Multivariate Normal Distribution Research Papers (original) (raw)

Many cost-effectiveness analyses (CEAs) use data from observational studies. Statistical methods can only address selection bias if they make plausible assumptions. No quality assessment tool is available for appraising CEAs that use... more

Many cost-effectiveness analyses (CEAs) use data from observational studies. Statistical methods can only address selection bias if they make plausible assumptions. No quality assessment tool is available for appraising CEAs that use observational studies. We developed a new checklist to assess statistical methods for addressing selection bias in CEAs that use observational data. The checklist criteria were informed by a conceptual review and applied in a systematic review of economic evaluations. Criteria included whether the study assessed the ‘no unobserved confounding’ assumption, overlap of baseline covariates between the treatment groups and the specification of the regression models. The checklist also considered structural uncertainty from the choice of statistical approach. We found 81 studies that met the inclusion criteria: studies tended to use regression (51%), matching on individual covariates (25%) or matching on the propensity score (22%). Most studies (77%) did not ...

Dalam perkembangan sistem ekonomi Indonesia, persaingan antar perusahaan pada era globalisasi semakin ketat dan menjadi hal yang wajar. Daya saing perusahaan sendiri tidak hanya terjadi dalam keunggulan produk yang ditawarkan, melainkan... more

Dalam perkembangan sistem ekonomi Indonesia, persaingan antar perusahaan pada era globalisasi semakin ketat dan menjadi hal yang wajar. Daya saing perusahaan sendiri tidak hanya terjadi dalam keunggulan produk yang ditawarkan, melainkan kualitas dan keamanan produk bagi kesehatan juga turut dipertimbangkan. Perusahaan “X” merupakan salah satu pabrik yang bergerak di industri kosmetik, utamanya produksi parfum remaja. Dengan target pasar remaja, dimana remaja lebih sensitif terhadap zat-zat kimia, perusahaan “X” menjaga kualitas produknya dengan menetapkan spesifikasi untuk karakteristik kualitas dalam produk parfum yang diproduksi. Pengendalian kualitas statistik merupakan teknik penyelesaian masalah yang digunakan untuk memonitor, mengendalikan, menganalisis, mengelola, dan memperbaiki produk dan proses menggunakan metode-metode statistik. Pada praktikum ini, akan dibahas mengenai pengendalian kualitas terhadap karakteristik kualitas pada parfum remaja yang diproduksi oleh Perusahaan “X” yang diukur dengan pH dan massa jenis menggunakan peta kendali Generalized Variance dan T2 Hotelling. Data yang dianalisis harus memenuhi asumsi dependen dan berdistribusi normal multivariat, dan selanjutnya akan dilakukan analisis menggunakan peta kendali Generalized Variance dan T2 Hotelling yang kemudian dilanjutkan dengan analisis kapabilitas proses. Dari pengujian yang dilakukan, diketahui bahwa data telah memenuhi asumsi dependen dan berdistribusi normal multivariat. Peta kendali Generalized Variance menunjukkan bahwa variabilitas proses produksi parfum remaja produksi perusahaan “X” telah terkendali secara statistik atau sudah stabil sehingga dapat dilanjutkan menganalisis dengan peta kendali T2 Hotelling. Pada peta kendali T2 Hotelling terdapat satu pengamatan yang out of control sehingga rata-rata proses produksi parfum remaja oleh perusahaan “X” belum terkendali secara statistik atau belum stabil. Pengamatan yang out of control tersebut adalah pengamatan ke-3 dan setelah diidentifikasi, diketahui penyebabnya adalah kedua karakteristik kualitas, yaitu pH dan massa jenis. Namun, pada praktikum ini diasumsikan telah in control. Pada keadaan in control diperoleh MCp sebesar 1,74 dan MCpk sebesar 1,08 sehingga dapat disimpulkan bahwa produk parfum remaja memiliki variabilitas rendah dan telah sesuai spesifikasi perusahaan yang artinya kualitas produk parfum remaja produksi perusahaan “X” telah baik.

Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance.... more

Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or kkk)-step Maximum Likelihood Estimators computed on a subsample obtained with such a procedure. We introduce different models which arise naturally from the ways in which the discarded data can be treated, leading to truncated or censored likelihoods, as well as to a likelihood based on an only outliers gross errors model. Results on existence, uniqueness, robustness and asymptotic properties of the proposed estimators are included. A remarkable fact is that the proposed estimators generally keep the breakdown point of the initial (robust) estimators, but they could improve the rate of convergence of the initial estimator because our estimators always converge at rate n1/2n^{1/2}n1/2, independently of the rate of convergence of the initial estimator.

