SMOOTH VARYING-COEFFICIENT ESTIMATION AND INFERENCE FOR QUALITATIVE AND QUANTITATIVE DATA

2010 ◽  
Vol 26 (6) ◽  
pp. 1607-1637 ◽  
Author(s):  
Qi Li ◽  
Jeffrey S. Racine
Keyword(s):  
Bandwidth Selection ◽  
Rates Of Convergence ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Qualitative And Quantitative ◽  
Varying Coefficient ◽  
Coefficient Estimation ◽  
Wide Range ◽  
Potential Applications ◽  
Frequency Estimator

We propose a semiparametric varying-coefficient estimator that admits both qualitative and quantitative covariates along with a test for correct specification of parametric varying-coefficient models. The proposed estimator is exceedingly flexible and has a wide range of potential applications including hierarchical (mixed) settings, small area estimation, etc. A data-driven cross-validatory bandwidth selection method is proposed that can handle both the qualitative and quantitative covariates and that can also handle the presence of potentially irrelevant covariates, each of which can result in finite-sample efficiency gains relative to the conventional frequency (sample-splitting) estimator that is often found in such settings. Theoretical underpinnings including rates of convergence and asymptotic normality are provided. Monte Carlo simulations are undertaken to assess the proposed estimator’s finite-sample performance relative to the conventional semiparametric frequency estimator and to assess the finite-sample performance of the proposed test for correct parametric specification.

Imputed Estimation For Varying Coefficient Models with Missing Covariates

2013 ◽  
Vol 787 ◽  
pp. 1089-1092
Author(s):  
Pei Xin Zhao
Keyword(s):  
Missing Data ◽  
Estimation Procedure ◽  
Estimating Equation ◽  
Equation Method ◽  
Missing Covariates ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Varying Coefficient

By using the imputation-based estimating equation method, an imputed estimation procedure for the coefficient functions is proposed. The proposed procedure can attenuate the effect of the missing data, and performs well for the finite sample.

scholarly journals Smooth varying-coefficient models in Stata

2020 ◽  
Vol 20 (3) ◽  
pp. 647-679
Author(s):  
Fernando Rios-Avila
Keyword(s):  
Computational Cost ◽  
Bandwidth Selection ◽  
Varying Coefficient Models ◽  
Varying Coefficient ◽  
Regression Methods ◽  
Nonparametric Models ◽  
Functional Forms ◽  
Potential Benefits ◽  
Standard Models ◽  
High Computational Cost

Nonparametric regressions are powerful statistical tools that can be used to model relationships between dependent and independent variables with minimal assumptions on the underlying functional forms. Despite their potential benefits, these models have two weaknesses: The added flexibility creates a curse of dimensionality, and procedures available for model selection, like crossvalidation, have a high computational cost in samples with even moderate sizes. An alternative to fully nonparametric models is semiparametric models that combine the flexibility of nonparametric regressions with the structure of standard models. In this article, I describe the estimation of a particular type of semiparametric model known as the smooth varying-coefficient model (Hastie and Tibshirani, 1993, Journal of the Royal Statistical Society, Series B 55: 757–796), based on kernel regression methods, using a new set of commands within vc_pack. These commands aim to facilitate bandwidth selection and model estimation as well as create visualizations of the results.

scholarly journals Robust estimation and inference for general varying coefficient models with missing observations

Test ◽  
2019 ◽  
Vol 29 (4) ◽  
pp. 966-988
Author(s):  
Francesco Bravo
Keyword(s):  
Nonlinear Least Squares ◽  
Missing At Random ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Varying Coefficient ◽  
Finite Sample Properties ◽  
Local Linear Estimation ◽  
Nonlinear Least Squares Estimation

AbstractThis paper considers estimation and inference for a class of varying coefficient models in which some of the responses and some of the covariates are missing at random and outliers are present. The paper proposes two general estimators—and a computationally attractive and asymptotically equivalent one-step version of them—that combine inverse probability weighting and robust local linear estimation. The paper also considers inference for the unknown infinite-dimensional parameter and proposes two Wald statistics that are shown to have power under a sequence of local Pitman drifts and are consistent as the drifts diverge. The results of the paper are illustrated with three examples: robust local generalized estimating equations, robust local quasi-likelihood and robust local nonlinear least squares estimation. A simulation study shows that the proposed estimators and test statistics have competitive finite sample properties, whereas two empirical examples illustrate the applicability of the proposed estimation and testing methods.

