Fikri Akdeniz Fikri Akdeniz Çağ University Department of Mathematics and Computer Science TURKEY 23rd IWMS,Ljubljana, Slonenia 11 June, 2014

OUTLINE *The problem and objective of presentation *Semiparametric regression model *Difference-based method *Generalized difference-based estimator with correlated errors

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

1. Semiparametric Regression Model (Partially Linear Model)

Some of the relations are believed to be of certain parametric form while others are not easily parameterized. We shall call f(t) the smooth part of the model and assume that it represents a smooth unparametrized functional relationship. * 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.

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 teknisyen ücretinin 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 ortalama kilowatt saatin logaritması life: log (remaining lifetime of fixed assets)- Dağıtım varlıklarının geri 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 müşteri için döşenen elektrik dağıtım kablosunun kilometresinin logaritması

MULTICOLLINEARITY PROBLEM

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

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

2. The Model and Difference-based Estimator

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

What is the advantage of differencing?  An important advantage of differencing procedures is their simplicity.  Increasing the order of differencing as sample size increases, the estimator of the linear component becomes asymptotically efficient (Yatchew 2003, p.72)

How does the approximation work?

Biased Estimation in Semiparametric Regression Models under Multicollinearity