Seiring dengan semakin diminatinya minuman wine, kebutuhan konsumen akan minuman ini meningkat dengan banyak negara yang juga mendukung pertumbuhan industri ini. Sertifikasi guna meyakinkan konsumen akan kualitas serta pencegahan terhadap... more

Seiring dengan semakin diminatinya minuman wine, kebutuhan konsumen akan minuman ini meningkat dengan banyak negara yang juga mendukung pertumbuhan industri ini. Sertifikasi guna meyakinkan konsumen akan kualitas serta pencegahan terhadap pemalsuan wine juga diperlukan. Oleh sebab itu, diperlukan penilaian kualitas anggur, di mana variabel yang masuk dalam penelitian ini adalah alkohol, asam malat dan ash. Dalam penelitian ini, akan dibahas mengenai statistika deskriptif serta analisis diskriminan menggunakan metode canonical pada data penilaian kualitas anggur Portugis "Vinho Verde" di tahun 2009. Dalam melakukan analisis, asumsi yang harus dipenuhi adalah bahwa data mengikuti distribusi normal multivariat dan asumsi homogenitas. Setelah dilakukan analisis, didapatkan hasil bahwa data mengikuti distribusi normal multivariat dan diasumsikan homogen sehingga memenuhi asumsi dalam melakukan analisis diskriminan. Berdasarkan hasil analisis diskriminan menggunakan metode canonical didapatkan nilai akurasi sebesar 92,38%, sehingga pengelompokan kualitas wine dengan analisis diskriminan menggunakan metode canonical dapat mengklasifikasikan kualitas wine sebesar 92,38%.

In this article, an improved method of computing tolerance factors for multivariate normal distributions is proposed. The method involves an approximation and simulation, and is more accurate than the several approximate methods... more

In this article, an improved method of computing tolerance factors for multivariate normal distributions is proposed. The method involves an approximation and simulation, and is more accurate than the several approximate methods considered in Krishnamoorthy and Mathew (1999). The accuracies of the tolerance regions are evaluated using Monte Carlo simulation. Simulation study shows that the new approach is very satisfactory

In this paper we compare some modern algorithms i.e. Direct Maximization of the Likelihood (DML), the EM algorithm, and Multiple Imputation (MI) for analyzing multivariate normal data with missing responses. We also compare two approaches... more

In this paper we compare some modern algorithms i.e. Direct Maximization of the Likelihood (DML), the EM algorithm, and Multiple Imputation (MI) for analyzing multivariate normal data with missing responses. We also compare two approaches for modeling incomplete data (1) ignoring missing data and (2) joint modeling of response and non-response mechanisms. Several types of Software which can be used

Understanding the dynamics of high dimensional non-normal dependency structure is a challenging task. This research aims at attacking this problem by building up a hidden Markov model (HMM) for Hierarchical Archimedean Copulae (HAC),... more

Understanding the dynamics of high dimensional non-normal dependency structure is a challenging task. This research aims at attacking this problem by building up a hidden Markov model (HMM) for Hierarchical Archimedean Copulae (HAC), where the HAC represent a wide class of models for high dimensional dependency, and HMM is a statistical technique to describe time varying dynamics. HMM applied to HAC provide flexible modeling for high dimensional non Gaussian time series. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application, where the model’s performance is compared with other dynamic models, and in the second application we simulate rainfall process.

This paper analyzes discrete time portfolio selection models with Lévy processes. We first implement portfolio models under the hypotheses the vector of log-returns follow or a multivariate Variance Gamma model or a Multivariate Normal... more

This paper analyzes discrete time portfolio selection models with Lévy processes. We first implement portfolio models under the hypotheses the vector of log-returns follow or a multivariate Variance Gamma model or a Multivariate Normal Inverse Gaussian model or a Brownian Motion. In particular, we propose an ex-ante and an ex-post empirical comparisons by the point of view of different investors. Thus, we compare portfolio strategies considering different term structure scenarios and different distributional assumptions when unlimited short sales are allowed.

