Use Of Nonparametric Estimation Research Articles

Non-parametric adaptive estimation of order 1 Sobol indices in stochastic models, with an application to Epidemiology

Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output's variance. In a deterministic framework, when the same inputs always give the same outputs, these indices are usually estimated by replicated simulations of the model. In a stochastic framework, when the response given a set of input parameters is not unique due to randomness in the model, metamodels are often used to approximate the mean and dispersion of the response by deterministic functions. We propose a new non-parametric estimator without the need of defining a metamodel to estimate the Sobol indices of order 1. The estimator is based on warped wavelets and is adaptive in the regularity of the model. The convergence of the mean square error to zero, when the number of simulations of the model tend to infinity, is computed and an elbow effect is shown, depending on the regularity of the model. Applications in Epidemiology are carried to illustrate the use of non-parametric estimators.

On the Impact of State Anti-inflation Policy on the Level of Poverty in Russia and Other Countries

The article deals with nominal and real inflation, both in the whole country and in various sectors of Russia, including individual product groups, and identifies the main trends of inflation processes. The authors made an attempt to assess the impact of anti-inflationary measures taken in different countries on the level of social stratification of the population using nonparametric criteria. The results of the study clearly demonstrate that the use of monetary policy measures to control inflation in different countries does not reduce the proportion of the population with incomes below the subsistence level. Economic factors are not the only drivers of the human capital development and the rise of living standards. Therefore, institutional reforms must have not only a general economic effect but also the effect of social utility. The aim of the study is to identify and quantify the impact of inflation policies on human development in developed and developing countries. To achieve this goal, the work has set and solved the following tasks: real and nominal inflation rates in Russia as a whole for the past 6 years have been assessed; consumer inflation rates for individual commodity groups have been estimated; the use of nonparametric methods of assessing the impact of anti — inflationary policies on the proportion of the population with incomes below the subsistence level has been proposed and tested. The methodological basis of this article comprises economic and statistical methods of analysis, including the use of nonparametric methods and criteria for assessing non-quantitative indicators in small samples, methods of generalizing indicators, and comparison methods. The work analyzes the relationship between the GDP deflator index and the poverty level using the 2 χ -test, Chuprov coefficient and Wolfe criterion with the amendment of Yates. With the use of nonparametric estimates it was established that at present, the main levers of the state policy should be directed not so much at the economic efficiency but at the development of the potential of each participant in the economy. Nonparametric methodology sufficiently allows us to evaluate the hypothesis of homogeneity and the assertion of independence of the applied anti-inflationary measures for solving social problems facing any state.

Heteroscedasticity testing for regression models: A dimension reduction-based model adaptive approach

Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. A dimension reduction-based model adaptive test is proposed which behaves like a local smoothing test as if the number of covariates was equal to the number of their linear combinations in the mean regression function, in particular, equal to 1 when the mean function contains a single index. The test statistic is asymptotically normal under the null hypothesis such that critical values are easily determined. The finite sample performances of the test are examined by simulations and a real data analysis.

PORTMANTEAU AUTOCORRELATION TESTS UNDER Q‐DEPENDENCE AND HETEROSKEDASTICITY

AbstractWe propose extensions of the Box–Pierce () portmanteau autocorrelation test to allow for two generalizations: (i) time series that exhibit unconditional heteroskedasticity and (ii) to test for the presence of autocorrelation only after a fixed lag q. These extensions involve a generalized quadratic form of the Box–Pierce test that uses the heteroskedasticity autocorrelation consistent‐type estimator. While we show that this modified test is robust to unconditional heteroskedasticity, the resulting power loss may be substantial. We therefore develop feasible weighted tests that make use of nonparametric estimates of the unobserved variance process. Simulation experiments show that the weighted tests have good size and superior power properties over the unweighted tests.

Portmanteau Autocorrelation Tests under <i>q</i>-Dependence and Heteroskedasticity

We propose extensions of the Box-Pierce (1970) portmanteau autocorrelation test to allow for two generalisations: (i) time series that exhibit unconditional heteroskedasticity and (ii) to test for the presence of autocorrelation only after a fixed lag q. These extensions involve a generalised quadratic form of the Box-Pierce test that uses the heteroskedasticity autocorrelation consistent (HAC)-type estimator. While we show this modified test is robust to unconditional heteroskedasticity, the resulting power loss may be substantial. We therefore develop feasible weighted tests that make use of nonparametric estimates of the unobserved variance process. Simulation experiments show that the weighted tests have good size and superior power properties over the unweighted tests.

