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We investigate wage differentials between German male and female graduates at labour market entrance at all percentiles of the wage distribution. The decomposition of the wage difference is based on a single index approach suggested by DiNardo, Fortin, and Lemieux (1996) and Fortin and Lemieux (1998). The pay gap is decomposed in endowment, price and return-to-skill function effects. These isolated differences are calculated at all percentiles of the wage distribution. Our results reveal higher starting salaries for men at all percentiles of the income distribution, with varying magnitude of the gender pay gap. We observe the endowment and price effect to be favourable for men throughout. The effect of the difference in the return-to-skill function advantages female graduates.

This research emphasizes the difference between risk and return on four group of index, which are LQ 45, SRI KEHATI, JII and ISSI. Test of significance conduct by doing Analysis of Varians Multivariate. The Analysis of Varians Multivariate results more accurate than repeatedly t-test among group. EGP Model mostly explained as Single Index Model in various textbook. Thus, Single Index Model only clarified influence of a Single Market Index for Individual Index, EGP Model use Reward to Volatility (RVOL) for measuring excess return to systematic risk. The results shows that after 15 years from sharia index introduce in Indonesian Stock Exchange, it shows significant difference between sharia index and conventional stock market. However, LQ 45 shows it persistence as high return high risk index consistently. The Analysis VariansMultivariate also shows SRI KEHATI, as an ethic businesses representative in Indonesian Stock Exchange as a weaker index. SRI KEHATI shows that various group portfolio form by EGP Model could not exceed JII performance. Therefore, it concludes that indexes provide by capital market to facilitise the preference of investor whereas,it is tremendously various. To invest in stock market, investor need to clarify their wants and needs. Whether their wants is to gain more return or to accommodate their risk, and their preferrence to invest in various kind of business or certain business such as business based on ethic or faith. Keywords: Analysis of Varians Multivariate; Risk and Return; EGP Model; Indexes; LQ 45; Sri-Kehati; Jakarta Islamic Index (JII); and Indeks Saham Syariah Indonesia (ISSI)

This article considers partially linear single-index models with errors in all variables. By using the Pseudo − θ method (Liang, Hardle, and Carroll 1999), local linear regression and simulation-ex...

In this work we propose a method for optimal treatment assignment based on individual covariate information for a patient. For the K treatment ([Formula: see text]) scenario, we compare quantities that are suitable surrogates to true conditional probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient specific scores constructed from patient-specific covariates. As opposed to methods based on conditional means, our method can be applied for a broad set of models and error structures. Furthermore, the proposed method has very desirable large sample properties. We suggest Single Index Models as appropriate models connecting outcome variables to covariates and our empirical investigations show that correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a Single Index Model structure. Furthermore, selection of a treatment using the proposed metric appears to incur no losses in terms of the average reward for cases when two treatments are close in terms of this metric. We also conduct a real data analysis to show the applicability of the proposed procedure. This analysis highlights possible gains both in terms of average response and survival time if one were to use the proposed method.

Ackert and Deaves (2010) said that most people have tendency to being risk averse, but with appropriate amount of compensation, people may take more risk. Understanding those circumstances, this research trying to figure risk involved in a Mean-Variance Model. This model has taken consideration about investor risk preference in composed VAR model. VAR define as a measure of the risk of investments, which in this research focuses on risk preferences. This research also conducts comparison between optimum portfolio model known as Single Index Model and Mean-Variance Mode. Robustness test taken too analyze the outcomes from different data input. Research showed that risk preference has an impact on generating portfolio based on Mean-Variance Mode (MVM). Meanwhile, Single Index Model (SIM) found to given a similar result as MVM in high risk preference. This has shown that SIM may not adequate for those who have low risk preference. Research also show that risk taker investor get more gain and endure more risk than risk averse investor. But, based on robustness test, we found that the lowest risk an investor bear is on the highest risk preference. Thus, we make a conclusion that variance is not the only factor that might cause VaR increased, data dispersion has became more major factor.Keywords: Value at risk, Single Index Model, Optimum Portfolio.

We propose a new hyper-elastic model that is based on the standard invariants of Green–Cauchy. Experimental data reported by Treloar (Trans. Faraday Soc. 40:59, 1944) are used to identify the model parameters. To this end, the data of uni-axial tension and equi-bi-axial tension are used simultaneously. The new model has four material parameters, their identification leads to linear optimisation problem and it is able to predict multi-axial behaviour of rubber-like materials. We show that the response quality of the new model is equivalent to that of the well-known Ogden six parameters model. Thereafter, the new model is implemented in FE code. Then, we investigate the inflation of a rubber balloon with the new model and Ogden models. We compare both the analytic and numerical solutions derived from these models.

This paper deals with the estimation of conditional distribution function based on the single-index model. The asymptotic normality of the conditional distribution estimator is established. Moreover, as an application, the asymptotic (1 − γ) confidence interval of the conditional distribution function is given for 0 < γ < 1.

