Fikri Akdeniz Çağ University Department of Mathematics and

1. Fikri Akdeniz Çağ University Department of Mathematics and ComputerScience TURKEY 23rd IWMS,Ljubljana, Slonenia 11 June, 2014

2. OUTLINE *The problem andobjective of presentation *Semiparametricregression model *Difference-basedmethod *Generalizeddifference-basedestimatorwithcorrelatederrors

3. THE PROBLEM and OBJECTIVE OF PRESENTATION *In this talk, a commonly used simplesemiparametric regression model is considered. The goal is toestimate the unknown parameter vector and nonparametric function f(t) from the data .

4. 1. Semiparametric Regression Model (Partially Linear Model)

5. Some of the relations are believed to be of certain parametric form while others are not easily parameterized.Weshallcallf(t) thesmoothpart of the model andassumethat it represents a smoothunparametrizedfunctionalrelationship. *SPRM is more flexible than the standard linear regression model since it combines both parametric and nonparametric components.Due to its flexibility,SPRM has been widely used in econometrics, finance, biology, sociology and so on. *Allows easier interpretation of the effect of each variable compared to a completely nonparametric regression.

10. tc:log (total cost per customer)-Her bir müşteri için toplam maliyetin logaritması • cust:log (number of customers)- Müşteri sayısının logaritması • wage:log (wage of lineman)- Elektrik şebekesini döşeyen teknisyenücretinin logaritması • pcap:log (price of capital)-Sermaye miktarının logaritması • PUC: public utility commission dummy- Kamu kuruluşu için yapay değişken(Ekonomik açıdan fayda sağlayabilen ve ek servisler sunabilen) • Kwh:log (kilowatt hour sales per customer)- Müşteri başına düşen ortalamakilowatt saatin logaritması • life:log (remaining lifetime of fixed assets)- Dağıtım varlıklarınıngeri kalan ömrünün logaritması- • lf:log (load factor)- Bir elektrik santralından alınan ortalama elektrik miktarının elde edilebilecek maksimum miktara oranı • kmwire:log (kilometers of distribution wire per customer)- Her bir müşteriiçin döşenen elektrik dağıtım kablosunun kilometresinin logaritması

11. MULTICOLLINEARITY PROBLEM

14. Figure 1. Plots of individual explanatory variables versus. dependent variable, linear fit (blue), kernel fit (red), %95 confidence bands (black)

15. Figure 2. Plots of individual explanatory variables versus dependent variable, linear fit (blue), kernel fit (red), %95 confidence bands (black)

17. 2. The Model and Difference-based Estimator

22. nonparametric variable(s) are made close by reordering the data ‘difference’ the data to ‘remove’ the effect of the nonparametric variable(s) run OLS regression of the differenced dependent variable on the differenced parametric explanatory variables Applying the differencing matrix permits direct estimation of the parametric effect. Estimation Procedure

23. What is the advantage of differencing? • An importantadvantage of differencingprocedures is theirsimplicity. • Increasingtheorder of differencing as sample size increases, theestimator of thelinearcomponentbecomesasymptoticallyefficient (Yatchew 2003, p.72)

24. How does the approximation work?

26. Biased Estimation in Semiparametric Regression Models under Multicollinearity