Nonparametric Kernel Regression Research Articles

Joint modeling of longitudinal and survival data with the Cox model and two-phase sampling.

A common objective of cohort studies and clinical trials is to assess time-varying longitudinal continuous biomarkers as correlates of the instantaneous hazard of a study endpoint. We consider the setting where the biomarkers are measured in a designed sub-sample (i.e., case-cohort or two-phase sampling design), as is normative for prevention trials. We address this problem via joint models, with underlying biomarker trajectories characterized by a random effects model and their relationship with instantaneous risk characterized by a Cox model. For estimation and inference we extend the conditional score method of Tsiatis and Davidian (Biometrika 88(2):447-458, 2001) to accommodate the two-phase biomarker sampling design using augmented inverse probability weighting with nonparametric kernel regression. We present theoretical properties of the proposed estimators and finite-sample properties derived through simulations, and illustrate the methods with application to the AIDS Clinical Trials Group 175 antiretroviral therapy trial. We discuss how the methods are useful for evaluating a Prentice surrogate endpoint, mediation, and for generating hypotheses about biological mechanisms of treatment efficacy.

Burned area prediction with semiparametric models

Wildfires are one of the main causes of forest destruction, especially in Galicia (north-west Spain), where the area burned by forest fires in spring and summer is quite high. This work uses two semiparametric time-series models to describe and predict the weekly burned area in a year: autoregressive moving average (ARMA) modelling after smoothing, and smoothing after ARMA modelling. These models can be described as a sum of a parametric component modelled by an autoregressive moving average process and a non-parametric one. To estimate the non-parametric component, local linear and kernel regression, B-splines and P-splines were considered. The methodology and software were applied to a real dataset of burned area in Galicia for the period 1999–2008. The burned area in Galicia increases strongly during summer periods. Forest managers are interested in predicting the burned area to manage resources more efficiently. The two semiparametric models are analysed and compared with a purely parametric model. In terms of error, the most successful results are provided by the first semiparametric time-series model.

FUSED KERNEL-SPLINE SMOOTHING FOR REPEATEDLY MEASURED OUTCOMES IN A GENERALIZED PARTIALLY LINEAR MODEL WITH FUNCTIONAL SINGLE INDEX.

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. The covariance structure is taken into account via a working model, which provides valid estimation and inference procedure whether or not it captures the true covariance. The estimation method is applicable to both continuous and discrete outcomes. We derive large sample properties of the estimation procedure and show different convergence rate of each component of the model. The asymptotic properties when the kernel and regression spline methods are combined in a nested fashion has not been studied prior to this work even in the independent data case.

A nonparametric kernel regression approach for pricing options on stock market index

ABSTRACTPrevious options studies typically assume that the dynamics of the underlying asset price follow a geometric Brownian motion (GBM) when pricing options on stocks, stock indices, currencies or futures. However, there is mounting empirical evidence that the volatility of asset price or return is far from constant. This article, in contrast to studies that use parametric approach for option pricing, employs nonparametric kernel regression to deal with changing volatility and, accordingly, prices options on stock index. Specifically, we first estimate nonparametrically the volatility of asset return in the GBM based on the Nadaraya–Watson (N–W) kernel estimator. Then, based on the N–W estimates for the volatility, we use Monte Carlo simulation to compute option prices under different settings. Finally, we compare the index option prices under our nonparametric model with those under the Black–Scholes model and the Stein–Stein model.

Forecasting Equity Premium: Global Historical Average Versus Local Historical Average and Constraints

The equity premium, return on equity minus return on risk-free asset, is expected to be positive. We consider imposing such positivity constraint in local historical average (LHA) in nonparametric kernel regression framework. It is also extended to the semiparametric single index model when multiple predictors are used. We construct the constrained LHA estimator via an indicator function which operates as “model-selection” between the unconstrained LHA and the bound of the constraint (zero for the positivity constraint). We smooth the indicator function by bagging, which operates as “model-averaging” and yields a combined forecast of unconstrained LHA forecasts and the bound of the constraint. The local combining weights are determined by the probability that the constraint is binding. Asymptotic properties of the constrained LHA estimators without and with bagging are established, which show how the positive constraint and bagging can help reduce the asymptotic variance and mean squared errors. Monte Carlo simulations are conducted to show the finite sample behavior of the asymptotic properties. In predicting U.S. equity premium, we show that substantial nonlinearity can be captured by LHA and that the local positivity constraint can improve out-of-sample prediction of the equity premium.

