• Title/Summary/Keyword: Small Sample Size Problem

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A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

  • Lee, Youngsaeng;Shin, Yonggwan;Park, Jeong-Soo
    • Communications for Statistical Applications and Methods
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    • v.24 no.5
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    • pp.493-505
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    • 2017
  • Maximum likelihood estimation (MLE) of the generalized extreme value distribution (GEVD) is known to sometimes over-estimate the positive value of the shape parameter for the small sample size. The maximum penalized likelihood estimation (MPLE) with Beta penalty function was proposed by some researchers to overcome this problem. But the determination of the hyperparameters (HP) in Beta penalty function is still an issue. This paper presents some data adaptive methods to select the HP of Beta penalty function in the MPLE framework. The idea is to let the data tell us what HP to use. For given data, the optimal HP is obtained from the minimum distance between the MLE and MPLE. A bootstrap-based method is also proposed. These methods are compared with existing approaches. The performance evaluation experiments for GEVD by Monte Carlo simulation show that the proposed methods work well for bias and mean squared error. The methods are applied to Blackstone river data and Korean heavy rainfall data to show better performance over MLE, the method of L-moments estimator, and existing MPLEs.

Technological Experience and Crop Production in Dryland Farming Systems in Africa : The Case of Draught Animal Power in Ghana

  • Panin, Anthony
    • Proceedings of the Korean Society for Agricultural Machinery Conference
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    • 1993.10a
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    • pp.591-600
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    • 1993
  • Considerable controversy exists about the trend of animal traction effects on crop production in dryland farming systems in sub-Saharan Africa (SSA). This problem arises on account of the failure of the few available empirical studies to recognise the important of technological experience of the individual adopting farmers. This study hence addresses this issue by examining the effects of experience in animal traction technology (ATT) on farm size, cropping emphasis, total crop output and farm productivity. It is based on farm management survey data on 42 small holder farm households fro Ghana. Thirty of these households used animal traction technology (ATT) fro crop cultivation and the rest, mainly hand-hoe. The animal traction sub-sample is classified into three groups according to farmers' years of experience with the technology , thus , those with 1-2, 3-10, and more than 10. Evidence from the study shows that the progression of years of experience with ATT leads to inten ification of labour and land use systems, enhancement of degree of motivation to enter into the market economy, increases in total crop output and farm productivity resulting for decreases in cultivated acreages. The implication of the findings is that institutioal and technical support that do accompany the introduction of such technologies should be structured to last for a relatively longer period to accomodate the learning process.

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Relevance-Weighted $(2D)^2$LDA Image Projection Technique for Face Recognition

  • Sanayha, Waiyawut;Rangsanseri, Yuttapong
    • ETRI Journal
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    • v.31 no.4
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    • pp.438-447
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    • 2009
  • In this paper, a novel image projection technique for face recognition application is proposed which is based on linear discriminant analysis (LDA) combined with the relevance-weighted (RW) method. The projection is performed through 2-directional and 2-dimensional LDA, or $(2D)^2$LDA, which simultaneously works in row and column directions to solve the small sample size problem. Moreover, a weighted discriminant hyperplane is used in the between-class scatter matrix, and an RW method is used in the within-class scatter matrix to weigh the information to resolve confusable data in these classes. This technique is called the relevance-weighted $(2D)^2$LDA, or RW$(2D)^2$LDA, which is used for a more accurate discriminant decision than that produced by the conventional LDA or 2DLDA. The proposed technique has been successfully tested on four face databases. Experimental results indicate that the proposed RW$(2D)^2$LDA algorithm is more computationally efficient than the conventional algorithms because it has fewer features and faster times. It can also improve performance and has a maximum recognition rate of over 97%.

Feature Extraction via Sparse Difference Embedding (SDE)

  • Wan, Minghua;Lai, Zhihui
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.11 no.7
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    • pp.3594-3607
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    • 2017
  • The traditional feature extraction methods such as principal component analysis (PCA) cannot obtain the local structure of the samples, and locally linear embedding (LLE) cannot obtain the global structure of the samples. However, a common drawback of existing PCA and LLE algorithm is that they cannot deal well with the sparse problem of the samples. Therefore, by integrating the globality of PCA and the locality of LLE with a sparse constraint, we developed an improved and unsupervised difference algorithm called Sparse Difference Embedding (SDE), for dimensionality reduction of high-dimensional data in small sample size problems. Significantly differing from the existing PCA and LLE algorithms, SDE seeks to find a set of perfect projections that can not only impact the locality of intraclass and maximize the globality of interclass, but can also simultaneously use the Lasso regression to obtain a sparse transformation matrix. This characteristic makes SDE more intuitive and more powerful than PCA and LLE. At last, the proposed algorithm was estimated through experiments using the Yale and AR face image databases and the USPS handwriting digital databases. The experimental results show that SDE outperforms PCA LLE and UDP attributed to its sparse discriminating characteristics, which also indicates that the SDE is an effective method for face recognition.