Double-smoothing in Kernel Hazard Rate Estimation

2008 ◽  
Vol 47 (02) ◽  
pp. 167-173 ◽  
Author(s):  
A. Pfahlberg ◽  
O. Gefeller ◽  
R. Weißbach
Keyword(s):  
Hazard Rate ◽  
Nearest Neighbor ◽  
Bandwidth Selection ◽  
Study Data ◽  
Computational Effort ◽  
Finite Sample ◽  
Adaptive Smoothing ◽  
Rate Estimation ◽  
Data Adaptive ◽  
Double Smoothing

Summary Objectives: In oncological studies, the hazard rate can be used to differentiate subgroups of the study population according to their patterns of survival risk over time. Nonparametric curve estimation has been suggested as an exploratory means of revealing such patterns. The decision about the type of smoothing parameter is critical for performance in practice. In this paper, we study data-adaptive smoothing. Methods: A decade ago, the nearest-neighbor bandwidth was introduced for censored data in survival analysis. It is specified by one parameter, namely the number of nearest neighbors. Bandwidth selection in this setting has rarely been investigated, although the heuristical advantages over the frequently-studied fixed bandwidth are quite obvious. The asymptotical relationship between the fixed and the nearest-neighbor bandwidth can be used to generate novel approaches. Results: We develop a new selection algorithm termed double-smoothing for the nearest-neighbor bandwidth in hazard rate estimation. Our approach uses a finite sample approximation of the asymptotical relationship between the fixed and nearest-neighbor bandwidth. By so doing, we identify the nearest-neighbor bandwidth as an additional smoothing step and achieve further data-adaption after fixed bandwidth smoothing. We illustrate the application of the new algorithm in a clinical study and compare the outcome to the traditional fixed bandwidth result, thus demonstrating the practical performance of the technique. Conclusion: The double-smoothing approach enlarges the methodological repertoire for selecting smoothing parameters in nonparametric hazard rate estimation. The slight increase in computational effort is rewarded with a substantial amount of estimation stability, thus demonstrating the benefit of the technique for biostatistical applications.

scholarly journals A Slot-Die Technique for the Preparation of Continuous, High-Area, Chitosan-Based Thin Films

Polymers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1566
Author(s):  
Oliver J. Pemble ◽  
Maria Bardosova ◽  
Ian M. Povey ◽  
Martyn E. Pemble
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
High Volume ◽  
Mechanical Anisotropy ◽  
Diverse Range ◽  
Direction Parallel ◽  
High Area ◽  
Wide Range ◽  
Slot Die ◽  
Potential Applications

Chitosan-based films have a diverse range of potential applications but are currently limited in terms of commercial use due to a lack of methods specifically designed to produce thin films in high volumes. To address this limitation directly, hydrogels prepared from chitosan, chitosan-tetraethoxy silane, also known as tetraethyl orthosilicate (TEOS) and chitosan-glutaraldehyde have been used to prepare continuous thin films using a slot-die technique which is described in detail. By way of preliminary analysis of the resulting films for comparison purposes with films made by other methods, the mechanical strength of the films produced was assessed. It was found that as expected, the hybrid films made with TEOS and glutaraldehyde both show a higher yield strength than the films made with chitosan alone. In all cases, the mechanical properties of the films were found to compare very favorably with similar measurements reported in the literature. In order to assess the possible influence of the direction in which the hydrogel passes through the slot-die on the mechanical properties of the films, testing was performed on plain chitosan samples cut in a direction parallel to the direction of travel and perpendicular to this direction. It was found that there was no evidence of any mechanical anisotropy induced by the slot die process. The examples presented here serve to illustrate how the slot-die approach may be used to create high-volume, high-area chitosan-based films cheaply and rapidly. It is suggested that an approach of the type described here may facilitate the use of chitosan-based films for a wide range of important applications.

scholarly journals Health Benefits of Uses and Applications of Moringa oleifera in Bakery Products

Plants ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 318
Author(s):  
Paula García Milla ◽  
Rocío Peñalver ◽  
Gema Nieto
Keyword(s):  
Moringa Oleifera ◽  
Essential Amino Acids ◽  
Bakery Products ◽  
Unani Medicine ◽  
Functional Value ◽  
Organoleptic Characteristics ◽  
Wide Range ◽  
Potential Applications ◽  
Medicinal Properties ◽  
Excellent Source

Moringa oleifera belongs to the Moringaceae family and is the best known of the native Moringa oleifera genus. For centuries, it has been used as a system of Ayurvedic and Unani medicine and has a wide range of nutritional and bioactive compounds, including proteins, essential amino acids, carbohydrates, lipids, fibre, vitamins, minerals, phenolic compounds, phytosterols and others. These characteristics allow it to have pharmacological properties, including anti-diabetic, anti-inflammatory, anticarcinogenic, antioxidant, cardioprotective, antimicrobial and hepatoprotective properties. The entire Moringa oleifera plant is edible, including its flowers, however, it is not entirely safe, because of compounds that have been found mainly in the root and bark, so the leaf was identified as the safest. Moringa oleifera is recognised as an excellent source of phytochemicals, with potential applications in functional and medicinal food preparations due to its nutritional and medicinal properties; many authors have experimented with incorporating it mainly in biscuits, cakes, brownies, meats, juices and sandwiches. The results are fascinating, as the products increase their nutritional value; however, the concentrations cannot be high, as this affects the organoleptic characteristics of the supplemented products. The aim of this study is to review the application of Moringa oleifera in bakery products, which will allow the creation of new products that improve their nutritional and functional value.

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