As an alternative to absolute error methods, such as the least square and least absolute deviation estimations, a product relative error estimation is proposed for a multiplicative single index regression model. Regression coefficients in the model are estimated via a two-stage procedure and their statistical properties such as consistency and normality are studied. Numerical studies including simulation and a body fat example show that the proposed method performs well.

This paper deals with a two-parameter new mix distribution called as RL (Rayleigh- Logarithmic) distribution withincreasing failure rate. Firstly, probability density function, distribution function, r th moment, survival and hazard functions of thistwo-parameter RL distribution are examined. Then, estimation of parameters by using standard statistical techniques such asmaximum likelihood method and entropy are given for the new mix model. In the application part, a real data set is receipted andwhen RL distribution compared with other distributions, this RL distribution is shown be a good competitor.

In this article, a new composite quantile regression estimation approach is proposed for estimating the parametric part of single-index model. We use local linear composite quantile regression (CQR...

In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.

This study uses Sharpe Single Index Model (SSIM) to construct an optimal portfolio. The sample for this study was based on the large listed Nigerian companies listed on NGSE. Monthly closing stock price of the companies was obtained from www.investing.com over the period of October 2019 to November 2019. The findings are highly encouraging as results show the cut-off rate and stocks with higher excess return to beta ratio which form the optimal portfolio. This study is highly useful for investors and companies.

Composite quantile regression (CQR) is becoming increasingly popular due to its robustness from quantile regression. Recently, the CQR method has been studied extensively with single-index models. However, the numerical inference of CQR methods for single-index models must involve iteration. In this study, we propose a non-iterative CQR (NICQR) estimation algorithm and derive the asymptotic distribution of the proposed estimator. Moreover, we extend the NICQR method to the analysis of massive datasets via a divide-and-conquer strategy. The proposed approach significantly reduces the computing time and the required primary memory. Simulation studies and two real data applications are conducted to illustrate the finite sample performance of the proposed methods.

The following thesis deals with the theory of portfolio section and two of its most known models. The portfolio selection model created by Harry M. Markowitz and the resulting Single-index model by William Sharpe. An elementary question somebody should ask before considering both models is: Is there an ideal financial portfolio? If so, how is it composed? The answer to the first question is yes and no. No, because the individuality of people does not allow an answer for the general public, and yes, because under certain assumptions, an investor can find an ideal portfolio in the financial market through plausible valuation methods. In this work methods are presented with which a so-called market portfolio, which appears to be ideal under suitable assumptions, can be calculated. To determine this, one uses methods from stochastics, such as the Monte Carlo method, and from optimization, such as the Lagrangian multiplier method. Taking permitted or prohibited short selling of financial products into account, these methods provide the ideal weighting of individual components in a portfolio. Of course, these individual components must also be evaluated for themselves beforehand and provided with parameters. This can be done on the one hand by taking the past of the financial market into account or on the other hand by using pre-defined relationships with other values. Taking contemporary topics, such as sustainability, into account, it is also possible to distinguish sustainable portfolios from non-sustainable portfolios. This approach to portfolio selection is only dealt with in theory in this thesis.Because all calculations, required for these considerations, would be far too complex by hand, programs are now used to do this work. Two of these programs, which were developed under the direction of Univ.-Prof. Dr. Gerhard Larchers existing LSQF project, are mentioned and presented at the end of this thesis. eingereicht von Mathias Lasselsberger Universität Linz, Masterarbeit, 2020 (VLID)5362241

The single-index model is a statistical model for intrinsic regression where responses are assumed to depend on a single yet unknown linear combination of the predictors, allowing to express the regression function as $ \mathbb{E} [ Y | X ] = f ( \langle v , X \rangle ) $ for some unknown \emph{index} vector $v$ and \emph{link} function $f$. Conditional methods provide a simple and effective approach to estimate $v$ by averaging moments of $X$ conditioned on $Y$, but depend on parameters whose optimal choice is unknown and do not provide generalization bounds on $f$. In this paper we propose a new conditional method converging at $\sqrt{n}$ rate under an explicit parameter characterization. Moreover, we prove that polynomial partitioning estimates achieve the $1$-dimensional min-max rate for regression of H\"older functions when combined to any $\sqrt{n}$-convergent index estimator. Overall this yields an estimator for dimension reduction and regression of single-index models that attains statistical optimality in quasilinear time.

This paper proposes the forecasting of correlation coefficients of the Dhaka Stock Exchange (DSE) market assets required for portfolio optimization using an ARIMA-LSTM hybrid model. DSE dataset contains a mix of linear and nonlinear data, where linearity means a direct relationship between the dependent and the independent variables and vice-versa for non-linear data. In relatable papers we came across, either linearity or non-linearity was handled within the dataset but none dealt with the combination of both. Our proposed model encompasses both linearity and non-linearity within the datasets of the DSE assets. This cannot be accomplished using other conventional statistical models. We have filtered the linear components in the datasets using the ARIMA model and passed the residuals obtained onto the LSTM model which deals with the non-linear components and random errors. We have compared the empirical results of this model with several other traditional statistical models used in portfolio management namely the Single Index model, Constant Correlation model, and Historical Model. We have also predicted the correlation coefficients using the ARIMA model to see how one of the models in our hybrid performs individually. The experimental results demonstrate that the hybrid model outperforms the other models in terms of accuracy and indicates that the ARIMA-LSTM hybrid model can be an effective way of predicting correlation coefficients required for portfolio optimization.