An Application of the Clustering Threshold Gradient Descent Regularization Method for Selecting Genes in Predicting the Survival Time of Lung Carcinomas

  • Lee, Seung-Yeoun;Kim, Young-Chul
    • Genomics & Informatics
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    • v.5 no.3
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    • pp.95-101
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    • 2007
  • In this paper, we consider the variable selection methods in the Cox model when a large number of gene expression levels are involved with survival time. Deciding which genes are associated with survival time has been a challenging problem because of the large number of genes and relatively small sample size (n<

A Study on the efficiency of the MCMC multiple imputation In LDA (선형판별분석에서 MCMC다중대체법의 효율에 관한 연구)

  • Yoo, Hee-Kyung;Kim, Myung-Cheol
    • Journal of the Korea Safety Management & Science
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    • v.11 no.3
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    • pp.189-198
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    • 2009
  • This thesis studies two imputation methods, the MCMC method and the EM algorithm, that take care of the problem. The performance of the two methods for the linear (or quadratic) discriminant analysis are evaluated under various types of incomplete observations. Based on simulated experiments, the effect of the imputation using the EM algorithm and the MCMC method are evaluated and compared in terms of the probability of misclassification and the RMSE. This is done for the various cases of incomplete observations. The cases are differentiated by missing rates, sample sizes, and distances between two classification groups. The studies show that the probability of misclassification and the RMSE of the EM algorithm method is lower than the MCMC method. Therefore the imputation using the EM algorithm is more efficient than the MCMC method. And the probability of misclassification of the method that all vectors of observations with missing values are omitted from analysis is lower than the EM algorithm and the MCMC method when the samples size is small and the rate of missing values is extremely big.

2D Direct LDA Algorithm for Face Recognition (얼굴 인식을 위한 2D DLDA 알고리즘)

  • Cho Dong-uk;Chang Un-dong;Kim Young-gil;Song Young-jun;Ahn Jae-hyeong;Kim Bong-hyun
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.30 no.12C
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    • pp.1162-1166
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    • 2005
  • A new low dimensional feature representation technique is presented in this paper. Linear discriminant analysis is a popular feature extraction method. However, in the case of high dimensional data, the computational difficulty and the small sample size problem are often encountered. In order to solve these problems, we propose two dimensional direct LDA algorithm, which directly extracts the image scatter matrix from 2D image and uses Direct LDA algorithm for face recognition. The ORL face database is used to evaluate the performance of the proposed method. The experimental results indicate that the performance of the proposed method is superior to DLDA.

A Study on Face Recognition based on Partial Least Squares (부분 최소제곱법을 이용한 얼굴 인식에 관한 연구)

  • Lee Chang-Beom;Kim Do-Hyang;Baek Jang-Sun;Park Hyuk-Ro
    • The KIPS Transactions:PartB
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    • v.13B no.4 s.107
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    • pp.393-400
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    • 2006
  • There are many feature extraction methods for face recognition. We need a new method to overcome the small sample problem that the number of feature variables is larger than the sample size for face image data. The paper considers partial least squares(PLS) as a new dimension reduction technique for feature vector. Principal Component Analysis(PCA), a conventional dimension reduction method, selects the components with maximum variability, irrespective of the class information. So, PCA does not necessarily extract features that are important for the discrimination of classes. PLS, on the other hand, constructs the components so that the correlation between the class variable and themselves is maximized. Therefore PLS components are more predictive than PCA components in classification. The experimental results on Manchester and ORL databases shows that PLS is to be preferred over PCA when classification is the goal and dimension reduction is needed.

Comparison of log-logistic and generalized extreme value distributions for predicted return level of earthquake (지진 재현수준 예측에 대한 로그-로지스틱 분포와 일반화 극단값 분포의 비교)

  • Ko, Nak Gyeong;Ha, Il Do;Jang, Dae Heung
    • The Korean Journal of Applied Statistics
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    • v.33 no.1
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    • pp.107-114
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    • 2020
  • Extreme value distributions have often been used for the analysis (e.g., prediction of return level) of data which are observed from natural disaster. By the extreme value theory, the block maxima asymptotically follow the generalized extreme value distribution as sample size increases; however, this may not hold in a small sample case. For solving this problem, this paper proposes the use of a log-logistic (LLG) distribution whose validity is evaluated through goodness-of-fit test and model selection. The proposed method is illustrated with data from annual maximum earthquake magnitudes of China. Here, we present the predicted return level and confidence interval according to each return period using LLG distribution.

Study on Financing and Liquidity in Early-Stage SMBs (창업초기 투자자금조달과 유동성에 대한 연구)

  • Kang, Won
    • Asia-Pacific Journal of Business Venturing and Entrepreneurship
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    • v.9 no.5
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    • pp.1-11
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    • 2014
  • This article studies the types of financing and the liquidity of small and medium size firms in their early-stage. The sample firms distinguish themselves from the established firms in the second year after foundation in that they rely heavily on external equity financing. However, they use the internal financing the most in the fourth year and do not show distinguishing feature any more. In the mean while, they do not show any serious liquidity problem either in the second year or in the fourth year. The empirical results imply that early-stage lasts rather short after the foundation for successful Korean firms, and that a distinguishing feature of early-stage firm can be found only in financing, not in liquidity. They also allow us to assert that Government-lead financial aid programs should be limited to two- or three-year-old firms and focused on helping their financing investments rather than easing their liquidity problem.

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