This paper presents Natural Evolution Strategies (NES), a recent family of algorithms that constitute a more principled approach to black-box optimization than established evolutionary algorithms. NES maintains a parameterized... more

This paper presents Natural Evolution Strategies (NES), a recent family of algorithms that constitute a more principled approach to black-box optimization than established evolutionary algorithms. NES maintains a parameterized distribution on the set of solution candidates, and the natural gradient is used to update the distribution's parameters in the direction of higher expected fitness. We introduce a collection of techniques that address issues of convergence, robustness, sample complexity, computational complexity and sensitivity to hyperparameters. This paper explores a number of implementations of the NES family, ranging from general-purpose multi-variate normal distributions to heavy-tailed and separable distributions tailored towards global optimization and search in high dimensional spaces, respectively. Experimental results show best published performance on various standard benchmarks, as well as competitive performance on others.

In this paper we present a new multi-asset pricing model, which is built upon newly developed families of solvable multi-parameter single-asset diffusions with a nonlinear smile-shaped volatility and an affine drift. Our multi-asset... more

In this paper we present a new multi-asset pricing model, which is built upon newly developed families of solvable multi-parameter single-asset diffusions with a nonlinear smile-shaped volatility and an affine drift. Our multi-asset pricing model arises by employing copula methods. In particular, all discounted single-asset price processes are modeled as martingale diffusions under a risk-neutral measure. The price processes are so-called UOU diffusions and they are each generated by combining a variable (Ito) transformation with a measure change performed on an underlying Ornstein-Uhlenbeck (Gaussian) process. Consequently, we exploit the use of a normal bridge copula for coupling the single-asset dynamics while reducing the distribution of the multi-asset price process to a multivariate normal distribution. Such an approach allows us to simulate multidimensional price paths in a precise and fast manner and hence to price path-dependent financial derivatives such as Asian-style and...

One of the crucial aspects in asset allocation problems is the assumption concerning the probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an... more

One of the crucial aspects in asset allocation problems is the assumption concerning the probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than in the Gaussian case. The aim of this paper is to propose a general Monte Carlo simulation approach able to solve an asset allocation problem with shortfall constraint, and to evaluate the exact portfolio risk-level when managers assume a misspecified return behaviour. We assume that returns are generated by a multivariate skewed Student-t distribution where each marginal can have different degrees of freedom. The stochastic optimization allows us to value the effective risk for managers. In the empirical application we consider a symmetric and heterogeneous case, and interestingly note that a multivariate Student-t with heterogeneous marginal distributions produces in the optimization problem a shortfall probability and a shortfall return level that can be adequately approximated by assuming a multivariate Student-t with common degrees of freedom. Thus, the proposed simulation-based approach could be an important instrument for investors who require a qualitative assessment of the reliability and sensitivity of their investment strategies in the case their models could be potentially misspecified. Copyright © 2007 John Wiley & Sons, Ltd.

In the last decade, substantial progress has been made on methods for imputation of missing data. Modern imputation methods have become widely available for practitioners through software products such as S-Plus 6.0 (Schimert, Schafer,... more

In the last decade, substantial progress has been made on methods for imputation of missing data. Modern imputation methods have become widely available for practitioners through software products such as S-Plus 6.0 (Schimert, Schafer, Hesterberg, Fraley, and Clarkson 2000), SAS PROC MI (SAS 2001), and SOLAS (2001) . The key idea underlying most of these methods is to impute missing

The main objective of this work is to calculate and compare different measures of multivariate skewness for the skew-normal family of distributions. For this purpose, we consider the Mardia (1970) [10], Malkovich and Afifi (1973) [9],... more

The main objective of this work is to calculate and compare different measures of multivariate skewness for the skew-normal family of distributions. For this purpose, we consider the Mardia (1970) [10], Malkovich and Afifi (1973) [9], Isogai (1982) [17], Srivastava (1984) [15], Song (2001) [14], Móri et al. (1993) [11], Balakrishnan et al. (2007) [3] and Kollo (2008) [7] measures of skewness. The exact expressions of all measures of skewness, except for Song’s, are derived for the family of skew-normal distributions, while Song’s measure of shape is approximated by the use of delta method. The behavior of these measures, their similarities and differences, possible interpretations, and their practical use in testing for multivariate normal are studied by evaluating their power in the case of some specific members of the multivariate skew-normal family of distributions.► We calculate different measures of multivariate skewness for skew-normal distributions. ► Exact expressions of 7 measures of skewness are derived for multivariate skew-normal distributions. ► Behavior, differences, interpretations and tests for normality against skew-normal on all these measures are studied and their power properties are assessed.