Is it necessary to change the number of samples for different forest types when evaluating plant species richness? A case study in a forested landscape in central Japan

We demonstrate a method for evaluating the appropriate number of samples required to estimate plant species richness in different forest types within a forested landscape. In each of 36 plots (0.1 ha each) from 5 forest types (deciduous broad-leaved secondary forest and 4 categories of coniferous plantation classified according to stand age) in central Japan, 40 quadrats of 1 × 1 m were set in a regular pattern; the total number of quadrats in each forest type ranged from 200 to 400. In each plot, the number of observed species in 40 quadrats ranged from 60 to 80% of the number of species estimated by the rarefaction method for each forest type. Sampling 30 quadrats detected approximately 90% of the observed species in each plot that were detected using 40 quadrats. In specific functional groups (i.e., tall trees and weed species), the ratios of both tall trees and weed species to all species were at equilibrium for 30 or more quadrats. For fewer than 30 quadrats these ratios were highly variable. No significant differences were found among forest types in the ratio of the observed number of species in each plot to the estimated number of species calculated using the rarefaction method, and in sampling efficiency estimated by use of non-parametric estimators. We concluded that the number of samples does not need to be changed according to forest type or plantation stand age in the studied landscape, and that the method used to evaluate the number of samples could be useful.

Assessing the performance of nonparametric estimators of species richness in meadows

To accurately measure the number of species in a biological community, a complete inventory should be performed, which is generally unfeasible; hopefully, estimators of species richness can help. Our main objectives were (i) to assess the performance of nonparametric estimators of plant species richness with real data from a small set of meadows located in the Basque campina (northern Spain), and (ii) to apply the best estimator to a larger dataset to test the effects on plant species richness caused by environmental conditions and human practices. Two non-asymptotic and seven asymptotic accumulation functions were fitted to a randomized sample-based rarefaction curve computed with data from three well sampled meadows, and information theoretic methods were used to select the best fitting model; this was the Morgan-Mercer-Flodin, and its asymptote was taken as our best guess of true richness. Then, five nonparametric estimators were computed: ICE, Chao 2, Jackknife 1 and 2, and Bootstrap; MMRuns and MMMeans were also assessed. According to the criteria set for our performance assessment (i.e., bias, precision, and accuracy), the best estimator was Jackknife 1. Finally, Jackknife 1 was applied to assess the effects of terrain slope and soil parent material, and also fertilization, grazing, and mowing, on plant species richness from a larger dataset (20 meadows). Results suggested that grass cutting was causing a loss of richness close to 30%, as compared to unmowed meadows. It is concluded that the use of nonparametric estimators of species richness can improve the evaluation of biodiversity responses to human management practices.

On forecasting daily stock volatility: The role of intraday information and market conditions

Several recent studies advocate the use of nonparametric estimators of daily price variability that exploit intraday information. This paper compares four such estimators, realised volatility, realised range, realised power variation and realised bipower variation, by examining their in-sample distributional properties and out-of-sample forecast ranking when the object of interest is the conventional conditional variance. The analysis is based on a 7-year sample of transaction prices for 14 NYSE stocks. The forecast race is conducted in a GARCH framework and relies on several loss functions. The realized range fares relatively well in the in-sample fit analysis, for instance, regarding the extent to which it brings normality in returns. However, overall the realised power variation provides the most accurate 1-day-ahead forecasts. Forecast combination of all four intraday measures produces the smallest forecast errors in about half of the sampled stocks. A market conditions analysis reveals that the additional use of intraday data on day t−1 to forecast volatility on day t is most advantageous when day t is a low volume or an up-market day. These results have implications for option pricing, asset allocation and value-at-risk.

