-Risk-Minimizing Portfolio

Advances in Decision Sciences ◽

10.1155/2012/980294 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Hiroyuki Taniai ◽

Takayuki Shiohama

Keyword(s):

Monte Carlo ◽

Quantile Regression ◽

Asymptotic Normality ◽

Asymptotic Properties ◽

Regression Method ◽

General Reference ◽

Regression Problem ◽

Efficient Construction ◽

Consistency And Asymptotic Normality ◽

Quantile Regression Method

We propose a semiparametrically efficient estimator for α-risk-minimizing portfolio weights. Based on the work of Bassett et al. (2004), an α-risk-minimizing portfolio optimization is formulated as a linear quantile regression problem. The quantile regression method uses a pseudolikelihood based on an asymmetric Laplace reference density, and asymptotic properties such as consistency and asymptotic normality are obtained. We apply the results of Hallin et al. (2008) to the problem of constructing α-risk-minimizing portfolios using residual signs and ranks and a general reference density. Monte Carlo simulations assess the performance of the proposed method. Empirical applications are also investigated.

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Nonparametric estimation of boundary measures and related functionals: asymptotic results

Advances in Applied Probability ◽

10.1239/aap/1246886612 ◽

2009 ◽

Vol 41 (2) ◽

pp. 311-322 ◽

Cited By ~ 6

Author(s):

Inés Armendáriz ◽

Antonio Cuevas ◽

Ricardo Fraiman

Keyword(s):

Asymptotic Normality ◽

Surface Area ◽

Nonparametric Estimation ◽

Strong Consistency ◽

Nonparametric Method ◽

Asymptotic Results ◽

Minkowski Content ◽

Compact Body ◽

Consistency And Asymptotic Normality ◽

The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝd (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

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On the estimation of the Bernoulli regression function using Bernstein polynomials for group observations

Georgian Mathematical Journal ◽

10.1515/gmj-2021-2132 ◽

2022 ◽

Vol 0 (0) ◽

Author(s):

Petre Babilua

Keyword(s):

Asymptotic Normality ◽

Bernstein Polynomial ◽

Bernstein Polynomials ◽

Regression Function ◽

Testing Hypothesis ◽

Consistency And Asymptotic Normality

Abstract The estimate for the Bernoulli regression function is constructed using the Bernstein polynomial for group observations. The question of its consistency and asymptotic normality is studied. A testing hypothesis is constructed on the form of the Bernoulli regression function. The consistency of the constructed tests is investigated.

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Estimating Parameters of the Autocorrelated Current Effects Model from Temporally Aggregated Data

Journal of Marketing Research ◽

10.1177/002224378602300408 ◽

1986 ◽

Vol 23 (4) ◽

pp. 379-386 ◽

Cited By ~ 3

Author(s):

Vinay Kanetkar ◽

Charles B. Weinberg ◽

Doyle L. Weiss

Keyword(s):

Monte Carlo ◽

Simple Procedure ◽

Monte Carlo Experiment ◽

Good Recovery ◽

Autocorrelation Coefficient ◽

Aggregated Data ◽

First Order ◽

Level Of Aggregation

The authors briefly review the literature associated with the autocorrelated current effects model and present a simple procedure that recovers its parameters from time-aggregated data when the level of aggregation is known. The procedure is based partly on the estimation of a first-order autocorrelation coefficient. The procedure is illustrated and its properties are compared with those of a GLS procedure by means of a Monte Carlo experiment. In many of the tested cases, there is good recovery of the microparameters with aggregated data.

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Nonparametric estimation of boundary measures and related functionals: asymptotic results

Advances in Applied Probability ◽

10.1017/s000186780000330x ◽

2009 ◽

Vol 41 (02) ◽

pp. 311-322 ◽

Cited By ~ 1

Author(s):

Inés Armendáriz ◽

Antonio Cuevas ◽

Ricardo Fraiman

Keyword(s):

Asymptotic Normality ◽

Surface Area ◽

Nonparametric Estimation ◽

Strong Consistency ◽

Nonparametric Method ◽

Asymptotic Results ◽

Minkowski Content ◽

Compact Body ◽

Consistency And Asymptotic Normality ◽

The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝ d (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

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Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality

Econometric Theory ◽

10.1017/s0266466600009166 ◽

1995 ◽

Vol 11 (2) ◽

pp. 258-289 ◽

Cited By ~ 167

Author(s):

Elias Masry ◽

Dag Tjøstheim

Keyword(s):

Time Series ◽

Asymptotic Normality ◽

Strong Convergence ◽

Nonparametric Estimation ◽

Strong Consistency ◽

Rates Of Convergence ◽

Regularity Conditions ◽

Nonlinear Functions ◽

Kernel Estimates ◽

Nonparametric Kernel

We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.

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