Economic effects of the biochar application on rice supply in Taiwan

The objective of the study is to analyze the economics of the bio-energy production for Taiwan in terms of the bio-energy production, social welfare and crop yield increase under the conventional bio-power, ethanol and pyrolysis. The effects on rice production patterns are also examined for the fast and slow pyrolysis plus the biochar application. In addition to adopting the mathematical programming model (Modified Taiwan Agricultural Sector Model) in the analysis of the bio-energy production and the crop cultivation patterns, the study further employs a nonparametric kernel regression model to forecast the increased benefits of rice from using biochar under various scenarios. With the biochar application, Taiwan’s rice production could increase ranging from 6308 to 38 118 tons annually, depending on the pyrolysis type and the plant location. The results indicate that the biochar utilization can potentially increase social benefits if rice is planted. The net increase of farmer›s and the environmental revenues can achieve up to NT$ 419 400. Moreover, we find that farmers should give priority to the improvement of nutrient saving to make higher benefits. Second, the total benefits could be improved if the seed use is efficient and harvesting and transporting costs for the energy crop and processing and the hauling cost of biochar are lower. Simulation results indicate that Taiwan benefits from the bio-energy production in terms of energy security, farmers revenue, social welfare and rice supply. The results show that, in general, pyrolysis plus the biochar application not only increase the domestic renewable energy supply but also enhance the farmers’ and environmental revenues significantly.

Herding in Chinese Stock Markets: A Non-Parametric Approach

The paper reports new evidence of herding in the Chinese A-type and B-Type markets by employing non-parametric kernel regression. We find statistically significant evidence of herding in A-type market under both extreme high and low market returns. Herding in B-type market, which predominantly consists of foreign investors, indicate only week evidence of herding. We do not find any statistically significant evidence of herding in the pre-2001 sample of B-type market, when only foreign investors could do the trading. Lack of knowledge and experience of local investors may be attributed to the presence of herd behaviour in the Chinese markets.

Variance estimation in ranked set sampling using a concomitant variable

We propose a nonparametric variance estimator when ranked set sampling (RSS) and judgment post stratification (JPS) are applied by measuring a concomitant variable. Our proposed estimator is obtained by conditioning on observed concomitant values and using nonparametric kernel regression.

ESG Impact on Market Performance of Firms: International Evidence

This study investigates how news-based scores in ESG (Environmental, Social, and corporate Governance) may have influenced the monthly stocks’ market return in Switzerland, the US, and the UK during the 2007–2011 period. We find that the variation of the overall ESG score is only significant in the UK. We also show that the changes in sub-category ratings of GRI (namely, governance, economic, environment, labor, human rights, society, and products) exhibit a small but significant impact on the stock’s performance during limited periods or on limited sectors, which varies among the countries. Finally, our non-parametric kernel regression highlights that the function linking a stock’s performance to its ESG-score changes is probably non-linear.

The effects of multilateral trading systems on risk and return in equity markets

The event study methodology of Brown and Warner (1985) is adopted and augmented to evaluate the effect of the launch of multilateral trading systems on risk and return in equity markets. The methodology is supplemented with various techniques, such as the nonparametric ranking test and kernel regression, to find out if announcements about the introduction of Chi-X Australia generated abnormal returns (ARs). Asset pricing models are fitted with interaction variables, while GARCH, threshold ARCH (TARCH), exponential GARCH (EGARCH) and power-ARCH (PARCH) are used to determine changes in systematic risk. We find evidence in favour of Fisher’s separation theorem and detect a new market anomaly, which we call the ‘Fisher market anomaly’. Our results show that Chi-X system testings affect ARs. Consistent with the adaptive expectations theory, we confirm that the first announcement about the launch of Chi-X affected systematic risk the most. In addition, we identify industry and firm effects in risk analysis.

Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

This paper discusses nonparametric kernel regression with the regressor being a \(d\)-dimensional \(\beta\)-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate \(\sqrt{n(T)h^{d}}\), where \(n(T)\) is the number of regenerations for a \(\beta\)-null recurrent process and the limiting distribution (with proper normalization) is normal. Furthermore, we show that the two-step estimator for the volatility function is consistent. The finite sample performance of the estimate is quite reasonable when the leave-one-out cross validation method is used for bandwidth selection. We apply the proposed method to study the relationship of Federal funds rate with 3-month and 5-year T-bill rates and discover the existence of nonlinearity of the relationship. Furthermore, the in-sample and out-of-sample performance of the nonparametric model is far better than the linear model.