Analysis of optimal portfolio allows investors to analyze appropriate to minimize the risks accepted by the objective of maximizing profit with the same risk among existing stocks. Data Envelopment Analysis (DEA) is used to determine the stocks with the efficient performance based on ratio analysis. Having selected some stocks efficient formation of optimal portfolio is then performed with a single index models and determined how much the proportion of funds invested in each stock. The sample data used are stocks in ISSI 2012-2017. Based on the analysis of efficiency as a candidate portfolio models used DEA - CCR and DEA - BCC generate 16 efficient stocks that forming the candidate portfolio. After the analysis of all 18 stocks that efficiently obtained 6 stocks forming the optimal portfolio Keywords: Optimal Portfolio,Data Envelopment Analysis (DEA), Efficiency Stocks, Relative Efficiency Score , Single Index Model.

We study the monotone single index model where a real response variable $Y $ is linked to a $d$-dimensional covariate $X$ through the relationship $E[Y | X] = \Psi_0(\alpha^T_0 X)$ almost surely. Both the ridge function, $\Psi_0$, and the index parameter, $\alpha_0$, are unknown and the ridge function is assumed to be monotone on its interval of support. Under some regularity conditions, without imposing a particular distribution on the regression error, we show the $n^{-1/3}$ rate of convergence in the $\ell_2$-norm for the least squares estimator of the bundled function $\psi_0({\alpha}^T_0 \cdot),$ and also that of the ridge function and the index separately. Furthermore, we show that the least squares estimator is nearly parametrically rate-adaptive to piecewise constant ridge functions., Comment: 54 pages

This study empirically investigates the effect of the addition of Indonesian firms in the sustainable and responsible investment index (SRI-KEHATI index) on stock performance. This study applies an event study methodology using a single index model. The empirical results reveal that there are two days with significant abnormal returns, namely d+1 and d+3. This finding implies that the Indonesian stock market is efficient in a semi-strong form. This study also finds that there is no difference in abnormal returns before and after the SKI announcement. The implication of this study is the investors do not have to consider their investment decisions based on the inclusion of a corporation in the SKI.

We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation accuracy depends almost exclusively on the components of the distribution that correspond to desired subspaces or directions. This is relevant and important for problems where the behavior of data along a lower-dimensional space is of specific interest, such as dimension reduction or structured regression problems. We also show that estimation of precision matrices is almost independent of the condition number of the covariance matrix. The presented applications include direction-sensitive eigenspace perturbation bounds, relative bounds for the smallest eigenvalue, and the estimation of the single-index model. For the latter, a new estimator, derived from the analysis, with strong theoretical guarantees and superior numerical performance is proposed., 25 pages, 9 figures

The single-index model is a semi-parametric regression model that avoids the curse of dimensionality because of the linear combination of p-regression coefficients and covariates. Most of the works in this setting done for the homogenous single index models are limited and based on the minimum average conditional variance estimation (MAVE). To overcome these drawbacks, in this paper, we provide a robust and efficient estimate with modal regression for the single-index model under the existence of heteroscedasticity. The EM algorithm and bandwidth selection are employed to prepare the estimation method. Simulation studies demonstrate the performance of the proposed estimation; this method outperforms MAVE in various situations even if the errors are generated from a heavy-tailed distribution while it achieves the same efficiency as well as MAVE for the normally distributed errors. Finally, the application of the proposed method is illustrated by a real example of the heteroscedastic model.

We propose a new bi-level feature selection method for high dimensional accelerated failure time models by formulating the models to a single index model. The method yields sparse solutions at both the group and individual feature levels along with an expedient algorithm, which is computationally efficient and easily implemented. We analyze a genomic dataset for an illustration, and present a simulation study to show the finite sample performance of the proposed method.

There are two considerations that investors need to notice if they want to invest in the capital market, namely, return and risk. An investor needs to diversify to gain benefits and minimize risk by forming the optimal stock portfolios. This research anal yz es the differences between Islamic stock ( based on JII) and non-Islamic stock ( based on LQ45) stock portfolio investment using the single index model . The samples were consistently listed on the JII and LQ45 stock indices in January 2018-December 2019. There are 3 5 s tocks for the LQ45 stock index and 25 stocks on the JII stock index. Sharia stocks' optimal portfolio comprises three stocks, while the optimal portfolio of non-Islamic stocks shall consist of four stocks. The Independent Sample T-Test was implemented to analyze the differences between the Islamic (JII) and non-Islamic (LQ45) optimal stock portfolios based on the Sharpe Ratio, Jensen Ratio, and Treynor Ratio. The results show that there is no significant difference between Islamic and non-Islamic stocks.

We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset.