A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).

EDGEWORTH EXPANSION FOR NEAREST NEIGHBOR- KERNEL ESTIMATE AND RANDOM WEIGHTING APPROXIMATION OF CONDITIONAL DENSITY

In this paper,Edgeworth expansion for the nearest neighbor\|kernel estimate and random weighting approximation of conditional density are given and the consistency and convergence rate are proved.

On the potential to predetermine dominant tree species based on sparse-density airborne laser scanning data for improving subsequent predictions of species-specific timber volumes

Background： Tree species recognition is the main bottleneck in remote sensing based inventories aiming to produce an input for species-specific growth and yield models. We hypothesized that a stratification of the target data according to the dominant species could improve the subsequent predictions of species-specific attributes in particular in study areas strongly dominated by certain species. Methods： We tested this hypothesis and an operational potential to improve the predictions of timber volumes, stratified to Scots pine, Norway spruce and deciduous trees, in a conifer forest dominated by the pine species. We derived predictor features from airborne laser scanning （ALS） data and used Most Similar Neighbor （MSN） and Seemingly Unrelated Regression （SUR） as examples of non-parametric and parametric prediction methods, respectively Results： The relationships between the ALS features and the volumes of the aforementioned species were considerably different depending on the dominant species. Incorporating the observed dominant species inthe predictions improved the root mean squared errors by 13.3-16.4 % and 12.6-28.9 % based on MSN and SUR, respectively, depending on the species. Predicting the dominant species based on a linear discriminant analysis had an overall accuracy of only 76 % at best, which degraded the accuracies of the predicted volumes. Consequently, the predictions that did not consider the dominant species were more accurate than those refined with the predicted species. The MSN method gave slightly better results than models fitted with SUR. Conclusions： According to our results, incorporating information on the dominant species has a clear potential to improve the subsequent predictions of species-specific forest attributes. Determining the dominant species based solely on ALS data is deemed challenging, but important in particular in areas where the species composition is otherwise seemingly homogeneous except being dominated by certain species.

On the Asymptotic Behavior of Nearest Neighbor Estimator of Conditional Median

This paper deals with the estimation in nonparametrio regression model.Sincethe conditional mean is sensitive to the tail behavior of the conditional distributionof the model,instead conditional median is considered.For estimation of theconditional median,the sequence of the nearest neighbor estimators is shown to beasymptotio normal and consistent.

ASYMPTOTIC NORMALITY OF THE NEAREST NEIGHBOR HAZARD ESTIMATES

The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar results for the n.n. hazard estimate have not been shown in the literature. In this paper, we develop a different approach to deal with the n.n. type estimator. For a mixed censorship-truneation model, we show that, under mild conditions, the n. n. estimate can be approximated by an estimate formed with a proper fixed bandwidth sequence and derive the asymptotic normality as a consequence.

Nonparametric Regression with Interval-Censored Data

In many medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease.In nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods directly.With the censored data,we construct a new response variable which has the same conditional expectation as the original one.Based on the new variable,we get a nearest neighbor estimator of the regression function.It is established that the estimator has strong consistency and asymptotic normality.The relevant simulation reports are given.