Real time air quality forecasting using integrated parametric and non-parametric regression techniques

This paper presents a model for producing real time air quality forecasts with both high accuracy and high computational efficiency. Temporal variations in nitrogen dioxide (NO2) levels and historical correlations between meteorology and NO2 levels are used to estimate air quality 48 h in advance. Non-parametric kernel regression is used to produce linearized factors describing variations in concentrations with wind speed and direction and, furthermore, to produce seasonal and diurnal factors. The basis for the model is a multiple linear regression which uses these factors together with meteorological parameters and persistence as predictors. The model was calibrated at three urban sites and one rural site and the final fitted model achieved R values of between 0.62 and 0.79 for hourly forecasts and between 0.67 and 0.84 for daily maximum forecasts. Model validation using four model evaluation parameters, an index of agreement (IA), the correlation coefficient (R), the fraction of values within a factor of 2 (FAC2) and the fractional bias (FB), yielded good results. The IA for 24 hr forecasts of hourly NO2 was between 0.77 and 0.90 at urban sites and 0.74 at the rural site, while for daily maximum forecasts it was between 0.89 and 0.94 for urban sites and 0.78 for the rural site. R values of up to 0.79 and 0.81 and FAC2 values of 0.84 and 0.96 were observed for hourly and daily maximum predictions, respectively. The model requires only simple input data and very low computational resources. It found to be an accurate and efficient means of producing real time air quality forecasts.

Fast pixel-based optical proximity correction based on nonparametric kernel regression

Optical proximity correction (OPC) is a resolution enhancement technique extensively used in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the layout is divided into small pixels, which are then iteratively modified until the simulated print image on the wafer matches the desired pattern. However, the increasing complexity and size of modern integrated circuits make PBOPC techniques quite computationally intensive. This paper focuses on developing a practical and efficient PBOPC algorithm based on a nonparametric kernel regression, a well-known technique in machine learning. Specifically, we estimate the OPC patterns based on the geometric characteristics of the original layout corresponding to the same region and a series of training examples. Experimental results on metal layers show that our proposed approach significantly improves the speed of a current professional PBOPC software by a factor of 2 to 3, and may further reduce the mask complexity.

UNIFORM CONSISTENCY FOR NONPARAMETRIC ESTIMATORS IN NULL RECURRENT TIME SERIES

This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our results can be viewed as a nonstationary extension of some well-known uniform consistency results for stationary time series.

Financial Health and the Intensive Margin of Trade

Although the existing literature agrees upon the effects of financial health on the extensive margin of trade, the empirical results based on the intensive margin of trade are mixed. This paper shows that such mixed results in the literature may be due to using parametric regressions that have restrictive assumptions on the functional form of the relationship between financial health and exports; this is an important restriction suppressing the role of firm characteristics on the relationship between finance and trade. Accordingly, we consider possible nonlinearities in that relationship by employing nonparametric kernel regression methods by using data on 2380 firms from nine emerging countries. The results, which are robust to the consideration of the nationality of firms and country-industry-time fixed effects, provide evidence for a nonlinear relationship by suggesting that the role of financial health on the intensive margin of trade depends on firm characteristics such as productivity and size.

Intraday liquidity patterns in limit order books

Purpose – Algorithmic trading attempts to reduce trading costs by selecting optimal trade execution and scheduling algorithms. Whilst many common approaches only consider the bid-ask spread when measuring market impact, the authors aim to analyse the detailed limit order book data, which has more informational content. Design/methodology/approach – Using data from the London Stock Exchange's electronic SETS platform, the authors transform limit order book compositions into volume-weighted average price curves and accordingly estimate market impact. The regression coefficients of these curves are estimated, and their intraday patterns are revealed using a nonparametric kernel regression model. Findings – The authors find that market impact is nonlinear, time-varying, and asymmetric. Inferences drawn from marginal probabilities regarding Granger-causality do not show a significant impact of slope coefficients on the opposite side of the limit order book, thus implying that each side of the market is simultaneously rather than sequentially influenced by prevailing market conditions. Research limitations/implications – Results show that intraday seasonality patterns of liquidity may be exploited through trade scheduling algorithms in an attempt to minimise the trading costs associated with large institutional trades. Originality/value – The use of the detailed limit order book to reveal intraday patterns in liquidity provision offers better insight into the interactions of market participants. Such valuable information cannot be fully recovered from the traditional transaction data-based approaches.