On Forecasting Daily Stock Volatility: The Role of Intraday Information and Market Conditions

Several recent studies advocate the use of nonparametric estimators of daily price variability that exploit intraday information. This paper compares four such estimators, realised volatility, realised range, realised power variation and realised bipower variation, by examining their in-sample distributional properties and out-of-sample forecast ranking when the object of interest is the conventional conditional variance. The analysis is based on a 7-year sample of transaction prices for 14 NYSE stocks. The forecast race is conducted in a GARCH framework and relies on several loss functions. The realized range fares relatively well in the in-sample fit analysis, for instance, regarding the extent to which it brings normality in returns. However, overall the realised power variation provides the most accurate 1-day-ahead forecasts. Forecast combination of all four intraday measures produces the smallest forecast errors in about half of the sampled stocks. A market conditions analysis reveals that the additional use of intraday data on day t-1 to forecast volatility on day t is most advantageous when day t is a low volume or an up-market day. The results have implications for value-at-risk analysis.

On the discretization of nonparametric isotropic covariogram estimators

In this article, we describe the discretization of nonparametric covariogram estimators for isotropic stationary stochastic processes. The use of nonparametric estimators is important to avoid the difficulties in selecting a parametric model. The key property the isotropic covariogram must satisfy is to be positive definite and thus have the form characterized by Yaglom's representation of Bochner's theorem. We present an optimal discretization of the latter in the sense that the resulting nonparametric covariogram estimators are guaranteed to be smooth and positive definite in the continuum. This provides an answer to an issue raised by Hall, Fisher and Hoffmann (1994). Furthermore, from a practical viewpoint, our result is important because a nonlinear constrained algorithm can sometimes be avoided and the solution can be found by least squares. Some numerical results are presented for illustration.

Evaluation and monitoring of the flora in a nature reserve by estimation methods

We tested the use of non-parametric estimators of species richness to evaluate the flora of a relatively large (431 ha) nature reserve, using a sampling area much lower than that used in previous studies. Different estimation methods were applied to floristic data obtained from 50 random plots: the number of observed species, the extrapolated accumulation curves based on the Michaelis–Menten model and the non-parametric estimators based on incidence data (Chao2, first-order Jackknife, second-order Jackknife and bootstrap). To test the performance of the estimators, five data sets were created on the basis of life-forms. The estimates were compared with reference values obtained by traditional floristic and vegetation sampling. The power of the different estimation methods could not definitively be determined, but the first- and second-order Jackknives seem to be the most precise. Although total species richness was underestimated, the sample-based approach provided accurate information for quantitative comparison of time series of data related to ecological changes, vegetation dynamics and environmental changes. This sample-based data included basic statistics on species richness and species frequency distributions as well as the life-form spectrum, at the plot and the whole site scales.

Statistical Models for the Evaluation of Portable Lead Measurement Technologies. Part I: Chemical Test Kits

regression model in order to describe test kit performance. This article discusses estimation of the OC curves from numerical and stochastic points of view. The use of nonparametric estimates in graphical and quantitative analyses is also discussed. Attention is given to the fact that the true lead levels were themselves estimated by a process that was affected by paint collection and laboratory analysis procedures.

Comparison of Three Estimators of Species Richness in Parasite Component Communities

Comparisons of species richness between parasite component communities are often confounded by uneven sampling effort and the possibility that rare species have been missed from some component communities. The use of nonparametric estimators of species richness could potentially alleviate this problem by allowing the number of missing species to be extrapolated from the observed data. The performance of 3 estimators and their sensitivity to true species richness and the frequency of rare species, i.e., species with low prevalence, were tested using computer-simulated parasite communities. When the number of hosts examined in a sample is large, the observed species richness is an accurate estimate of true richness; no extrapolation is necessary even when rare species make up a large part of the community. At small sample sizes, observed species richness is a poor underestimate of true richness. The jackknife estimator and Chao's estimator both improve the estimate of species richness, but they are imprecise and can seriously overshoot the true richness value when the community includes many rare species. The bootstrap estimator. on the other hand, gives a better estimate than observed richness. Bootstrap estimates are also less variable and less likely to overestimate true richness, independently of how frequent rare species are in the community. This estimator provides a better, but conservative, estimate of true richness than observed richness and should be used to correct for inadequate host sampling. Data from natural communities suggest that the use of richness estimators is often justified, and that many parasite species may regularly escape detection.