Bandwidth choice for nonparametric classification

It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple crossing points, then bandwidths of conventional size are generally appropriate. The range of different modes of behavior is narrower in multivariate settings. There, the optimal size of bandwidth is generally the same as that which is appropriate for pointwise density estimation. These properties motivate empirical rules for bandwidth choice.Comment: Published at http://dx.doi.org/10.1214/009053604000000959 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bandwidth choice for nonparametric classification

It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple crossing points, then bandwidths of conventional size are generally appropriate. The range of different modes of behavior is narrower in multivariate settings. There, the optimal size of bandwidth is generally the same as that which is appropriate for pointwise density estimation. These properties motivate empirical rules for bandwidth choice

Unimodal Kernel Density Estimation by Data Sharpening

Abstract: We discuss a robust data sharpening method for rendering a standard kernel estimator, with a given bandwidth, unimodal. It has theoretical and numerical properties of the type that one would like such a technique to enjoy. In particular, we show theoretically that, with probability converging to 1 as sample size diverges, our technique alters the kernel estimator only in places where the latter has spurious bumps, and is identical to the kernel estimator in places where that estimator is monotone in the correct direction. Moreover, it automatically splices together, in a smooth and seamless way, those parts of the estimator that it leaves unchanged and those that it adjusts. Provided the true density is unimodal our estimator generally reduces mean integrated squared error of the standard kernel estimator

Nonparametric Comparison of Multiple Regression Curves in Scale-Space

This paper concerns testing the equality of multiple curves in a nonparametric regression context. The proposed test forms an ANOVA type test statistic based on kernel smoothing and examines the ratio of between and within group variations. The empirical distribution of the test statistic is derived using a permutation test. Unlike traditional kernel smoothing approaches, the test is conducted in scale-space so that it does not require the selection of an optimal smoothing level, but instead considers a wide range of scales. The proposed method also visualizes its testing results as a color map and graphically summarizes the statistical differences between curves across multiple locations and scales. A numerical study using simulated and real examples is conducted to demonstrate the finite sample performance of the proposed method

Study on the fatty acid profile of phospholipid and neutral lipid in Hanwoo beef and their relationship to genetic variation

Maize which has very high omega-6 fatty acid content has been used as a main feed grain for Hanwoo beef production to increase marbling, and thus omega-6 to omega-3 fatty acids ratio in Hanwoo beef is expected to be biased. To elucidate the current status of omega fatty acids ratio in Hanwoo beef, fatty acid profiles of neutral lipid and phospholipid fraction were analyzed separately using 55 Hanwoo steers’ longissimus dorsi muscle slaughtered at Pyeongchang, Korea from Oct. to Nov. 2015. In addition, an association study was conducted to evaluate associations between single nucleotide polymorphism (SNP) markers from references and omega fatty acid profiles in phospholipid of Hanwoo beef samples using analysis of variance (ANOVA). In neutral lipid fraction, composition of saturated and monounsaturated fatty acids was higher and polyunsaturated fatty acids was lower compared to those in phospholipid fraction. The mean n-6/n-3 ratios of Hanwoo were 56.059 ± 16.180 and 26.811 ± 6.668 in phospholipid and neutral lipid, respectively. There were three SNPs showing statistically significant associations with omega fatty acid content. GA type of rs41919985 in fatty acid synthase (FASN) was significantly associated with the highest amount of C20:5 n-3 (p = 0.031). CC type of rs41729173 in fatty acid-binding protein 4 (FABP4) was significantly associated with the lowest amount of C22:2n-6 (p = 0.047). AG type of rs42187261 in FADS1 was significantly linked to the lowest concentration of C20:4 n-6 (p = 0.044). The total n-6/n-3 ratio of the steer which has all four SNP types in above loci (27.905) was much lower than the mean value of the total n-6/n-3 ratio in phospholipid of the 55 Hanwoo steers (56.059 ± 16.180). It was found that phospholipid and neutral lipid of Hanwoo have very high n-6/n-3 ratios compared to the reported data from different cow breeds. Four SNPs in genes related with fatty acid metabolism showed significant associations with the fatty acid profile of phospholipid and may have potential as SNP markers to select Hanwoo steers in terms of n-6/n-3 balance in the future

Molecular Subgroup Analysis of Clinical Outcomes in a Phase 3 Study of Gemcitabine and Oxaliplatin with or without Erlotinib in Advanced Biliary Tract Cancer

AbstractBACKGROUND: We previously reported that the addition of erlotinib to gemcitabine and oxaliplatin (GEMOX) resulted in greater antitumor activity and might be a treatment option for patients with biliary tract cancers (BTCs). Molecular subgroup analysis of treatment outcomes in patients who had specimens available for analysis was undertaken. METHODS: Epidermal growth factor receptor (EGFR), KRAS, and PIK3CA mutations were evaluated using peptide nucleic acid–locked nucleic acid polymerase chain reaction clamp reactions. Survival and response rates (RRs) were analyzed according to the mutational status. Sixty-four patients (48.1%) were available for mutational analysis in the chemotherapy alone group and 61 (45.1%) in the chemotherapy plus erlotinib group. RESULTS: 1.6% (2/116) harbored an EGFR mutation (2 patients; exon 20), 9.6% (12/121) harbored a KRAS mutation (12 patients; exon 2), and 9.6% (12/118) harbored a PIK3CA mutation (10 patients, exon 9 and 2 patients, exon 20). The addition of erlotinib to GEMOX in patients with KRAS wild-type disease (n = 109) resulted in significant improvements in overall response compared with GEMOX alone (30.2% vs 12.5%, P = .024). In 95 patients with both wild-type KRAS and PIK3CA, there was evidence of a benefit associated with the addition of erlotinib to GEMOX with respect to RR as compared with GEMOX alone (P = .04). CONCLUSION: This study demonstrates that KRAS mutational status might be considered a predictive biomarker for the response to erlotinib in BTCs. Additionally, the mutation status of PIK3CA may be a determinant for adding erlotinib to chemotherapy in KRAS wild-type BTCs