Performance evaluation of an acoustic indoor localization system based on a fingerprinting technique

We present an acoustic location system that adopts the time of arrival of the path of maximum amplitude as a signature and estimates the target position through nonparametric kernel regression. The system was evaluated in experiments for two main configurations: a privacy-oriented configuration with code division multiple access operation and a centralized configuration with time division multiple access operation. The effects of the number and positions of sources on the performance of the privacy-oriented system was studied. Moreover, the effect of the number of fingerprint positions on the performance of both systems was investigated. Results showed that our privacy-oriented scheme provides an accuracy of 8.5 cm with 87% precision, whereas our centralized system provides an accuracy of 2.7 cm for 93% of measurements. A comparison between our privacy-oriented system and another acoustic location system based on code division multiple access operation and lateration was conducted on our test bench and revealed that the cumulative error distribution function of the fingerprint-based system is better than that of the lateration-based system. This result is similar to that found for Wi-Fi radio-based localization. However, our experiments are the first to demonstrate the detrimental effect that reverberation has on naive acoustic localization approaches.

Investigating the complex relationship between in situ Southern Ocean $$pCO_{2}$$ p C O 2 and its ocean physics and biogeochemical drivers using a nonparametric regression approach

The objective in this paper is to investigate the use of a non-parametric approach to model the relationship between oceanic carbon dioxide \((pCO_2)\) and a range of ocean physics and biogeochemical in situ variables in the Southern Ocean, which influence its in situ variability. The need for this stems from the need to obtain reliable estimates of carbon dioxide concentrations in the Southern Ocean which plays an important role in the global carbon flux cycle. The main challenge involved in this objective is the spatial limitation and seasonal bias of the in situ data. Moreover, studies have also reported that the relationship between \(pCO_2\) and its drivers is complex. As such, in this paper, we use the non-parametric kernel regression approach since it is able to accurately capture the complex relationships between the response and predictor variables. In this analysis we use the in situ data obtained from the SANAE49 return leg journey between Antarctic to Cape Town. To the best of our knowledge, this is the first time this data set has been subjected to such analysis. The model variants were developed on a training data subset, and the ‘goodness’ of the models were assessed on an “unseen” test data subset. Results indicate that the nonparametric approach consistently captures the relationship more accurately in terms of mean square error, root mean square error and mean absolute error, over a standard parametric approach (multiple linear regression). These results provide a platform for using the developed nonparametric regression model based on in situ measurements to predict \(pCO_2\) for a larger spatial region in the Southern Ocean based on satellite biogeochemical measurements of predictor variables, given that satellites do not measure \(pCO_2\).

Nonparametric Forecasting for Biochar Utilization in Poyang Lake Eco-Economic Zone in China

Agriculture is the least profitable industry in China. However, even with large financial subsidies from the government, farmers’ living standards have had no significant impact so far due to the historical, geographical, climatic factors. The study examines and quantifies the net economic and environmental benefits by utilizing biochar as a soil amendment in eleven counties in the Poyang Lake Eco-Economic Zone. A nonparametric kernel regression model is employed to estimate the relation between the scaled environmental and economic factors, which are determined as regression variables. In addition, the partial linear and single index regression models are used for comparison. In terms of evaluations of mean squared errors, the kernel estimator, exceeding the other estimators, is employed to forecast benefits of using biochar under various scenarios. The results indicate that biochar utilization can potentially increase farmers’ income if rice is planted and the net economic benefits can be achieved up to ¥114,900. The net economic benefits are higher when the pyrolysis plant is built in the south of Poyang Lake Eco-Economic Zone than when it is built in the north as the southern land is relatively barren, and biochar can save more costs on irrigation and fertilizer use.

An Introduction to Dimension Reduction in Nonparametric Kernel Regression

Nonparametric regression is a powerful tool to estimate nonlinear relations between some predictors and a response variable. However, when the number of predictors is high, nonparametric estimators may suffer from the curse of dimensionality. In this chapter, we show how a dimension reduction method (namely Sliced Inverse Regression) can be combined with nonparametric kernel regression to overcome this drawback. The methods are illustrated both on simulated datasets as well as on an astronomy dataset using the R software.